This document contains a post-test for an educational technology course. It consists of 37 multiple choice questions testing concepts related to instructional design, instructional materials, and the appropriate use of educational technologies. Some sample questions addressed domains of educational technology, systematic processes for preparing instructional materials, and principles for selecting effective instructional materials.
Instructional Materials & Technology Used in TeachingJewel Jem
Instructional Materials and/or technology used in the modern teaching of the 20th Century for teachers. Slides include a short description of each Modern instructional material used within the modern day teaching.
Instructional Materials & Technology Used in TeachingJewel Jem
Instructional Materials and/or technology used in the modern teaching of the 20th Century for teachers. Slides include a short description of each Modern instructional material used within the modern day teaching.
Sample of License Examination of Teachers and Educators in Philippines conducted by Philippines Regulatory Commission. Department of Education is accepting only if they pass BLEPT.
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Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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Chapter 3 - Islamic Banking Products and Services.pptx
02-let reviewer st louis-reviewer_1_1
1. St. Louis Review Center, Inc.
Eneelsus Bldg. Gen. Luna St., Davao City
Tel. no. (082) 224-2515 or 222-8732
ED-TECH
POST – TEST
1. Which of the following statements is correct about the
domains of educational technology?
A. Design is the production stage while development is
the planning stage.
B. Both the design and development are the planning
stage,
C. Evaluation is synonymous with implementation.
D. Utilization is the action phase.
2. Ms. Cruz was hired in a well-equipped school but she has
to start preparing her instructional materials before
classes begin. Which of the following is a systematic
process in preparing her materials?
A. design – utilization – evaluation - development
B. design – development – utilization – evaluation
C. development – design – utilization – evaluation
D. development – utilization – evaluation – design
3. Ms. Briones is planning to integrate technology in her
Mathematics class. Which of the following would be her
second step?
A. set the objectives
B. analyze the learners
C. utilize the materials with showmanship
D. evaluate the performance of the students
4. Which of the following should Ms. Gomez primarily
consider in determining her teaching and learning
objectives and use of instructional media?
A. the learner C. the instructional activity
B. the teacher D. the instructional strategy
5. Which is the best reason why teachers state the
objectives before using instructional media?
A. To be able to practice how to operate the
equipment.
B. To determine which media to use best.
C. To prepare the materials beforehand.
D. To secure available materials.
6. Ms. Villegas is thinkingof an educational technology that
can relay information clearly to her class.Which principle
will guide her in the selection of the material?
A. interest C. cost effectiveness
B. meaningfulness D. communication effectiveness
7. Mrs. Zinampan presented real samples of rocks when she
discussed the different forms of rocks. What principle in
the selection of instructional material did she apply?
A. interest C. cost effective
B. B authenticity D. responsiveness
8. Which of the following is a limitation of conventional
technologies in teaching and learning?
A. They pose problems on storage..
B. They are less abstract and more concrete.
C. They are readily available in the environment,
around school, and in the home.
D. They provide hands-on learning experiences and
emphasize real-world
E. applications
9. which of the followingis nota contribution of technology
to the learning process? .
A. The quality of learning can be improved
B. The delivery of instructions can be more interesting
C. The role of the teacher can be changed into a
demonstrator.
D. The method of teaching and learning becomes more
interactive
10. In what way can instructional aids foster learning?
A. Reinforce learning
B. Entertain students
C. Take the place of the teacher
D. Holds students in the classroom
11. With the pervasiveness of technologies nowadays, a
learner-centered instruction can be promoted. Which of
the following statements support this approach to
teaching?
I. It focuses on transformation of facts.
II. It supports the use of lecture and drill methods.
III. It gives emphasis on collaboration and authentic
assessment.
IV. Students work on tasks determined and controlled by
the teacher.
A. I and II only C. II and IV only
B. I and III only D. III and IV only
12. Prof. Villamin’sstudents usecooperative learning,inquiry
based and project-based learningapproaches in creating
their digital unit plans. What can be developed among
the learners through these approaches?
A. repetition and active learning
B. repetition & information delivery
C. information processing and active learning
D. construction of knowledge and information
exchange
13. Which of these technologies are arranged from the most
symbolic to multisensory?
A. real objects,print, audio-visual materials, and visual
materials
B. visual materials, audio visual materials, print and
computers
C. visual materials, print, audio-visual materials and
realia
D. print, audio, visual materials, and computers
14. Which group of technologies has the highest degree of
abstraction?
A. book, imaginative literature, programmed
instruction
B. digital video, film, versatile compact disc
C. video, pictures and television
D. realia and computer
15. Mrs. Soriano, a Grade V teacher prefers to use textbooks
than other instructional materials. What could be her
reason for using it?
A. Textbooks can be easily duplicated.
B. Textbooks quickly become updated.
C. Textbooks address the needs of diverse students.
D. Textbooks contain most of the materials they need
to learn in the course.
16. It is impractical to bring real objects to the classroom so
Ms. Simangan constructed a threedimensional visual
instead. Which of the following did she construct?
A. cartoon C. graphic
B. chart D. model
17. If a teacher wants to teach her pupils theskill to organize
and integrate related concepts, which of the following is
the most appropriate graphic organizer to use?
A. timeline C. venn diagram
B. fishbone D. semantic webbing
18. Which graphic organizer is used to show how a series of
events interact to produce a set of results again and
again?
A. Series of events chart C. cycle
B. Web D. timeline
19. Which instructional aid requires pupils to verbalize?
A. graphic C. . model
B. diorama D. . video
20. Which of the following is inappropriate in using printed
visuals such as charts, graphs, and drawings?
A. Providewritten or verbal cues to highlight important
aspects of visuals.
B. Allow the students to pass the materials from one
person to another.
C. Use materials that everyone can see.
D. Present the material one at time.
2. 21. Under what category will a globe as an instructional
material fall?
A. Realia C. solid model
B. mock up D. cutaway model
22. Prof. Agustin would like to provide hands-on experience
on the expansion and contraction of matter. Which of
the following materials would be the best to use?
A. models C. realias
B. pictures D. slides
23. Ms. Sarah finds the chalkboard an effective instructional
material up to present. However, just like any other
materials, it also has its limitations. Which one is it?
A. It allows spontaneity, speed and change.
B. Absent students cannot keep up with their
assignments.
C. It is valuablefor emphasizing the major points of the
lesson.
D. It can be used for displaying pictures and important
clippings.
24. With which learningstyle group are manipulatives MOST
effective?
A. Master style group
B. Interpersonal style group
C. Understanding style group
D. Self- expressive style group
25. Which does a pupil use when s/he sings a concept to a
familiartune in order to help himself commit the concept
to memory?
A. rap C. pop
B. jingle D. lullaby
26. Prof. Arcilla would like to use audiocassette tape in
teaching a lesson in English. In which activity is
audiocassette tape very effective in the teaching-learning
process?
A. in developing listening skills
B. in teaching creative writing
C. in composing poems
D. in building concepts
27. Romalyn is going to discuss about The ADDIE Model to a
big class. She is planning to use a technology by which
parts of her presentation could be partly hidden to make
it more exciting and interesting. What do you think shall
she use?
A. model C. transparency
B. realia D. video
28. Marife wants to make a presentation material wherein
more additional transparent sheets with information can
be placed over a base transparency. Which one should
she make?
A. cut-out C. silhouette
B. puppet D. overlay
29. Which one is used with 2D and 3D materials?
A. Opaque projector C. digital projector
B. overhead projector D. slide projector
30. After watching the film, “Muro Ami’, the students of Mrs.
Tamaray are expected to show a demonstrative proof of
what they have learned. How is the technology used in
thissituation?
A. entertainment C. instructional
B. informational D. entertainment and informational
31. Self made charts and illustrations serve as universal aid
for bringing fascinating and exciting experiences in the
classroom. To tap the optimum potentials of these
materials, which of the following should be avoided?
A. Giving due consideration to lettering.
B. Presenting materials with accurate facts.
C. Giving more importance to austerity over legibility.
D. Focusing on the main idea of the lesson presented.
32. Kamyl used overhead transparencies when she
presented her assigned topic to class. What type of
educational technology are transparencies?
A. printed material C. projected material
B. graphic material D. non-projected material
33. Which instructional material/s is/are MOST fit in
contextualized learning?
A. TV C. pictures
B. Slides D. field trip
34. Ms. Villanueva wants to teach the students the
performance of a certain skill such as dancing. Which
technology would be the most appropriate and
convenient to use?
A. film C. television
B. video D. printed material
35. Slides are miniature transparencies. They can be created
with simplecameras and simple equipment. They display
color in a realistic manner. However, they also havesome
limitations. Which one is it?
A. They can be easily updated and revised.
B. They can be adapted to group or to individual use.
C. They can get out of sequence if handled individually.
D. They can be combined with taped narration for
greater effectiveness.
36. Mrs. Santos used a film clip in teaching science concepts
to her Grade Six class.However, she found out that itwas
inefficiently used in the classroom. When is a technology
considered inefficient?
A. When it makes viewing more interesting.
B. When it increases the time to master the lesson.
C. When it helps attain the objectives of the lesson.
D. When it enhances understanding of new lesson.
37. Prof. Manantan’s lesson in EPP is about “Pagtatanim ng
halaman” to her students. How can she make her lesson
more interesting and meaningful?
A. Have a viewing activity about the lesson.
B. Have them read their EPP book.
C. Give them a collaborative work.
D. Let them listen to a gardener.
38. Prof. Delos Santos would like her students to give more
accurate observations about plants in the environment.
Which technique would help her attain her objective?
A. Bring them to the garden.
B. Bring actual plants to class.
C. Show colorful pictures to the class.
D. Let the class read books about the topic.
39. Which of the following should be avoided in presenting
visuals?
A. Show visuals with an element of suspense.
B. Shut off the overhead projector when explaining
lengthily.
C. Present all the materials simultaneously to hold the
learners’ interest.
D. Erase any writing on the chalkboard or whiteboard
when you no longer need it.
40. After listing down the advantages and disadvantages of
computers, Mrs. Muñoz decided to purchase a computer
for her class.Which do you think is the lastconsideration
in purchasing the equipment?
A. Computers can make her more efficient.
B. Computers can be a form of entertainment.
C. Computers can enhance teaching and learning.
D. Computers can be used for interactivepresentations.
41. Marnel prepares his school research works using
computer to submit his requirements on time. Does the
computer make him productive and efficient? Why?
I. Yes, because it can generate its own data.
II. Yes, because it can make one’s work easier.
III. Yes, because it can perform tasks fast and accurately.
A. I and II C. II and III
B. I and III D. I, II and III
42. Prof. Aguinaldo would like to integrate technology in
writing a friendly letter. How can he do it effectively?
A. Let the pupils surf a friendly letter from the Internet.
B. Have the pupils write a friendly letter and send it
through an email.
3. C. Have the pupils forward a downloaded friendly letter
to others via email.
D. Let the pupils write a friendly letter using word
processing and have it critiqued by
E. their peers.
43. Which of the following is known for its strength of giving
immediate feedback?
A. video C. digital encyclopedia
B. story book D. computer-assisted instruction
44. Which of the following computer-based instructional
material can be used to learn new concepts?
A. games C. simulation
B. tutorial D. drill and practice
45. 45. Prof. Natividad would like to create a presentation
material for his lesson on the types of computer-assisted
Instruction. Which tool should he use?
A. communicative tool C. productivity tool
B. Informative tool D. situating tool
46. Prof. De Guzman uses an online learning approach by
which content provides links to information at other
locations and serves as a focal point for a distance
education experience. Which of the following does he
use?
A. computer-aided instruction
B. web-based instruction
C. self-paced program
D. teleconferencing
47. Mr. Villena searches for related literature by accessing
several databases in the library computer that is
connected with other computers that have databases.
How is this termed?
A. CD ROM search C. mechanical search
B. computer search D. online search
48. Which pair of tools provide synchronous
communication?
A. chatroom and email
B. email and bulletin board
C. video conferencing and blogs
D. instant messaging and chatroom
49. Should Mrs. Reyes allow her pupils to surf the Internet in
creating a group newsletter during her English class?
Why?
A. No, because pupils may justbe exchangingmessages
via email.
B. No, because the pupils might open undesirable
websites.
C. Yes, to allow the pupils to chat with their friends.
D. Yes, as long as it is used effectively.
50. Which of the following should you ask yourself in
evaluating the content of an instructional material?
A. Do the materials reinforce learning effectively?
B. Are the materials of high technical quality?
C. Does the content match the curriculum?
D. Is it appropriate for the students?
51. Which of the following statements does NOT describe
educational technology?
i. It includes hardware and software.
ii. It refers to the efficiency of teachers in using
computers
iii. It is the development, application, and evaluation of
systems, techniques and aids to improve human learning.
A. i only C. Both ii and iii
B. ii only D. Both i and iii
52. What should Mr. Asuncion determine first in the
selection of media in teaching?
A. needs of the students C. technique to be used
B. availability of the media D. objectives of the lesson
53. Which is the most important reason why teachers
preview materials to be used in class?
A. To gain confidence in using them.
B. To encourage viewers to be more focused.
C. To avoid potential problems that might occur while
materials are in use.
D. To ensure appropriateness of the materials with the
objectives and target audience.
54. After Ms. Raca planned her lesson in English, she found
out that the materials at hand do not match her
objectives. Which is the best thing that she can do?
A. Modify the available materials.
B. Teach the lesson the following day.
C. Change the objectives to match with the available
materials.
D. Carry out the lesson as planned and use the
materials at hand.
55. Prof. Balagtas used worksheets, manipulatives and
models in teaching math to help her students understand
the lesson and love the subject. What did she bear in
mind when she used these materials?
A. appropriateness C. breadth
B. balance D. variety
56. Ms. Torres always makes sure that text, animation and
color do not confuse students in her presentation
materials. Which principle is applied?
A. simplicity C. responsiveness
B. variety D. cost effectiveness
57. Mrs. Reyes, a librarian, informed the students as well as
the teachers that several software are available for
classroom instruction and individual learning. Which
material is she referring to?
A. Computers C. Television set
B. CD-ROM D. VCD and DVD players
58. Susan’s mother tongue is a vernacular. Which of the
following materials would be the most efficient and
effective material to learn a second language?
A. interactive multimedia
B. pictures and print materials
C. audio compact discs and radio
D. printed materials and real objects
59. Computer can be a good tool for individualized
instruction. Which of the following aspects can be a
deterrent for its full utilization in the classrooms?
A. economic C. social
B. physical D. technical
60. With the increasinguse of educational technology inside
the classroom, what roles are expected of the teacher?
A. facilitator C. knowledge giver
B. demonstrator D. source of information
61. Which of the following technologies are properly
classified?
A. computers, compact discs, film, television
B. imaginative literature, book, programmed
instruction
C. versatile compact disc, printed material, diagram,
sketches
D. digital video, phonograph, compact discs, radio,
audio tape
62. Which of the following technologies are arranged from
the most concrete to the most abstract?
A. motion pictures, verbal symbols, visual symbols,
radio, realias
B. realias, visual symbols, television, motion pictures,
still pictures
C. realias,motion pictures,still pictures,visual symbols,
verbal symbols
D. verbal symbols,still pictures,visual symbols,models,
motion pictures
63. Which is the best way to present instructional materials?
A. concrete ->semi-concrete-> abstract->semi-abstract
B. semi-concrete-> concrete -> abstract->semi-abstract
C. abstract->semi-abstract-> semi-concrete-> concrete
D. concrete ->semi-concrete-> semi-abstract->abstract
64. Which of the following technologies provide iconic
experiences?
A. videos and computer
B. books and periodicals
C. audio and audio materials
4. D. printed and verbal symbols
65. How can Prof. Ubiña best promote the use of multimedia
in teaching Science to her coteachers?
A. Sell multimedia at low cost.
B. Demonstrate its use to them.
C. Explain the literature supporting its use.
D. Convince the principal to require the use of
technology.
66. There are countless things in the environment that you
and your students can use to learn from such as trees,
globes, pebbles, blocks etc. These real objects and
models are really effective if they are utilized properly.
Which of the following is incorrect about the use of real
objects and models?
A. Familiarize yourself with the object or model.
B. Allow passing of a single object around the class.
C. Make sure that objects/models are large enough to
be seen by the whole class.
D. Encourage students’ participation through
questioning and having students
E. decide the next step.
67. Aaron constructed a three dimensional material to
simulate the circulation of blood. Which of the following
did he construct?
A. A solid model C. mock-up model
B. cutaway model D. cross-sectional model
68. Which is a two-dimensional representation of the earth’s
geographic and/or political features?
A. globe C. mock-up
B. map D. model
69. You asked your students to illustrate what they have
understood from what they have read. Which of the
following non-projected visuals are you referring to?
A. printed visuals C. models
B. graphics D. realias
70. Which software should Dr. Balagtas to manipulate
numerical data in the computer?
A. Spreadsheet C. word processing
B. desktop publishing D. multimedia
71. Prof. Silva uses projected visuals such as OHP in
presenting her lesson. What could be her main reason in
using such an educational technology?
A. The materials are readily available.
B. Most visuals can be obtained at no cost.
C. It is more abstract than any other visuals.
D. She can easily prepare her own transparencies in
advance.
72. Ms. Pacheco showed a segment of matter in “sine
skwela” to her pupils without a follow-up activity. Thus,
the pupils got low in the test. What does this imply?
A. TV makes viewing enjoyable.
B. TV promotes mastery of the lesson.
C. TV induces alienation on the part of the learners.
D. TV is effective when learners attain the lesson
objectives.
73. Which activity is closest to the real thing?
A. hear C. watch a demonstration
B. view images D. perform in a presentation
74. Your department would like to purchase a computer set
as your project. Which of the following advantages of
computer will be your lastconsideration in purchasingit?
A. It can enhance the teaching and learning process.
B. It can be used for interactive presentation.
C. It can be used for research activity
D. It can be used for entertainment.
75. Prof. Orencia will have a digitized presentation to pre-
service teachers. Which of the following will make her
presentation appealing and effective?
A. Observe maximum use of animations and graphics
together.
B. Apply as many computer effects per slide as
possible.
C. Reinforce textual information with graphic
organizers.
D. Use as many color as possible.
76. Why are computers increasingly becoming pervasive in
schools nowadays?
A. Schools advocate the use of computers.
B. They increase efficiency and productivity.
C. Anybody can operate computers without formal
training.
D. Students have access to computers in school and at
home.
77. There are several reasons why teachers are reluctant in
using electronic media in the teaching-learning process.
Which is the most common reason?
A. The difficulty in integrating them in the curriculum.
B. The limited exposure of teachers to new equipment.
C. Their incompatibility to diverse needs of the
learners.
D. The excessive availability of local technology in the
community.
78. With the number of senses to be stimulated as criterion,
which one should be first in thelist?
A. multi sensory aid C. visual aid
B. audio-visual aid D. audio aid
79. Which of the followingis considered in terms of technical
quality of a material?
A. stereotyping C. color and size of text
B. vocabulary level D. students’ achievement
80. Which statement is true about the opaque projector and
overhead projector?
A. An opaque projector allows more flexibility than an
overhead projector.
B. An overhead projector allows more flexibility than an
opaque projector.
C. Opaque and overhead projectors can
instantaneously project 3D visuals well.
D. The series of still visuals in an opaque projector are
arranged in a fixed pattern but not in an overhead
projector.
81. A grade II teacher wanted to show the parts of a seed by
using a large, wooden seed visual aid with detachable
cotyledons and tiny seed. Under what classification does
wooden structure fall?
A. assembly model C. realia
B. cutaway model D. solid model
82. Which term refers to a model which is constructed so as
to emphasize a particular part or function?
A. audio recording C. mock-up
B. simulation D, realia
83. Which is the best use of computers to students like you?
A. They are used for chatting and surfing the net.
B. They are used for research and collaboration.
C. They are used for playing online games.
D. They are used for watching movies.
84. Which statement makes technology ineffective in
student learning?
A. It develops higher thinking skills.
B. It prepares students for the workforce.
C. It enhances students’ collaborative skills.
D. It decreases achievement in content learning.
85. You plan to useinstructional materialsto a big class-size.
Which of these will you not use?
A. pictures C. 27-inch television
B. projection device D. computer with LCD projector
86. Computers can be classified according to the roles they
play namely communicative tool, informative tool, and
5. constructive tool. What is the other role of computes in
the options below?
A. instructional tool C. utility tool
B. situating tool D, application tool
87. Which of the following categories of CAI will you use in
your classif your objective is to increase proficiency in a
newly learned skill or refresh an existing one?
A. tutorial C. simulation
B. drill and practice . D. Instructional game
88. Which of the following is an ineffective use of
presentation software?
A. Darken the room
B. Use appropriate pacing
C. Read directly from the slides.
D. Allow interaction with the learner.
89. Which of the following is NOT an example of
communicative tool?
A. multimedia encyclopedia
B. teleconferencing
C. electronic mail
D. chat
90. Which is a characteristicof the teaching machines of B. F.
Skinner?
A. It does not need any feedback.
B. It requires teacher’s assistance.
C. It is meant for a collaborative work.
D. It allows a student to learn at his/her own pace.
91. Why is one-way delivery of information a misuse of
communication tools?
A. because the teacher expects the student to study
more
B. because it requires activities that focus on thinking
than responding
C. because it enables the users to focus more on higher
level cognitive activities
D. because this kind of practice lessens interaction
capabilities of communication tools
92. Internet consists of thousands of connected computer
networks around the world. Which term does NOT refer
to Internet?
A. A. NET C. “Cyberspace”
B. B. Online D. “Information Superhighway”
93. Your class adviser is planning to have an asynchronous
communication with your classmates. Which technology
tools can she use?
A. chat and blog
B. chat and instant messaging
C. blog and video conferencing
D. electronic bulletin board and email
94. In your computer subject, you allowyour class to chat as
a part of your motivation before discussing them the
roles of computer. How is chat used in this context?
A. Communicative tool C. Application tool
B. Informative tool D. Situating tool
95. Your mother wanted to finish her long dreamed course
but she wanted to do it at home during her free time.
How could you help your mother in pursuing her dream?
A. Encourage her to hirea helper so that she can attend
regularly to her class.
B. Give up your study so that your mother can attend
her classes.
C. Enroll her to the school where you enrolled.
D. Enroll her in distance education
96. The following statements are true about computer
conferencing. Which is an exception?
A. It refers to live student interaction with an expert.
B. It is also known as discussion forum or bulletin
board.
C. It also refers to online class discussions, forums or
debates
D. It permits two or more individuals to engage in
asynchronous text-based dialogue.
97. Which instructional tool application will you introduce to
your class if your objective is to help them find and use
information resources available in the internet?
A. Webquests C. Scavenger Hunt
B. Hybrid course D. Distance education
98. Maryjane is looking for an organized instructional
program in which the teacher and learners can be
physically separated. Which of the following will she
choose?
A. Distance Education
B. Uniform Resource Locator
C. Web Quests
D. Computer-Based Instruction
99. Prof. Ruscoe would like to show Rizal’s museum to the
students but due to financial constraint, she couldn’t
bring them there. What should she do to make the
teachinglearning process more realistic?
A. Conduct a virtual tour.
B. Use DVD with less resolution.
C. Show pictures of the museum to the whole class.
D. Go to the museum and relate all observations made.
100. Which of the following should you avoid if you were
asked to evaluate the effectiveness of an instructional
game after using it in teaching a lesson in high school
science?
A. Present problems which are relevant to learning
objectives.
B. Allow learners to select different content materials.
C. Provide a cooperative learning atmosphere.
D. Provide a scoring system.
* * * * * T H E E N D * * * * *
POST TEST
ED-TECH
1. Which of the following statements is correct about the
domains of educational technology?
1. D 51. B
2. B 52 A
3 A 53 D
4 A 54 A
5 B 55 D
6 D 56 A
7 B 57 B
8 A 58 A
9 C 59 A
10 A 60 A
11 B 61 B
12 D 62 C
13 D 63 D
14 A 64 A
15 D 65 B
16 D 66 B
17 D 67 C
18 C 68 B
19 A 69 B
20 B 70 A
21 C 71 D
22 C 72 D
23 B 73 D
24 C 74 D
25 B 75 C
26 A 76 B
27 C 77 B
28 D 78 A
29 A 79 C
30 C 80 A
31 C 81 A
32 C 82 C
6. 33 D 83 B
34 B 84 D
35 C 85 A
36 B 86 B
37 C 87 B
38 A 88 C
39 C 89 A
40 B 90 D
41 C 91 D
42 D 92 B
43 D 93 D
44 B 94 A
45 C 95 D
46 B 96 A
47 D 97 C
48 D 98 A
49 D 99 A
50 B 100 B
FILIPINO
POST – TEST
I. Panuto: Bilugan ang titik ng wastong sagot.
1. Agad na sumigaw ang bata ____ makitang dumating ang
kanyang kapatid
a. ng b. nang
2. Ang mga mag-aaral ay nagkasundo _____ sa iminungkahi
ng guro.
a. din b. rin
3. Ang bawat tao _____ ay kailangang isakatuparan ang
kanyang mithiin sa buhay.
a. Daw b. raw
4. Ang kirot ay unti-unti ______ nawawala.
a. ng b. nang
5. Ayon kay Jose Rizal, ang mga bata _____ ang siyangpag –
asa ng bansa.
a. daw b. raw
6. Sa Sabado _____ gabi mawawalan ng kuryente.
a. ng b. nang
7. Hindi na nakaramdam ng gutom si Kuya mula _____ siya
ay natulog.
a. ng b. nang
8. _____ dalang pusa ang Inay nang umuwi.
a. May b. Mayroon
9. Maya-maya ay sisingaw _____ ang amoy ng Patay.
a. din b. rin
10. Ang dunong ay kailangan ng tao ngunit kailangan _____
niya ang tulong ng Maykapal.
a. din b. rin
11. Sino ba ang sumisigaw _____ at nagtatakbuhan ang mga
tao.
a. doon b. roon
12. _____ tainga ang lupa, may pakpak ang balita.
a. May b. Mayroon
13. Ang bawat tao sa mundo ___ ay dapat magkaunawaan
para sa kanilang ikabubuti.
a. Daw b. raw
14. Ang Pilipinas ay malakas ____ tulad ng Singapore kung
karapatan ang Pag-uusapan.
a. din b. rin
15. Unti- unti ____ humuhupa ang kanyang galit.
a. Ng b. nang
II. Ibinigay ang kahulugan ng salitang may salungguhit.
16. Narinig ko ang alawat ng mga bata sa silid ng mag-
asawang Maria at Jose.
a. ingay c. sigaw
b. mahinang alingawngaw d. tawanan
17. Ang Itay ay alimbuyaw nang dumating kanina.
a. Aburido c. Patakbo
b. Masaya d. sumigaw
18. Si Tj ay isang anluwagi nang mapangasawa ni Luisa.
a. Guro c. karpintero
b. katulong d. pulis
19. Kakarampot ang nakuha kong ulam sa mesa.
a. marami c. malalaki
b. katiting d. mamhahaba
20. Alumpihit ang Itay habang hinihintay ang Inay.
a. Kabang-kaba c. Di-mapalagay
b. Siyang- siya d. Tuwang-tuwa
21. Iyon ang kinamihasnan ng babaeng iyon sa bundok kaya
di-makaunawa sa iyo.
a. natutuhan c. napag-aralan
b. kinagawian d. nagustuhan
22. Ang alipustahin angmga dukha ay di kanais-nais na pag-
uugali.
a. layuan c. talikdan
b. apihin d. kagalitan
23. Nakita kong pakimod na sumagot ang babae sa dalaga
nang mag-usap sila.
a. Paismid c. patawa
b. Pangiti d. pasigaw
24. Isang indihente ang tumawag ng aking pansin dahil sa
nakakatawang ayos nito.
a. Maralita c. mag-asawa
b. Matanda d. paslit
25. Naging Cum Laude si Memi dahil siya ay nagsunog ng
kilay gabi-gabi.
a. nagbubunot c. nag-aahit
b. puspos sa pag-aaral d. nag-aayuno
26. Parang balat-sibuyas ang kutis ng babaeng ito.
a. namumula sa bilog c. mahaba at payat
b. napakaputi at malinis d. pino at malambot
27. Kapit-tuko sa isat’-isa habang naglalakad ang
magkasintahang Heart at Echo.
a. away nang away
b. mahigpit na magkahawak-kamay
c. malayo ang agwat
d. patakbo
28. Ang langitngit ng mga bintana ay gumigising nang lubos
sa katahimikan ng silid-aralan.
a. Alatiit c. dekorasyon
b. kulay d. sira
29. Mataginting na tinanggap ng batang paslit ang pangaral
ng guro.
a. maingay c. mapayapa
b. pasigaw d. paismid
30. Ang paswit ay sa aso, ang Oo ay sa tao.
a. Palo c. buto
b. Sipol d. sigaw
III. Ibinigay ang tamang sa mga tulang bayani
31. Ang tawag sa mga tulang bayani
a. dalit c. senakulo
b. epiko d. duplo
32. Tinaguriang Joseng Batute ng Pilipinas
a. Jose Garcia Villa c. Jose Corazon de Jesus
b. Francisco Baltazar d. Modesto de Castro
33. Mga sagisag na ginamit ni Rizal
a. Piping Dilat c. Pudpod at Plaridel
b. Dolores Manapat d. Dimasalang at laong laan
34. Ang “ prinsipe” ng makatang Tagalog
a. Modesto de Castro
b. Francisco Baltazar
7. c. Fernando bagong Lanta
d. Jose Garcia Villa
35. Siya ay tinaguriang “ Ama ng Balarila ng Wikang
Pambansa”
a. Jose Villa Panganiban c. Severino Reyes
b. Lope K. Santos d. Rafael Palma
36. Isang dula noong panahon ng Hapon na isinulat ni
Francisco Soc Rodrigo
a. Panibugho c. Panday Pira
b. Sa pula, Sa Puti d. Luha ng Buwaya
37. Ama ng Katipunan
a. Emilio Jacinto c. Apolinario Mabini
b. Andres Bonifacio d. Marcelo H. del Pilar
38. Isang uri ng panitikan na nagsasaad ng simulain ng mga
bagay o tao sa daigdig
a. tula c. alamat
b. tibag d. maikling kwento
39. Pinakabantog at pinakamahalagang awit na nasulat ni
Francisco Baltazar
a. Senakulo c. duplo
b. epiko d. Florante at Laura
40. Ang kauna-unahang Pilipinong manlilimbag
a. Marcelo del Pilar c. Jose Maria Panganiban
b. Tomas Pinpin d. Emilio Aguinaldo
41. Ang tawag sa ating unang alpabeto
a. Alpabetong Romano c. Kartilya
b. Alibata d. Romanisasyon
42. Ang taong may “memorya fotograpica”
a. Jose Maria Panganiban
b. Jose Garcia Villa
c. Jose Corazon de Jesus
d. Jose Rizal
43. “Ama ng Dulang Pilipino”
a. Julian Balmaceda c. Lope K. Santos
b. Severino Reyes d. Emilio Jacinto
44. Siya ay tinaguriang Joseng Sisiw
a. Jose Villa Panganiban c. Jose dela Cruz
b. Pedro Paterno d. Modesto de Castro
45. Ang kilalang epiko ng mga Muslim
a. Hudhud c. Hinalawod
b. Darangan d. Bantugan
46. Ang kauna-unahang aklat na nalimbag sa pilipinas
a. Pasyon c. Doctrina Christiana
b. Barlaan at Josaphat d. Florante at Laura
47. Ama ng Wikang Pambansa
a. Emilio Aguinaldo c. Aurelio Tolentino
b. Manuel L. Quezon d. Florante at Laura
48. Ang “ Orator ng Pagbabago”
a. Graciano Lopez Jaena c. Urbana at Feliza
b. Mariano Ponce d. Jose Buhain
49. Isang dulang nagwagi ng kauna-unahang Gatimpalang
Palanca
a. Medusa c. Urbana at Feliza
b. Tibag d. Hulyo 4, 1946 A.D
50. Ang may-akda ng “Ang Cadaquilaan ng Dios”
a. Emilio Aguinaldo c. Julian Felipe
b. Marcelo H. del Pilar d. Lopez Jaena
51. Baston ni Adan Hindi mabilang-bilang
a. buhok c. dahon
b. ulan d. palay
52. Ang dalawa’Y tatlo na,
Ang maitim ay maputi na
Ang bakod ay lagas na
a. aso c. matandang tao
b. kalabaw d. punong kahoy
53. Ang anak ay nakaupo na
Ang ina’y gumagapang pa
a. kalabasa c. sanggol
b. saging d. aso
54. Kung araw ay bumbong
Kung gabi ay dahon
a. saging c. atip ng bahay
b. banig d. paying
55. Isang reyna
Nakaupo sa tasa
a. kandila c. kasoy
b. kapa d. santol
56. Dalawang magkaibigan,
unahan nang unahan.
a. trak c. bibig
b. paa d. mata
57. Dalawang bolang sinulid
Umaabot hanggang langit
a. bola c. lobo
b. mata d. saranggola
58. May ulong walang mukha
May katawan, walang sikmura
Namamahay nang sadya
a. pako c. upo
b. palito ng posporo d. talong
59. Bumili ako ng alipin
Mataas pa sa akin
a. payong c. sombrero
b. atip d. bahay
60. Tubig sa ining-ining
Di mahipan ng hangin
a. ilog c. ulan
b. balon d. dagat
61.
a. eskursiyon c. exkursion
b. iskursiyon d. excursion
62.
a. scout c. iskawt
b. escout d. skawt
63.
a. colisiyon c. koliseum
b. kolisiyum d. coliseum
64.
a. Istadyum c. Estadyum
b. Stadium d. estadium
65.
a. Matematika c. matimatika
b. Mathematica d. matemateka
66. Karamihan sa mga sugapa ay mula sa wasak na tahanan.
a. malaki ang sita ng bahay
b. maliit lamang ang bahay
c. magkahiwalay ang magulang
d. walng magulang
67. Matagal na lumagay sa tahimik si Marcia. Ang ibig
sabihinay _______.
a. matagal na namatay c. hindi na nagpakita
b. nag-asawa na d. nanganak na
68. Alin ang salawikain sa sumusunod:
a. Nasa Diyos ang awa
Nasa Tao ang gawa
b. Di-maliparang uwak
c. May puno walang bunga
May dahon walang sanga
d. Nag-bubuhat ng sariling bangko
69. Ang bagong alpabetong Filipino ay may ______ ng letra.
a. 20 b. 24 c. 28 d. 30
70. Ito ay bahagi ng aklat na makikita sa likod. Ito ay talaan
ng lahat na mahalagang paksa kasama ang pahina. Ang
mga paksa ay nakasulat sa paalpabeto.
a. Talatuntunan c. Talahulugan
b. Talatinigan d. Talaan ng nilalaman
71. Isang kuwento ng ang gumagapang ay mga hayop na
kumikilos at nagsasalita na parang tao.
a. Parabola c. kuwento
b. pabula d. alamat
8. 72. Ito ay isang uri ng dula na nawawakas a pagkamatay ng
pangunahing tauhan.
a. komedya c. melodrama
b. epiko d. trahedya
73. Isang kuwento hango sa banal na kasulatan na umaakay
sa tao sa matuwid na landas ng buhay. Ito ay may aral.
a. Anekdota c. parabola
b. alamat d. sanaysay
74. Isangtagisan ngmga talino sa pamamagitan ng katwiran
sa pamamaraang patula.
a. balagtasan c. tula
b. talumpati d. duplo
75. Si severino Reyes na lalong kilala sa tawag na Lola
Basyang ay higit na kilala sa larangan ng:
a. dulaan c. pag-awit
b. pagtula d. balagtasan
76. Ang Kumitang ay isang uri ng awiting bayan. Ito ay may
karaniwang inaawit sa:
a. paghaharana c. paghehele
b. pakikidigma d. pamamangka
77. Ang senakulo ay isangpanrelihiyon;ito ay naglalayon na
a. ipaala ang kapanganakan ni Hesukristo
b. ipakita ang pagkakapatiran ng mga Kristiyano at
Muslim
c. magsalarawan ngmga pinagdaanang buhay at
kamatayan ni Hesukristo
d. magligtas sa mga kasalanan
78. Sa akda niyang “Guryon”, ipinalintulad ni Idelfonso
Santos ang Guryon sa:
a. buhay ng tao c. anyo ng pagpapalipad
b. tibay ng pisi d. hanging habagat
79. “Unupo si Itim,sinulotni Pula,heto na si Puti na bubuga-
buga.” Ito ay halimbawa ng isang:
a. bugtong c. alamat
b. salawikain d. kuwentong bayan
80. “Ang sinuman ay makabubuo ng matibay na lubid kung
pagsasamahin ang sinulid.” Ang ibig sabihin ng
kasabihang ito ay:
a. Mahirap magkaisa ang mga tao.
b. Madali ang gumawa ng lubid kung may sinulid
c. Kailangan natin ang lubid sa ating mga Gawain.
d. Magkakaroon tayo ng lakas kung tayo’y magkakaisa.
81. “Ang taong nagigipit sa patalm kumapit.” Ano ang ibig
sabihin ng salawikaing ito:
a. Ang kaligtasan ng taong nagigipit ay sa tapang ng
dibdib
b. Susuungin ng tao kahit ani mang panganib upang
malunasan ang kanyang problema
c. Malapit sa panganib ang mga taong nagigipit.
d. Huwag makiharap sa taongnagigipitsapagkatsiya ay
siguradong galit
82. Alin sa sumusunod anghindi tuluyanganyo ng panitikan?
a. korido c. kuwentong bayan
b. alamat d. maikling kuwento
83. Tukuyin kung anong uri ng panitikan ang“Isangbayabas,
pito ang butas.”
a. Sawikain c. Salawikain
b. Idyoma d. Bugtong
84. “Ano man ang tibay ng piling abaka ay wala ring lakas
kapag nag-iisa.” Isinasasaad ng salawikaing ito ang
kahalagaan ng :
a. pagkakaisa’t pagtutulungan
b. tibay ng dibdib at lakas kahit nag-iisa
c. pagkakaroon ng lakas kahit nag-iisa
d. pagpapalakas ng loob lalo’t nag-iisa
85. Sa akin lipain doon nagmula
Lahat ng pagkain nitong ating bansa
Ang lahat ng tao mayaman o dukha
Sila’y umaasa sa pawis ko’t gawa.
Ano ang ipinahihiwatig ng saknong?
a. Lahat ng pagkain ay sa magsasaka nagmumula
b. Lahat ng magsasaka ay may lupang sinasaka
c. Lahat ng tao’t bagay ay galling sa lupa
d. Lahat ng umaasa sa biyayang galling sa magsasaka.
86. Ang kaibigan ko ay isa lamang maralita.
a. mangmang c. mabait
b. maliliit na tao d. mahirap
87. Si Nena ay inaruga ng kanyang lola mula pa noong siya’y
maulila.
a. pinabayaan c. inalagaan
b. pinamigay d. kinuha
88. Palasak na ang desenyong iyan.
a. pambihira c. magastos
b. pangkaraniwan d. wala sa moda
89. Ang mga salbahe ay kinamuhian niya
a. kinakalinga c. kinatatakutan
b. kinukumusta d. kinasusuklaman
90. Ang mga kawal na lumabag sa utos ay binigyan ng
babala.
a. sundalo c. kusinero
b. kaibigan d. pulis
91. Nangangamba ka ba na hindi ka niya pagbibigyan?
a. nasisiyahan c. nababanas
b. natatakot d. naiinis
92. Ang pagpunta sa Saudi Arabia ay di-gawang biro.
a. Madali c. mahirap
b. masayang Gawain d. maayos
93. Si Miguel ay sumakabilang buhay na noong Linggo.
a. nagpaalam c. nagpunta sa siyudad
b. namatay d. nagbayad ng utang
94. Bakit mukhang Biyernes Santo si Marko.
a. malungkot c. mukhang masaya
b. lumuluha d. tumatawa
95. Nakaririmarim ang nangyaring sakuna sa dagat.
a. nakalulungkot c. nakaiinis
b. nakatatakot d. nakapangingilabot
96. Ang dayuhang siyang pinakamatalik na kaibigan ni Rizal
ay
a. Austin Craig c. Otley beyer
b. Ferdinand Blumentritt d. Don Eulogio Despujl
97. Dahil sa tulong at pagmamalasakit ni
a. Dona Aurora A. Quezon
b. Tandang Sora
c. Luz B. Magsaysay
Sa kapakanan ng mga sinalanta ng sakuna, siyay
tinaguriang Ina ng Kruz na Pula.
98. Kung ano ang “Urbana at felisa” sa mga tagalog ang
a. Lagda c. Bidasari
b. Maragtas d. Hudhud
ay siya naman sa mga Bisaya.
99. Sa mga tauhan ng Noli Me Tangere ni Rizal, si
a. Basilio c. Capitan Tiago
b. Elias d. Simon
Ang nagligtas kay Ibarra sa kapahamakan
100. Ang aklat ng mga tinipong tula sa Tagalog ni Lope K.
Santos ay pinamagatang
a. Damdamin c. Tungkos ng Alaala
b. Puso at Diwa d. Mga Dahong Ginto
* * * * * T H E E N D * * * * *
WORK HARD, DREAM HARDER
filipino
1 B 51 B
2 B 52 C
3 B 53 A
4 B 54 B
5 B 55 C
6 A 56 B
7 B 57 B
9. 8 A 58 B
9 B 59 C
10 A 60 B
11 A 61 B
12 A 62 C
13 B 63 B
14 A 64 A
15 B 65 A
16 B 66 C
17 A 67 B
18 C 68 A
19 B 69 C
20 C 70 A
21 B 71 B
22 B 72 D
23 A 73 C
24 A 74 A
25 B 75 A
26 D 76 B
27 B 77 C
28 A 78 A
29 C 79 A
30 B 80 D
31 A 81 B
32 C 82 A
33 D 83 D
34 B 84 A
35 B 85 D
36 B 86 D
37 B 87 C
38 C 88 B
39 D 89 D
40 B 90 A
41 A 91 B
42 A 92 C
43 B 93 B
44 C 94 A
45 B 95 D
46 C 96 B
47 B 97 A
48 A 98 D
49 D 99 D
50 B 100 B
HUMAN GROWTH AND DEVELOPMENT
POST-TEST April 2010
Multiple Choices:
1. The process by which certain potentials are inherited
from the parents for his development
a. Life c. Heredity
b. Birth d. Character
2. This theory states that there are 8 basic development
stages that the individual has to pass through his life
a. Learning Theory
b. Psychoanalytic Theory
c. Psychosocial Theory
d. Cognitive Development
3. Transition age from childhood to adulthood where rapid
physical changes and sex maturity occur resulting in
changes in ways of feelings, thinking and acting.
a. Puberty c. Early adulthood
b. Adolescence d. Stage V
4. Modifying an existing scheme after an individual’s
interaction with the environment, resulting in the
creation of a new scheme.
a. Assimilation c. Recognition
b. Interaction d. Accommodation
5. Theory statingthat a person’s behavior can be motivated
by urges towards self satisfaction.
a. Psychoanalytic Theory
b. Cognitive development theory
c. Psychosocial Theory
d. Moral development theory
6. The ability of a child to conceptualize the retention and
preservation of the same quantity under various
changes.
a. Recognition c. Assimilation
b. Reversibility d. Conservation
7. Refers to the idea that no individual are exactly the same
or alike.
a. Cognitive theory c. Individual differences
b. Exclusivity theory d. Emotional quotient
8. He is known as the Father of Modern I.Q. Test
a. Lewis Terman c. Laurence Kohlberg
b. Erick Erickson d. Martin Lesley
9. “Intellectual appreciative Experience” is …
a. base on the premise that all learning has emotional
correlates
b. obtained in the field of music, art and literature
c. the acquisition and retention o acts and information
d. assumes that human activities arebased on stimulus
and response
10. These statements imply that children at the early
learning stage consider parents and teachers as
authorities and models.
a. Parents and teachers should always coordinate
children’s activities
b. Parents should enforce strictdiscipline at home and
teachers in school
c. Parents and teachers should be the role models at
all times
d. Parents and teachers should always consult each
other with regards the child’s intellectual
development
11. Any change in the behavior of an individual
a. Learning c. Change
b. Response d. Development
12. Which of the following principles IS NOT considered
under Classical Conditioning by Ivan Pavlov?
a. Excitation
b. Adhesive Principle
c. Stimulus Generalization
d. None of the above
13. The reinforcement of a person’s responses by
presentation or removal of rewards and punishment.
a. Operant conditioning c. Feedback Principle
b. Transfer of learning d. Discipline
14. This stimulation of action best explains the behavior of
an individual to take what he perceives to be the shortest
route to his goals.
a. Recognition c. Response
b. Assimilation d. Motivation
15. The process by which an individual acquires the social
and cultural heritage o the society where he belongs.
a. Socialization c. Integration
b. Internalization d. Acquisition
16. Philosophy of education’s main function.
a. Aid the leaner to build his own personal philosophy
b. Definition o goals and setting of directions from
which education
c. Educations carries on a lifetime cycle
d. Provision of academic background prerequisite to
learning
17. According to Froebel, kindergarten is also known as
“____________?
a. children have fun and enjoyment
b. Garden where children could grow
10. c. He learning Center for Life
d. Where new beginnings begin
18. Which of the following statements is given emphasis by
“humanistic education?”
a. The great works of man such as the classics should
be enjoyed.
b. Man should learn the different philosophies of
education
c. “Build a man who is distinctly civilized, educations
and refined”
d. Develop man into a thinking individual
19. A teacher who advocates the pragmatic philosophy of
education believes that experience should follow
learning, thus, she has to?
a. require her student mastery of the lessons
b. encourage her students to memorize facts
c. equip her students with basic skills and abilities
d. provideher student with opportunities to apply their
skills and abilities
20. How are institutions of learning encouraged to set higher
standards over and above the minimum requirement for
state recognition?
a. Scholastic achievement
b. Faculty development
c. Academic freedom
d. Voluntary accreditation
21. The period of physical, especially sexual, and mental
maturation which is characterized by rapid somatic
growth is known as
a. infancy c. puberty
b. early childhood d. adulthood
22. Claustrophobia is an irrational fear of
a. Darkness c. closed space
b. strangers d. height
23. An eye defect characterized by clear vision in one
dimension but unfocused vision on the other is called
a. myopia c. hyperopia
b. astigmatism d. presbyopia
24. Which of the following statements does not apply to
adolescents?
a. they desire the approval of their peers
b. they seek dependence on their parents
c. they have a marked sex development
d. none of the above
25. As young people mature, society expects them to
develop competencies and assume social roles in a
conventional manner.
a. expectation of parents
b. influence of peers groups
c. influence of formal education
d. cultural demands
26. The founder of the theory of psychology called
psychoanalysis was
a. Lock c. Freud
b. Hume d. leibnitz
27. When the learner reaches a point where no further
improvement can be expected, he is in a so-called
a. development crisis c. regression
b. learning plateau d. depression
28. Regarding the sexual maturation o boys and girls,
teachers should bear in mind that:
a. girls mature at a late stage than boys
b. girls mature at an earlier stage than boys
c. boys and girls mature at the same time
d. there are no marked differences in heir time of
maturity
29. Rationalization is used by student who
a. always give explanation or reason for their failures
rather than own their faults
b. like to take the blame for their faults
c. bribe their elders with promises
d. substitute words for deeds
30. Which of the following is true of Abnormal Psychology?
a. it studies the cause of personality defects
b. it measures the accomplishments of the individual
c. it concentrates on the scholastic performance of the
individual
d. it investigates the educational background of the
individual
31. Which of the following is a continuous variable?
a. weight c. nationality
b. sex d. race
32. Which of the following is true about one’s IQ?
a. it remains fairly constant
b. it is highly changeable
c. it is affected by attitude
d. it is never constant
33. Transfer of training easily takes place if the activities
involved
a. Are different
b. Have identical element
c. Occur in the same place
d. Vary in difficulty
34. When the learner is well-motivated, he performs his task
a. with indifference c. with arrogance
b. with disinterest d. with enthusiasm
35. A six-year-old child who has a mental age of eight years
has an IQ of
a. 120 b. 130 c. 132 d. 133
36. The ratio obtained by dividing mental age by
chronological age times 100 is called
a. derived quotient
b. deviation
c. intelligence quotient or IQ
d. intelligence ratio
37. Which of the following was written by Plato?
a. Sic et Non c. The Republic
b. The School and Society d. Emile
38. Who among those below asserted that “Education is for
complete living”
a. Dewey c. Kant
b. Spencer d. Froebel
39. The right of an educational institution and its faculty to
prescribe the methods/strategies of teaching refers to:
a. building style
b. choice of curriculum
c. academic freedom
d. co and extra curricular program
40. The 1987 Constitution provides that religious institution
can be given
a. with the students’ consent
b. with the parent/guardian approval
c. with mayor’s permit
d. with the school’s support
41. Public schools in the Philippines are the contribution of
which colonizer?
a. American c. Japanese
b. British d. Spanish
42. Hardship allowance is given to a teacher when
a. he’s assigned in a depressed area
b. he’s given additional teaching load
c. he’s in lahar area
d. he’s assigned in a hazardous area
43. The ability for quantitative learning of the relations of
facts taken from newspaper readings, letter writing and
the like is called:
a. functional literacy c. Knowledge outcome
b. adjustment learning d. Social competence
44. A teacher who gives a uniform assignment to be worked
out by all learners in Arithmetic is not observing a
11. characteristic of a good assignment.Which characteristic
is overlooked?
a. It should be definite
b. It should be stimulating
c. It should emphasize the essential
d. It should provide for individual differences
45. If a student ask a question which the teacher does not
have a ready answer, the latter should:
a. dismiss the question as irrelevant
b. offer a bluff
c. admit the fact that he doesn’t know the answer
d. ask volunteers to answer the question and do
research on it later.
46. The heredity traits acquired by a person in his lifetime;
a. are transmissible to his offspring
b. reappear in his future grandparent
c. Have no influence on the offspring
d. Become recessive traits
47. When student are given a chance to settle differences of
opinion by discussion, they develop:
a. fair play c. irritants
b. tolerance d. sociability
48. The school’s responsibility towards teenagers “gang age”
is:
a. provide the gang all the freedom it needs
b. gives classroom activities to give direction to out-of-
school youth activities
c. supervise gang activities
d. set up norms of conduct or the member of the gang
49. In an intelligence test, a 13-year old girl got a score
equivalent to that of a 15-year old. This means:
a. that the girl must be accelerated
b. that the girl is 2-years older mentally
c. that the girl has a chronological age of 15
d. that she has a mental age of 13
50. Which statement is not necessary to achieve the
learner’s interest in a learning activity?
a. the activity must lead to a practical end
b. the activity must be within the ability of the learner
c. the activity must fill a need recognized by the learner
d. the learner must have the experience that will
furnish the background for the activity
51. He is responsible for the theory which recognizes the
importance of developing multiple intelligence
a. Jean Piaget c. Frederick Freobel
b. Howard Gardner d. Sigmund Freud
52. The need to recognize and develop special sensitivity to
language, thus helping the learners to use the right word,
phrase and/ or graph to grasp new meaning refers to
a. visual intelligence c. feelings sensitivity
b. linguistic intelligence d. jargon
53. The sensitivity to tone and pitch, allowing one to
produce musical scoring is intelligence in?
a. musical c. quantitative exercises
b. verbal ability d. qualitative analysis
54. One’s ability to do abstract reasoning and manipulate
symbols refers to what type of intelligence?
a. musical
b. personality identification
c. mental ability
d. mathematical-logical
55. The ability to perceive how objects are related in order to
mentally perceive what is seen, thus creating concrete
visual images from memory refers to?
a. visual-spatial intelligence
b. musical
c. language
d. logical reasoning
56. The capacity to analyzeone’s feelings and thus be able to
understand and be able to know the motives of other
people’s actions.
a. spatial c. logical
b. personal d. diametric
57. The type of intelligence which enables a person to
understand other person’s feelings, behavior and
motivation.
a. emotional c. social intelligence
b. spatial d. quantitative and qualitative
58. The type of intelligence which characterizes actress,
actors, mimes, dancers and people of the Arts?
a. bodily-kinesthetic c. research
b. scientific d. emotions
59. An emerging thrust in determining one’s personality,
whether pleasant or unwholesome, this type of
personality measurement is the wholesomeness of one’s
virtues,i.e., values,relationships with other, adjustments
to varying situations, behavior an motivations
a. emotional quotient (E.Q.)
b. intelligence quotient (I.Q.)
c. maladjustment personality
d. anticipated behavior
60. It is a measurement of personality which is the result by
dividing the mental age by the chronological age.
a. emotional quotient (E.Q.)
b. intelligence quotient (I.Q.)
c. multiple Intelligence
d. forecasted behavior quotient
61. The teacher must be aware that both heredity and
environment represent complex factors, exerting many
specific influences on an individual’s growth. Which of
the following statements best represents the influence of
heredity and environment?
a. Heredity counts; environment is less important.
b. If the environment is changed, heredity becomes
less important.
c. The relative influences of heredity and environment
can vary widely in an individual’s growth.
d. In the long run, both tend to cancel each other’s
influences
e. None of the above
62. The best possible way to measure the influence of
heredity is by:
a. keeping the environment constant.
b. Ignoring the environment
c. Studying only fraternal o normal capability
d. Studying only identical twins of normal capability
e. Doing none of the above
63. Educators who contributed to the “open education”
movement includes:
a. Neill and piaget c. Bruner and Silberman
b. Kohl and kozol d. All of the above
64. A child’s social skills can be measured by:
a. direct observation and parent-teacher conferences
b. psychological test
c. adaptive behavior scales
d. A and C above
65. A teacher uses behavioral modification techniques in his
classes. Which of the following student behaviors would
he find most difficult to change?
a. Aggressive tendencies toward classmates
b. Poor habits in organizing work materials
c. Interrupting a speaker
d. Abandoning a project before it is finished
66. Learning-disabled children most characteristically have:
a. low IQ
b. poor socio-economic backgrounds
c. an average level of intelligence
12. d. minimal brain damage
67. Which of the following is true about educable mentally
retarded children?
a. Their IQ range between 50 and 70
b. They have short attention spans and experience
difficulty in generalizing
c. Their reading,writing, and arithmetic skillscannotbe
improved
d. A and B above
68. Which of the following is characteristics of a dyslexic
child
a. Mirror writing
b. listlessness
c. Below-average intelligence
d. Hyperactivity
69. Primary reading retardation is presumed to be
neurologically based, related to parietal lobe
dysfunction?
a. Inability to relate sound to letter symbols
b. Inadequate auditory information processing
c. Left-right directional confusion
d. Speech aphasia
70. Students with secondary readingproblems have capacity
to read, but are non-readers because of:
a. auditory problems
b. congenital defects
c. visual-acuity impairment
d. environmental or emotional actors
71. If a teacher accepts Maslow’s theory on the hierarchy of
needs, he or she will probably structure objectives to:
a. meet both the physiological and intellectual needs of
students
b. eliminate testing
c. eliminate extrinsic motivations
d. maintain a certain anxiety level for increased
competition
72. The knowledge explosion has led to crowding more and
more information into curriculum courses. A likely result
is that:
a. the textbook will no longer be the main instructional
medium in many classes
b. the child may spend more time in school
c. the teacher may have to rely more on the se of
multimedia materials
d. all of the above
73. During the learning process the teacher has most control
over:
a. the learners
b. the learning environment
c. the learning process
d. the behavior of the learners
74. Which of the following conditions does NOT contribute
to a climate psychologically suited to learning?
a. The teacher acts like a “real person.”
b. The teacher makes all of the decisions about
students’ learning activities.
c. The teacher accepts students as they are
d. The teacher shows trust in students’ decisions
75. WilliamGlasser advocates the frequent use of classroom
meetings, with teacher and students sitting in a small
circle. Which one of the following types of discussion
would NOT be appropriate in such a setting?
a. An educational-diagnostic conference on the
learning weaknesses of individual students.
b. An open-ended meeting for the purpose of exploring
and discussing student’s ideas about the curriculum
c. A social-problem-solving meeting to resolve teacher
or student problems elating to the school, the class,
or any individual member.
d. A sensitivity-training meeting for the purpose of
helping students ace their school-related problems
and learn how their actions can affect others
76. Which of the following does NOT represent a teacher’s
contribution to the emotional environment of the
classroom?
a. A strident, compelling voice.
b. A sustained sense of expectation where student
achievement is concerned
c. A well-written lesson plan
d. A sense of humor in a tense situation
77. According to Jones, student commitment to
accomplishing a learning goal depends on all of the
following EXCEPT:
a. how interesting the goal is
b. how likely it seems that the goal can be
accomplished
c. what degree of challenge the goal presents
d. whether the learner will be ableto tell if the goal has
been accomplished
e. whether materials are ready assembled for
undertaking the goal
78. The teacher who understands the adolescent’s need to
conform will:
a. use sarcasm as a disciplinary device
b. disregard unique responses in discussion and on
examinations
c. establish a learning climate that fosters feelings of
security
d. lecture students on their weakness o character
79. The best public relations agents for a school are the:
a. pupils c. PTA members
b. Teachers and pupils d. principals
80. The structured curriculum is in decided contrast to the
child-centered curriculum, which:
a. emphasizes fundamental education
b. is changeable and is built around student interest
and needs
c. is oriented to the needs of a democratic society.
d. Utilizes the theory of mental discipline
81. According to Bruner, teacher working with young
children should
a. Push the children to maximum cognitive
development as rapidly as possible
b. Present all information verbally so the children will
listen well
c. Present new material from the concrete to the
abstract
d. Present new information from the abstract to the
concrete
82. from the educational viewpoint, intelligence is:
a. an abstract concept
b. a trait that can be manipulated
c. good judgment
d. a form of behavior
83. Every taxonomy of educational objectives:
a. describes increasingly difficult learning activities
b. describes levels of goals for learner development
c. suggest evaluation measure for teacher use
d. Classifies learning outcomes
13. 84. A mathematics teacher following Gagne’s theory of
learning believes that:
a. learning can take place under all conditions
b. learningis mainly a mater of accuratediscrimination
c. learning takes place only when the student is in a
receptive state
d. learningis reinforced chiefly by classical conditioning
85. Under which of the following conditions is a child’s IQ
more likely to increase?
a. If the emotional climate in the classroom improves
b. If the child is given a large “research” project.
c. If the child enjoys problem solving and is given
ample opportunity for it
d. If A and C are true
86. Intelligence is the basis of education. Education is the
effective means for national development, hence, a
country spends a large portion of its budget for the
systematic training of the learner to attain full
development
Why is education one major concern of every c
country? Because
a. intelligence has many facets
b. intelligence is useful in testing
c. intelligence is a safe gauge for budgetary allocation
d. intelligence test when carefully conducted, can help
in determining need for future facilities for national
building
87. There are no two individuals who are the same.
Individual differences, when early recognize and
provided for, enable the teacher to provide different
motivations and approaches in guiding the learning
process. Each pupil differs physically, mentally, socially
and emotionally from other children. Unless the teacher
provides for this nature of the learner, no amount of
modern approaches in teaching can elicit favorable
results.
a. The paragraph highlights the need or motivating
learning
b. Individual differences is an important consideration
in guiding the learner
c. The above paragraph focuses on teacher-pupil
relationship
d. It takes about the nature of the learning process
88. Robert Craig, et al, wrote of the phase of steps in every
learning process. These include: 1.) the focusing of
attention to the stimulation at hand, 2.) the interplay of
the learner and the social factors that surround him, 3.)
the acquisition of a new response or behavior he gives to
the new learning and 4.) Retention which presupposes
that the new learning is acquired.
The above paragraph emphasizes
a. the learning process
b. the steps/phase of how individuals learn
c. the manifestations of learning
d. why learning is a difficult process
89. Approaches in teaching change from time to time
depending on the traditional of sophistication attached
to the course being taught. Some mentors believe that
the tie tested ways to teaching is effective. Other are
easily carried away to use modern approaches in
imparting new subject matter. It maybe safe to conclude
that once results are realized in teaching, no specific
method can be considered the one-and-only method to
use.
When teaching a subject area, it is safe to
a. stick to the traditional way
b. be modern and most recent
c. get results in teaching
d. to try any method as they are all theories after all
90. In the early 1980’s programmed teaching became
popular in helping teachers to provide for individual
differences in learners. The chunks of the subject matter
which are divided into units are supposed to help the
learner master the lesson,sinceitis simply to understand
the frame of the lessons. No test o mastery of the units
are done because the purpose is to provide information
on certain subject matter
Would you as a teacher use programmed instruction
if you handle a subject on Values Education?
a. yes, definitely
b. no, not important for the subject matter
c. I don’t know
d. Why not if the subject matter calls for it
91. The data/subject matter to teach are gathered in
different ways, These include historical sources like
surveys, systematic observations, experimentation,
interviews, etc. to be reliable and valid, the data
collected must be organized, properly analyzed and
interpreted. From these processes, some conclusion or
generalization are done to reveal certain relationships
like cause & effect. Data gathering involves:
a. tedious and serious study
b. easy does it
c. data gathered are tested and filed, then verified
before being used
d. no follow-up needed
92. Heredity and environment play important roles in the
function of human beings. DNA or Deoxyribonucleic Acid
is the biological (heredity) band of our genes. Our
environment includes the house, school and the
community where we live. Whether we become
successful or a failure will depend on the interplay of
both nature and nurture.
If heredity and environment affect the individual,
thus, we can conclude that
a. both actors play equal roes in one’s life
b. one factor, either heredity or environment exerts
more influence than the other
c. neither factor is important
d. nurture and nature are the same
93. The first systematic philosopher to work in the field of
education was
a. Socrates c. Plato
b. Aristotle d. Rousseau
94. The first state in the world’s history where all human
capabilities were allowed to develop freely
a. Rome c. Sparta
b. Athens d. Germany
95. They are the most practical, pragmatic people who
absorbed themselves in the management of their state
affairs
a. Spartans c. Romans
b. Athens d. Chinese
96. Invented the first system of writing in the orient
a. Phoenicians c. Greeks
b. Chinese d. Romans
97. first to introduce the use of printing press in the
Philippines
a. Romans c. Greeks
b. Chinese d. Japanese
98. conducted the world’s first civil service test
a. Greeks c. Chinese
b. Romans d. English
99. To develop the capacity of man only for war was the
educational aim of the ancient
a. Romans c. Athenians
b. Spartans d. Chinese
14. 100. To produce a young man who would be charming
in person and graceful in manner, e.g. a beautiful soul in
a beautiful body is the educational aim of education of
the
a. Romans c. Spartans
b. Athens d. Italians
* * * * * T H E E N D * * * * *
WORK HARD, DREAM HARDER
human growth and development
1 c 51 c
2 c 52 b
3 b 53 a
4 d 54 d
5 a 55 a
6 d 56 b
7 c 57 c
8 a 58 a
9 a 59 a
10 c 60 b
11 a 61 c
12 d 62 d
13 c 63 d
14 d 64 d
15 a 65 a
16 b 66 c
17 a 67 d
18 c 68 a
19 d 69 d
20 d 70 d
21 c 71 a
22 c 72 d
23 b 73 b
24 b 74 b
25 d 75 a
26 c 76 c
27 b 77 e
28 b 78 c
29 a 79 b
30 a 80 b
31 a 81 c
32 a 82 a
33 b 83 b
34 d 84 c
35 d 85 d
36 c 86 d
37 c 87 b
38 b 88 b
39 c 89 c
40 b 90 b
41 a 91 a
42 c 92 a
43 d 93 c
44 d 94 b
45 a 95 c
46 a 96 b
47 b 97 b
48 b 98 c
49 b 99 b
50 a 100 b
15. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 15
LICENSURE EXAMINATION FOR TEACHERS (LET)
Refresher Course
Content Area: MATHEMATICS
Focus: ANALYTIC GEOMETRY
Prepared by: Daisy de Borja-Marcelino
Competencies:
1. Solve problems involving coordinates of a point, midpoint of a line segment, and distance between two
points.
2. Determine the equation of the line relative to given conditions: slope of a line given its graph, or its
equation, or any two points on it.
3. Determine the equation of a non-vertical line given a point on it and the slope of a line, which is either
parallel or perpendicular to it.
4. Solve problems involving
a. the midpoint of a line segment, distance between two points, slopes of lines, distance between a
point and a line, and segment division.
b. a circle, parabola, ellipse, and hyperbola.
5. Determine the equations and graphs of a circle, parabola, ellipse and hyperbola.
I. The Cartesian Plane
Below is a diagram of a Cartesian plane or a rectangular coordinate system, or a coordinate plane.
An ordered pair of real numbers, called the coordinates of a point, locates a point in the Cartesian plane. Each
ordered pair corresponds to exactly one point in the Cartesian plane.
The following are the points in the figure on the right:
A(-6,3), B(-2,-3), C (4,-2), D(3,4), E(0,5), F(-3,0).
For numbers 1-2, use the following condition: Two insects M and T are initially at a point A(-4, -7) on a Cartesian
plane.
1. If M traveled 7 units to the right and 8 units downward, at what point is it now?
Solution: (-4+7, -7-8) or (-3,-15)
2. If T traveled 5 units to the left and 11 units downward, at what point is it now?
Solution: (-4-5, -7-11) or (-9, -18)
II. The Straight Line
A. Distance Between Two Points
A. The distance between two points (x1,y1) and (x2,y2) is given by
2
2
1
2
2
1 )
(
)
( y
y
x
x
.
Example: Given the points A(2,1) and B(5,4). Determine the length AB.
Solution: AB = 18
9
9
3
9
4
1
5
2
2
2
2
2
or 2
9 or 2
3 .
Exercises: For 1-2, use the following condition: Two insects L and O are initially at a point (-1,3) on a Cartesian plane.
1. If L traveled 5 units to the left and 4 units upward, at what point is it now?
A) (-6, 7) B) (4, 7) C) (-6, -1) D) (4, -7)
2. If O traveled 6 units to the right and 2 units upward, at what point is it now?
A) (7, 5) B) (5,5) C) (-7, 5) D) (-5, -5)
The two axes separate the plane into
four regions called quadrants. Points can lie in
one of the four quadrants or on an axis. The
points on the x-axis to the right of the origin
correspondtopositive numbers;whiletothe left
of the origin correspond to negative numbers.
The points on the y-axis above the origin
correspond to positive numbers; while below
the origin correspond to negative numbers.
16. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 16
3. Two buses leave the same station at 9:00 p.m. One bus travels at the rate of 30 kph and the other travels at 40 kph. If
they go on the same direction, how many km apart are the buses at 10:00 p.m.?
A) 70 km B) 10 km C) 140 km D) 50 km
4. Two buses leave the same station at 8:00 a.m. One bus travels at the rate of 30 kph and the other travels at 4 0 kph. If
they go on opposite direction, how many km apart are the buses at 9:00 a.m.?
A) 70 km B) 10 km C) 140 km D) 50 km
5. Two buses leave the same station at 7:00 a.m. One bus travels north at the rate of 30 kph and the other travels east at
40 kph. How many km apart are the buses at 8:00 a.m.?
A) 70 km B) 10 km C) 140 km D) 50 km
6. Which of the following is true about the quadrilateral with vertices A(0,0), B(-2,1), C(3,4) and D(5,3)?
i) AD and BC are equal
ii) BD and AC are equal
iii) AB and CD are equal
A) both i and iii B) ii only C) both ii and iii D) i, ii, and iii
7. What is the distance between (-5,-8) and (10,0)?
A) 17 B) 13 C) 23 D) -0.5
B. Slope of a line
a) The slope of the non-vertical line containing A(x1,y1) and B(x2,y2) is
2
1
2
1
x
x
y
y
m
or
1
2
1
2
x
x
y
y
m
.
b) The slope of the line parallel to the x-axis is 0.
c) The slope of the line parallel to the y-axis is undefined.
d) The slope of the line that leans to the right is positive.
e) The slope of the line that leans to the left is negative.
C. The Equation of the line
In general, a line has an equation of the form ax + by + c = 0 where a, b, c are real numbers and that a and b
are not both zero.
D. Different forms of the Equation of the line
General form: ax + by + c = 0.
Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Point slope form: )
( 1
1 x
x
m
y
y
where (x1, y1) is any point on the line.
Two point form: )
( 1
1
2
1
2
1 x
x
x
x
y
y
y
y
where (x1, y1) and (x2, y2) are any two points on the line.
Intercept form: 1
b
y
a
x
where a is the x-intercept and b is the y-intercept.
Reminders:
A linethat leans to the righthas positiveslope.The steeper the line, the higher the slopeis.
p q r
The slopes of lines p, q, r are all positive.Of the three slopes,the slopeof line p is the lowest, the slopeof r is the
highest.
A linethat leans to the left has negative slope. The steeper the line,the lower the slopeis.
t s u
The slopes of lines t, s, u are all negative. Of the three slopes, t is the highest, while u has the lowest (because the values
are negative.)
Exercises
17. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 17
1. What is the slope of 5 4 12 0
x y
- + = ?
A)1.25 B) -1.25 C) 0.8 D) -0.8
2. What is the slope of x = -9?
A) 4 B) 1 C) 0 D) undefined
3. What is the slope of y= 12?
A) 7 B) 1 C) 0 D) undefined
4. What is the slope of 1
4 9
x y
+ = ?
A) 4
.
0 B) 2.25 C) - 4
.
0 D) - 2.25
E. Parallel and Perpendicular lines
Given two non-vertical lines p and q so that p has slope m1 and q has slope m2.
If p and q are parallel, then m1 = m2.
If p and q are perpendicular to each other, then m1m2 = -1.
F. Segment division
Given segment AB with A(x1,y1) and B(x2,y2).
The midpoint M of segment AB is )
2
,
2
( 2
1
2
1 y
y
x
x
M
.
If a point P divides AB in the ratio
2
1
r
r
so that
2
1
r
r
PB
AP
, then the coordinates of P(x,y) can be obtained using
the formula
2
1
1
2
2
1
r
r
x
r
x
r
x
and
2
1
1
2
2
1
r
r
y
r
y
r
y
.
G. Distance of a point from a line
The distance of a point A(x1,y1) from the line Ax + By + C = 0 is given by
2
2
1
1
B
A
C
By
Ax
d
.
Exercises
1. Write an equation in standard form for the line passing through (–2,3) and (3,4).
a. 5x – y = -13 b. x – 5y = 19 c. x – y = -5 d. x – 5y = –17
2. Write an equation in slope intercept form for the line with a slope of 3 and a y-intercept of 28.
a. y = –3x + 28 b. y = 0.5x + 28 c. y = 3x + 28 d. y = 3x + 21
3. Write the equation in standard form for a line with slope of 3 and a y-intercept of 7.
a. 3x – y = –7 b. 3x + y = 7 c. 3x + y = 7 d. –3x + y = –7
4. Which of the following best describes the graphs of 2x – 3y = 9 and 6x – 9y = 18?
a. Parallel b. Perpendicular c. Coinciding d. Intersecting
5. Write the standard equation of the line parallel to the graph of x – 2y – 6 = 0 and passing through (0,1).
a. x + 2y = –2 b. 2x – y = –2 c. x – 2y = –2 d. 2x + y = –2
6. Write the equation of the line perpendicular to the graph of x = 3 and passing through (4, –1).
a. x – 4 = 0 b. y + 1 = 0 c. x + 1 = 0 d. y – 4 = 0
7. For what value of d will the graph of 6x + dy = 6 be perpendicular to the graph 2x – 6y = 12?
a. 0.5 b. 2 c. 4 d. 5
III. Conic Section
A conic section or simply conic, is defined as the graph of a second-degree equation in x and y.
In terms of locus of points,a conic is defined as the path of a point, which moves so that its distance from a fixed
point is in constant ratio to its distance from a fixed line. The fixed point is called the focus of the conic, the fixed line is
called the directrix of the conic, and the constant ratio is called the eccentricity, usually denoted by e.
If e < 1, the conic is an ellipse. (Note that a circle has e=0.)
If e = 1, the conic is a parabola.
If e > 1, the conic is hyperbola.
A. The Circle
1. A circle is the set of all points on a plane that are equidistant from a fixed point on the plane. The fixed point is
called the center, and the distance from the center to any point of the circle is called the radius.
18. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 18
x
y
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2. Equation of a circle
a) general form: x2 + y2 + Dx + Ey + F = 0
b) center-radius form: (x – h)2 + (y – k)2 = r2 where the center is at (h,k) and the radius is equal to r.
3. Line tangent to a circle
A line tangent to a circle touches the circle at exactly one point called the point of tangency. The tangent line is
perpendicular to the radius of the circle, at the point of tangency.
Exercises
For items 1-2, use the illustration on the right.
1. Which of the following does NOT lie on the circle?
a. (3,-1) b. (3,0)
c. (2,-1) d. (3,-2)
2. What is the equation of the graph?
a. 1
3
2
x
y b. 1
3
)
1
( 2
x
y
c. 1
3
)
1
( 2
x
y d. 1
3
)
1
( 2
x
y
B. The Parabola
1. Definition. A parabola is the set of all points on a plane that are equidistant from a
fixed point and a fixed line of the plane. The fixed point is called the focus and the fixed line is the directrix.
2. Equation and Graph of a Parabola
a) The equation of a parabola with vertex at the origin and focus at (a,0) is y2 = 4ax. The parabola opens to
the right if a > 0 and opens to the left if a < 0.
b) The equation of a parabola with vertex at the origin and focus at (0,a) is x2 = 4ay. The parabola opens
upward if a > 0 and opens downward if a < 0.
c) The equation of a parabola with vertex at (h , k) and focus at (h + a, k) is (y – k)2 = 4a(x – h).
The parabola opens to the right if a > 0 and opens to the left if a < 0.
d) The equation of a parabola with vertex at (h , k) and focus at (h, k + a) is (x – h)2 = 4a(y – k).
e) The parabola opens upward if a > 0 and opens downward if a < 0.
f) Standard form: (y – k)2 = 4a(x – h) or (x – h)2 = 4a(y – k)
g) General form: y2 + Dx + Ey + F = 0, or x2 + Dx + Ey + F = 0
3. Parts of a Parabola
a) The vertex is the point, midway between the focus and the directrix.
b) The axis of the parabola is the line containing the focus and perpendicular to the directrix. The parabola is
symmetric with respect to its axis.
c) The latus rectum is the chord drawn through the focus and parallel to the directrix (and therefore
perpendicular to the axis) of the parabola.
d) In the parabola y2=4ax, the length of latus rectum is 4a, and the endpoints of the latus rectum are (a, -2a)
and (a, 2a).
In the figure at the right, the vertex of the parabola is the origin,
the focus is F(a,o), the directrix is the line containing '
LL ,
the axis is the x-axis, the latus rectum is the line containing '
CC .
19. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 19
The graph of y
x
3
16
2
. The graph of (y-2)2 = 8 (x-3).
C. Ellipse
1. An ellipse is the set of all points P on a plane such that the sum of the distances of P from two fixed points F’ and F on
the plane is constant. Each fixed point is called focus (plural: foci).
2. Equation of an Ellipse
a) If the center is at the origin, the vertices are at ( a, 0), the foci are at ( c,0), the endpoints of the minor axis
are at (0, b) and
2
2
2
c
a
b
, then the equation is 1
2
2
2
2
b
y
a
x
.
b) If the center is atthe origin,the vertices are at(0, a), the foci areat (0, c), the endpoints of the minor axis
are at ( b, 0) and
2
2
2
c
a
b
, then the equation is 1
2
2
2
2
a
y
b
x
.
c) If the center is at (h, k), the distance between the vertices is 2a, the principal axis is horizontal and
2
2
2
c
a
b
, then the equation is 1
)
(
)
(
2
2
2
2
b
k
y
a
h
x
.
d) If the center is at(h, k), the distancebetween the vertices is 2a,the principal axisisvertical and
2
2
2
c
a
b
, then the equation is 1
)
(
)
(
2
2
2
2
b
h
x
a
k
y
.
4. Parts of an Ellipse
For the terms described below, refer to the ellipse
shown with center at O, vertices at V’(-a,0) and V(a,0),
foci at F’(-c,0) and F(c,0), endpoints of the minor axis
at B’(0,-b) and B(0,b), endpoints of one latus rectum
at G’ (-c,
a
b2
) and G(-c,
a
b2
) and the other at
H’ (c,
a
b2
) and G(c,
a
b2
).
a) The center of an ellipse is the midpoint of the segment joining the two foci. It is the intersection of the axes
of the ellipse. In the figure above, point O is the center.
b) The principal axis of the ellipse is the line containing the foci and intersecting the ellipse at its vertices. The
major axis is a segment of the principal axis whose endpoints are the vertices of the ellipse. In the figure,
V
V ' is the major axis and has length of 2a units.
c) The minor axis is the perpendicular bisector of the major axis and whose endpoints are both on the ellipse.
In the figure, B
B' is the minor axis and has length 2b units.
d) The latus rectum is the chord through a focus and perpendicular to the major axis. G
G' and H
H' are the
latus rectum, each with a length of
a
b2
2
.
x
y
O
B(0,b
)
B’(0,-
b)
F’(-
c,0)
F(c,0
)
V’(-
a,0)
V(a,0
)
)
,
(
2
a
b
c
)
,
(
2
a
b
c
)
,
(
2
a
b
c
)
,
(
2
a
b
c
x
y
O
(-4,0) (4,0) (5,0)
)
5
9
(4,
(-5,0)
)
5
9
(4,-
)
5
9
(-4,
)
5
9
(-4,-
(0, -3)
(0, 3)
x
y
O
(12,1)
(2,-4)
(-8,1)
(2,6)
(-6,4)
(2,1)
(8,5)
(8,3)
20. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 20
The graph of 1
9
25
2
2
y
x
. The graph of 1
25
)
1
(
100
)
2
( 2
2
y
x
.
4. Kinds of Ellipses
a) Horizontal ellipse.An ellipseis horizontal if its principal axis is horizontal. The graphs above are both horizontal
ellipses.
b) Vertical ellipse. An ellipse is vertical if its principal axis is vertical.
D. The Hyperbola
1. A hyperbola is the set of points on a plane such that the difference of the distances of each point on the set from two
fixed points on the plane is constant. Each of the fixed points is called focus.
2. Equation of a hyperbola
a) If the center is at the origin, the vertices are at ( a, 0), the foci are at ( c,0), the endpoints of the minor axis are
at (0, b) and
2
2
2
a
c
b
, then the equation is 1
2
2
2
2
b
y
a
x
.
b) If the center is at the origin, the vertices are at (0, a), the foci are at (0, c), the endpoints of the minor axis are
at ( b, 0) and
2
2
2
a
c
b
, then the equation is 1
2
2
2
2
b
x
a
y
.
c) If the center is at(h, k), the distancebetween the vertices is 2a,the principal axisis horizontal and
2
2
2
a
c
b
, then the equation is 1
)
(
)
(
2
2
2
2
b
k
y
a
h
x
.
d) If the center is at (h, k), the distance between the vertices is 2a, the principal axis is vertical and
2
2
2
a
c
b
,
then the equation is 1
)
(
)
(
2
2
2
2
b
h
x
a
k
y
2. Parts of a hyperbola
For the terms described below, refer to the hyperbola shown which has its center at O, vertices at V’(-a,0) and
V(a,0), foci at F’(-c,0) and F(c,0) and endpoints of one latus rectum at G’ (-c,
a
b2
) and G(-c,
a
b2
) and the other at
H’ (c,
a
b2
) and H(c,
a
b2
).
a) The hyperbola consists of two separate parts called branches.
b) The two fixed points are called foci. In the figure, the foci are at ( c,0).
c) The line containing the two foci is called the principal axis. In the
figure, the principal axis is the x-axis.
d) The vertices of a hyperbola are the points of intersection of the
hyperbola and the principal axis. In the figure, the vertices are at ( a,0).
e) The segment whose endpoints are the vertices is called the transverse axis. In the figure V
V ' is the transverse axis.
f) The line segment with endpoints (0,b) and (0,-b) where
2
2
2
a
c
b
is called the conjugate axis, and is a
perpendicular bisector of the transverse axis.
g) The intersection of the two axes is the center of the hyperbola .
21. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 21
h) The chord through a focus and perpendicular to the transverse axis is called a latus rectum. In the figure, G
G' is a
latus rectum whose endpoints are G’ (-c,
a
b2
) and G(-c,
a
b2
) and has a length of
a
b2
2
.
3. The Asymptotes of a Hyperbola
Shown in the figure on the right is a hyperbola
with two lines as extended diagonals of the
rectangle shown.
These two diagonal lines are said to be the asymptotes of the curve, and are helpful in sketching the graph of a
hyperbola. The equations of the asymptotes associated with 1
2
2
2
2
b
y
a
x
are x
a
b
y and x
a
b
y
. Similarly, the
equations of the asymptotes associated with 1
2
2
2
2
b
x
a
y
are x
b
a
y and x
b
a
y
.
The graph of 1
27
9
2
2
y
x
. The graph of 1
27
9
2
2
x
y
.
PRACTICE EXERCISES
Directions: Choose the best answer from the choices given and write the corresponding letter of your choice.
For items 1-5, use the illustration on the right.
1. Which of the following are the coordinates of A?
a. (1,2) b. (2,1) c. (-3,3) d. (2,-3)
2. What is the distance between points M and T?
a. 61 units b. 6 sq. units c. 51 units d. 8 units
3. Which of the following points has the coordinates (-3,-1)
a. M b. A c. T d. H
4. Which of the following is the area of the triangle formed with vertices M, A and H?
a. 5 sq. units b. 10 sq. units c. 5 units d. 10 units
5. Which of the following is the equation of the line containing points A and T?
a. y= 2 b. x=2 c. y+2x=3 d. y-2x+3=0
6. Suppose that an isosceles trapezoid is placed on the Cartesian plane as shown
On the right, which of the following should be the coordinates of vertex V?
a. (a,b) b. (b+a, 0) c. (b-a,b)d. (b+a,b)
7. The points (-11,3), (3,8) and (-8,-2) are vertices of what triangle?
a. Isosceles b. Scalene c. Equilateral d. Right
8. What is the area of the triangle in #7?
a. 40.5 sq units b. 41.8 sq units c. 42 sq units d. 46.8 sq units
9. Which of the following sets of points lie on a straight line?
a. (2,3), (-4,7), (5,8) b. (-2,1), (3,2), (6,3) c. (-1,-4), (2,5), (7,-2) d. (4,1), (5,-2), (6,-5)
10. If the point (9,2) divides the segment of the line from P1(6,8) to P2(x2,y2) in the ratio r =
7
3
, give the coordinates of P2.
x
y
F’(-6,0) O
(-3,0) (3,0) F(6,0)
(6,9)
(6,-9)
x
y
F’(0,-6)
O
(0,3)
F(0,6)
(0,-3)
(-9,6) (9,6)
0
3
x
y
0
3
x
y
x 1
2
3
1 2 3
-3 -2 -1
-3
-2
-1
M
A
T
H
y
x
D(a,0) E(b,0)
O(0,b) V
0
0
22. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 22
x
y
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
x
y
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
x
y
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
-15
-10
-5
0
5
10
15
x
y
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
a. (16,–12) b. (–16, 15) c. (14,15) d. (12,–12)
11. Give the fourth vertex, at the third quadrant, of the parallelogram whose three vertices are (-1,-5), (2,1) and (1,5).
a. (-3,-2) c. (-3,-4) c. (-4,-1) d. (-2,-1)
12. The line segment joining A(-2,-1) and B(3,3) is extended to C. If BC = 3AB, give the coordinates of C.
a. (17,12) b. (15,17) c. (18,15) d. (12,18)
13. The line L2 makes an angle of 600 with the L1. If the slope of L1 is 1, give the slope of L2.
a. (3 + 20.5) b. (2 + 20.5) c. –(2 + 30.5) d. –(3 + 30.5)
14. The angle from the line through (-4,5) and (3,m) to the line (-2,4) and (9,1) is 1350. Give the value of m.
a.7 b. 8 c. 9 d. 10
15. Which equation represents a line perpendicular to the graph of 2x + y = 2?
a. y = -0.5x – 2 b. y = –2x + 2 c. y = 2x – 2 d. y = 0.5x + 2
16. Which of the following is the y – intercept of the graph 2x – 2y + 8 = 0?
a. -4 b. -2 c. 2 d. 4
17. Which of the following may be a graph of x – y = a where a is a positive real number?
a. b. c. d.
18. Write an equation in standard form for a line with a slope of –1 passing through (2,1).
a. x + y = –3 b. –x + y = 3 c. x + y = 3 d. x – y = –3
b.
For items 19-22, use the illustration on the right.
19. Which of the following are the coordinates of A?
a. (1,1) b. (1,-1)
c. (-1,1) d. (-1,-1)
20. What is the distance between points A and H?
a. 61 units b. 6 sq. units
c. 51 units d. 8 units
21. Which of the following points has the coordinates (-2,-2)?
a. M b. A
c. T d. H
22. Which of the following is the equation of the given graph?
a. 2
2
x
y . b. 2
2
x
y . c. 2
2
x
y . d. 2
2
x
y .
23. Which of the following is the equation of the line containing points M and T?
a. y= 2 b. x=2 c. y-2x-2=0 d. y+2x+2=0
24. What is the shortest distance of y
x 8
2
from 3
x ?
a. 1 unit b. 2 units c. 3 units d. 8 units
25. Which of the following is a focus of 1
4
12
2
2
x
y
?
a. (0,-4) b. (-4,0) c. (0,4) d. (4,0)
26. What are the x-intercepts of 1
9
4
2
2
y
x
?
a. none b. 2
c. 3
d. 4
27. Which of the following is a graph of a hyperbola?
a. b.
c. d.
28. Which of the following is an equation of an ellipse that has 10 as length of the major axis and has foci which are 4
units away from the center?
x
y
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
y y y y
x x x x
A
H
M
T
23. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 23
x
y
-30 -20 -10 0 10 20 30
-10
0
10
x
y
-30 -20 -10 0 10 20 30
-10
0
10
a. 1
9
25
2
2
x
y
b. 1
16
9
2
2
x
y
c. 1
3
5
2
2
x
y
d. 1
25
16
2
2
x
y
For items 29-31, consider the graph on the right.
29. Which of the following is the equation of
the graph?
a. 2500
25
100 2
2
x
y
b. 2500
25
100 2
2
y
x
c. 2500
25
100 2
2
x
y
d. 2500
25
100 2
2
y
x
30. What are the x-intercepts of the graph?
a. none b. 2
c. 5
d. 10
31. What kind of figure is shown on the graph?
a. circle b. ellipse c. hyperbola d. Parabola
32. Which of the following is the center of the graph
shown on the right?
a. (0,0) b. (0,10)
c. (10,0) c. (0,-10)
33. Which of the following is a focus of the graph
shown on the right?
a. (0,0) b. (0,10)
c. (0,5) c. (0,-10)
34. What is the area of the shaded region?
a. 4 units b. 4 square units
c. 16 units d. 16 square units
LICENSURE EXAMINATION FOR TEACHERS (LET)
24. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 24
Refresher Course
Content Area: MATHEMATICS
Focus: ADVANCED ALGEBRA
Prepared by: Daisy de Borja-Marcelino
Competencies: Show mastery of the basic terms,concepts and equations in Advanced Algebra i nvolvingradicals, rational
exponents and functions. Solve, evaluate and manipulate symbolic and numerical problems in above areas by applying
fundamental principles and processes.
KEY IDEAS
Some Helpful Tips in Answering the LET
1 Read the question/s or the items carefully and understand what they say.
2 Determine what is/arewanted or what is/areasked for.
3 Find out what is/aregiven and which data are needed to solvethe problem.
4 Reason out what processes (operations) to apply and the order in which they areto be applied.
5 Summarize the problem by means of an open number sentence.
6 Compute carefully. Check each step in the computations.
7 Decide the reasonableness of the result.
8 Check the resultby seeing to it that the result satisfies all theconditions of the problem.
RATIONAL EXPONENTS
If a is a real number and n is any positive integer, the symbol
n
a denotes the nth power of a. The real number a is
called the base and n is called the exponent. In symbols,
a
a
a
a
an
... .
n factors
Examples: a) 4
3
3
3
3
3 or 81. b) .
2
2
2
2
3
m
m
m
m
c) .
2
1
2
1
2
1
2
1
2
1
4
d) .
3
.
1
3
.
1
3
.
1
2
e)
math
math
math
2
. e) .
2
2
2
m
m
m
Note that any base raised to the power of 1, is just the base. Moreover, any base raised to the power of 0 is 1,
while 00 is indeterminate.
Examples: a) .
1
90
b) .
4
41
c) (-m)1 = - m. d) z0 = 1.
e) 1
0
3
2
e
op
h . f) 1
23
.
38
0
. g) 5
3
2
1
5
3
2
y
o
j
y
o
j . h) a
a
m
4
1
4
1 1
0
.
Laws of Exponents
If a and b are real numbers and m and n are positive real numbers, then the following are true.
n
m
n
m
a
a
a
. nm
m
n
a
a .
If n
m and 0
a , then
n
m
n
m
a
a
a
. n
n
n
b
a
ab .
If m
n and 0
a , then m
n
n
m
a
a
a
1
. If 0
b , then n
n
n
b
a
b
a
.
If 0
a , then 1
0
a
a
a
n
n
.
Examples: a) .
4
4 6
3
2
b) .
32
2
2
2
2 5
2
3
2
3
c) (3 x 4 )2 = 32 x 42.
d)
.
1
3
3
2
2
e) .
27
3
3
3
3 3
2
5
2
5
f). .
27
1
3
1
3
3
3
3
3
3
5
2
5
2
Exercises
1. In the expression 8m5, 5 is called the ________.
A. base B. coefficient C. constant D. exponent
2. Evaluate
0
10
8
6
0
14
3
9
0
2
0
10
20
5
25
m
n
s
s
n
m
m
m
.
A. 5 B. 23m12n4s-2 C. 20
2
m D. undefined
25. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 25
3. Anthony wrote 4
1
4
3 b
a =
( )4
1
3a + 4
1
4b . Which of the following is his misconception?
A. It is possible to factor out the exponent.
B. It is possible to distribute exponents over a sum.
C. The exponents should be multiplied with the base.
D. The coefficient inside the parentheses should be added.
4. Is
2
3
4
3
5
s
r
equal to ?
9
25
5
6
s
r
Why or why not?
A. Yes, for the exponents inside the parenthesis and the numerical coefficients should be added to 2.
B. No, for the exponents inside the parenthesis and the numerical coefficients should be subtracted from 2.
C. Yes, for the exponents inside the parenthesis should be added and the numerical coefficients should be
raised to 2.
D. No, for the exponent insidethe parenthesis should be multiplied by 2 and the numerical coefficients should
be raised to 2.
5. Explain why 3
12
x
x
is not equal to x4?
A. Because the exponents should be added.
B. Because the exponents should be multiplied.
C. Because the numerator should be divided by the denominator.
D. Because the exponent of the numerator should be subtracted by the exponent of the denominator.
6. Which of the following is the product of x5y3z and x2y4z2?
A. 2x102y122z2 B. x10y12z2 C. 2x72y72z3 D. x7y7z3
7. Give the product of a
5 and .
11
2 5
3
a
a
a
A.
2
5
4
55
10
5 a
a
a
C. a
a
a 55
10
5 6
3
B.
2
6
4
55
10
5 a
a
a
D. a
a
a 55
10
5 5
3
8. Marlon claims that
5
3
2
2 is equal to
8
2 . Is he correct? Why or why not?
A. Yes, for the exponents inside the parenthesis and the numerical coefficients should be added to 5.
B. No, for the exponents inside the parenthesis should be multiplied by 2 and the numerical coefficients
should be raised to 5.
C. No, for the exponents should be multiplied.
D. Yes, for the exponents should be added.
The mentioned laws of exponents also hold when m and n are positive rational numbers.
Examples: The following are true if there is no zero denominator.
a) 3
3
3
3
3 1
2
1
2
1
2
1
2
1
. b) 3
7
3
5
3
2
3
5
3
2
m
m
m
m
.
c) 3
1
3
1
3
2
3
1
3
2
5
5
5
5
. d) 7
2
7
3
7
5
7
3
7
5
p
p
p
p
.
e)
1
0
3
2
3
2
3
2
3
2
e
e
e
e
. f) 12
8
4
4
3
4
2
4
1
4
3
2
3
3
3 y
x
y
x
y
x
.
g)
5
2
5
2
5
2
xy
art
xy
art
. h)
2
3
4
6
4
5
4
11
4
11
4
5
1
1
1
y
y
y
y
y
y
x
x
x
x
x
.
Negative Exponents
If a is a nonzero real number and n is any rational number, then a-n = n
a
1
.
To simplify algebraic expressions with negative exponents is just to express the given expression into an
equivalent quantity where the exponents become positive.
Examples: Simplify the following such that they only have positive exponents.
a)
2
1
3
b) 4
3
7
c) 4
1
2
m
Solution: a) .
3
1
3
2
1
2
1
b) .
7
1
7
4
3
4
3
c)
.
2
1
2
4
1
4
1
m
m
Examples: Simplify the followingsuch that they only have positive exponents. Assume nonzero bases and no denominator
is zero.
a) 4
2
4
16
b) 3
4
m
m
c) 2
a
a
d) 3
3
t
t
26. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 26
e) 3
2
3
4
3
4
2
4
16
t
a
m
at
m
f) 3
1
3
4
h
g
g
m
g) 2
1
3
5
h) 2
2
x
Solution:
a) 4
2
4
16
=
4
2
2
4
4
1
4
4
4
4
. b) 3
4
m
m
=
m
m
m
m
1
1
3
4
3
4
.
c) 2
a
a
=
3
2
1
2
1
a
a
a
d) 3
3
t
t
= 1.
e) 3
2
3
4
3
4
2
4
16
t
a
m
at
m
= .
4
4
16
4 3
3
4
4
3
3
3
4
3
4
2
3
2
3
4
m
a
t
m
t
a
m
t
m
t
aa
m
f) 3
1
3
4
h
g
g
m
=
3
1
3
4
3
1
3
4
1
1
1
h
g
m
h
g
g
m
=
4
3
4
4
3
1
3
m
h
g
m
h
g
.
g) 2
1
3
5
=
2
3
2
5
2
3
2
5
)
2
1
)(
3
(
)
2
1
)(
5
(
.
h) 2
2
x =
2
2
1
x
or
2
2
1
x
x
or
4
4
1
2
x
x
.
Note that
2
2
1
x
x
is equal to
2
1
x
2
1
x
but
4
4
1
2
x
x
is not equal to
4
1
4
1
1
2
x
x
.
Whenever the exponent of a base is in rational form
b
a
where b 0, the expression can always be expressed in
radical form.
RADICALS
If n is a positive integer and a is a real number for which n
a
1
is defined, then the expression
n
a is called a
radical, and
n
a = n
a
1
.
The symbol is a radical sign, the number a is the radicand and n is the index of the radical
n
a .
Examples: a) In the expression
3
5 , the number 3 is called the index and 5 is the radicand.
b) The expression 4
1
27 can be written as
4
27 .
When a radical notation has no index, it is understood that n=2 or we are going to extract the square roots of the
radicand.
Examples: a) .
49
49
2
b) .
3
3
3 2
2
1
Simplified radicals
An expression with radicals is simplified when all of the following conditions are satisfied.
Exponents of the radicand and index of the radical have no common factor except 1.
The radicand has no factor raised to a power greater than or equal to the index.
All indicated operations have been performed (if possible).
No denominator contains a radical.
The radicand has no fractions.
Radical notation of n
m
a
If a is a real number, m is an integer and
n
a is a real number, then n
m
a = m
n
a =
n m
a .
Examples: Write each exponential expression using radical notation.
a) 3
1
a b) 4
3
m c) 2
3
5
Solution: a) 3
1
a =
3
a . b) 4
3
m =
3
4
)
(
m . c) 2
3
5 =
2 3
5 = 3
2
5 or
3
5 .
Examples: Write each radical expression using exponential notation and simplify.
a) 22 b)
3
27
c)
3 6
x
27. St. Louis Review Center-Inc-Davao Tel. no. (082) 224-2515 27
Solution: a) 22 = 2
1
22 . b)
3
27
=
3
1
)
27
( = 3
3 3
1
3
. c)
3 6
x =
3
6
x =
2
x .
If n is an even positive integer, then a
a
n n
= = a
and if n is an odd positive integer then a
a
n n
= .
Examples: Simplify each of the following and give all the roots.
a) 625 b)
4
81 c)
6
169x d) 3 9
6
27 y
x
Solution:
a) 25
25
625 2
. b)
4
81 =
4 4
3 = 3.
c)
6
169x = 2
3
2
13 x = 13x3.
d) 3 9
6
27 y
x =
3 3
3
3
2
3
3 y
x =3x2y3.
For all real numbers a and b, and positive integers m and n for which the indicated roots are real numbers, the
following are true.
( )( ) n
n
n
ab
b
a = . mn
m n
a
a .
n
n
n
b
a
b
a
where b is not equal to zero.
Examples: The following are true.
a) .
15
5
3
b) 8
4
2
4
81
81
81 x
x
x
. c)
6
12 x
12
3
x
.
Examples: Simplify each of the following.
a) 3
125
8
b) 4
5
243
32y
Solution: a)
.
5
2
5
2
5
)
2
(
5
8
125
8 3 3
3 3
3
3
b) 4
5
243
32y
=
4
4
4 4
4 4
4
4
4 4
3
3
2
2
3
3
2
2
3
81
2
16 y
y
y
y
y
y
=
4
3
2
3
2 y
y
=
3
54
2 4 y
y
.
Operations on Radical Expressions
Addition and Subtraction
Radicalswith the same radicand and the same index are called like radicals. Like radicalsareadded or subtracted
by using the distributive property of real numbers. Moreover, only like radicals can be combined.
Examples: a) Give the sum of
3
7 , 3
3
7 , 2
3
7 and 4
3
7 .
b) Evaluate 10 15 +3 15 - 15 .
c) If the lengths of the sides of a triangle is 24 cm, 6
2 cm and 4cm, give its perimeter.
Solution: a)
3
7 +3
3
7 +2
3
7 + 4
3
7 =10
3
7 .
b) 10 15 +3 15 - 15 = 12 15 .
c) Given a triangle, its perimeter is determined by adding the lengths of its sides. Hence,
24 cm + 6
2 + 4cm = 6
4 cm + 6
2 cm + 4cm
= 6
2 cm + 6
2 cm+ 4cm = 6
4 cm + 4cm.
Multiplication of Radicals
Note that
n
ab =
n
a n
b allows multiplication of radicals with the same index.
Examples: Give the product of the following in simplest form. Take only the positive roots.
a) 8
6
10
9 b)
)
3
(
2 3 2
3
3 2
m
m
m
c)
7
3
( +
)
8 7
3
( -
)
8
Solution: a) 8
6
10
9 =
5
216
5
4
54
5
16
54
80
54
10
8
9
6
.