Arithmetic to Analytic Geometry!
Before learning CALCULUS there are 10 points you need to reconsider as you continue your journey to the college life.
This exam offers word problems which includes branches like trigonometry, logarithms, functions, algebra, arithmetic and so forth. It ranges from 7th Grade to 10th Grade. It assess your basic knowledge of numbers and analytical skills. Hurry up and try!
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILESChuckry Maunes
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILES
Video Presentation Link: https://www.youtube.com/watch?v=bRYWBbvOMpo
Reference: Grade 10 Mathematics LM
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILESChuckry Maunes
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILES
Video Presentation Link: https://www.youtube.com/watch?v=bRYWBbvOMpo
Reference: Grade 10 Mathematics LM
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
Sets is the first lesson in Mathematics 7. This lesson introduces the basic terms. For more presentations visit me on YouTube. https://www.youtube.com/channel/UCltDbhOXh6r9FyYE52rWzCQ/playlists?shelf_id=18&view_as=subscriber&sort=dd&view=50
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Courtship, Dating, and Marriage - MAPEH 8 (Health 2nd Quarter)Carlo Luna
NOTE: Please download and install first the fonts listed at the end of the presentation.
2nd Quarter Grade 8 HEALTH
Unit 2: Family Life
Leasson 1: Courtship, Dating, and Marriage
A. Infatuation or Love
B. Courtship
C. Dating
D. Engagement
E. Marriage
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
Sets is the first lesson in Mathematics 7. This lesson introduces the basic terms. For more presentations visit me on YouTube. https://www.youtube.com/channel/UCltDbhOXh6r9FyYE52rWzCQ/playlists?shelf_id=18&view_as=subscriber&sort=dd&view=50
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Courtship, Dating, and Marriage - MAPEH 8 (Health 2nd Quarter)Carlo Luna
NOTE: Please download and install first the fonts listed at the end of the presentation.
2nd Quarter Grade 8 HEALTH
Unit 2: Family Life
Leasson 1: Courtship, Dating, and Marriage
A. Infatuation or Love
B. Courtship
C. Dating
D. Engagement
E. Marriage
This pdf is free to download. This document is prepared by tutor Kundan sir from Vista's Learning.Keep learning CBSE Class 1 0 maths by signing up in Vista's Learning portal here
https://v-learning.in/live-course/1114/ncert-solutions-for-maths-chapter-2-polynomials-part-8-vistas-learning
SINCE I CREATED IN 2010 VERSION AND SAVED IN OLD VERSION MOST OF FEATURES DISABLED. CONTENT NOT AFFECTED.
TCS written test procedure for 2014 batch.& Eligibility 60% with 2 back logs.
------------------------------------------------------------
80 minutes-30 questions,(aptitude),
10 minutes- 1 question ,(verbal)
------------------------------------------------------------
90 minutes-31 questions(total)
------------------------------------------------------------
next- round technical oral test only. Requirements for Mech,ece,eee branches (c- programme,data structures,data base concept.)
For cse ,it branches(java, operating systems, students may be asked to explain their project,)
You are leading a project team of 15 members. As you have found that the team members are not irregular in submission of weekly time sheets , you are required to stress the need to submit without fail. Using the following phrases, write an email with a minimum of 70 words and a maximum of 100 words to your team members informing the same.
can be accessed online – lead to loss of pay – every week – do not default – used to bill client – actual working hours – by friday – failure to adhere – time sheet filling application
Using the following phrases, write an email with a minimum of 70 words to a company requesting them to sponsor your college cultural festival.
pdf file – reputed institute - 10 days - 200 college – sparkling performance – extravaganza – sponsor the event – request appointment – brochure attached
More companies in the process of recruitment, play more emphasis in the topic of numbers in numerical aptitude. Especially for AMCAT aspirants this is very much useful.
American Period to Post War Republic (CPAR 11/12)John Labrador
Contemporary Philippine Arts from the Region
American Colonial Period (1898-1940)
Japanese Colonial Period (1941-1945)
Post War Republic (1946-1969)
Featured:
Notable artists and their artworks
Distinct historical events
Artistic concepts and techniques
A document tackling about the basis of Thunderstorms:
-What is Thunderstorm?
-How do the Thunderstorms form?
-What is the difference between thunder and lightning?
Between a water spout and a tornado?
-What are the types of Lightning? of a Thunderstorm?
-What are some signs of an approaching thunderstorm?
-What are some precautionary measures to do before and during a thunderstorm?
-Case of Thunderstorms in the Philippines and on Planes
Arguments and Fallacies: Philosophy SHSJohn Labrador
What should we consider when looking at arguments or opinions?
Arguments often take the form of statements that either claims or facts and are phrased in such way that they seem reasonable
There is an abundant number of minerals around the world, one of which is on the category called oxide minerals. Lets dig in through the depths of the world among the 5 examples of oxide minerals and their properties and purposes.
GLOBALISASYON.
Hindi lang mga magagandang bagau ang dulot ng pagmimigrate sa ibang bansa. Maraming mga isyung kalakip sa kilusang paggawa sa ibang bansa at isa na rito ang forced labor at human trafficking
Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn. ... The methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of statistical hypotheses.
Hypothesis Testing. Inferential Statistics pt. 2John Labrador
A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis.
INFERENTIAL STATISTICS: AN INTRODUCTIONJohn Labrador
For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
1. 1
HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)
NAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORE::::
INSTRUCTIONS:INSTRUCTIONS:INSTRUCTIONS:INSTRUCTIONS: Read and solve each problem carefully. Choose the letter of the correct answer.
Calculators are not allowed in this test, you are allowed to guess between the 4 choices available but make
sure at the end of this exam you come up to the best solution. Good Luck!
1111----TRIGONOMETRYTRIGONOMETRYTRIGONOMETRYTRIGONOMETRY(9(9(9(9THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Find the solution set on [0, ߨ] for the equation: sin ݔ + tan ݔ − tan ݔ sin ݔ − 1 = 0
a) ߨ b)
గ
ଶ
c)
గ
ଷ
d)
గ
ସ
2. Solve the equation3 tan ߠ + sec ߠ + 1 = 0, for all non-negative θ less than 360⁰.
a) 180⁰ b) 315⁰ c) 135⁰ d) 0⁰
3. Below are the solutions included in the solution set of the equation
2 tan ߠ + √3 sin ߠ ܿ݁ݏଶ
ߠ = 0, ݓℎ݁݁ݎ 0 ≤ ߠ ≤ 2ߨ except
a) 0 b)
గ
c)
ହగ
d)
గ
4. If sin(2ߙ) =
ଶ
ଷ
, compute the numerical value of ݊݅ݏ
ܽ + ܿݏ
ܽ
a) 1 b)
ସ
ଽ
c)
ଶ
ଷ
d)
ଷ
ସ
5. A flagpole, which is 34 ft. high, stands on top of a tower, which is 30 ft. high. From a certain point in
the same horizontal plane with the base of the tower, the angle subtended by the pole is equal to
the angle of elevation of the top of the tower. Find the distance from this point to the base of the
tower.
a) 60 ft. b) 90 ft. c) 120 ft. d) 64 ft.
2222----LOGARITHMSLOGARITHMSLOGARITHMSLOGARITHMS(8(8(8(8THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Suppose that logଶ(logଷ(logହ(log(logଵଵ ܰ)))) = 13. How many different prime numbers are factors
of N?
a) 2 b) 3 c) 5 d) 1
2. What are the positive numbers x which satisfy the equation:
logଶ ݔ logଷ ݔ logହ ݔ = logଶ ݔ logଷ ݔ + logଶ ݔ logହ ݔ + logଷ ݔ logହ ݔ ?
a) (1, 40) b) (1, 30) c) (1, 20) d) (1, 10)
3. Express as a single logarithm. 2 log௫ ܽ − 2 log௫ ܾ + 3 log௫ √ܾ −
ଵ
ଷ
log௫ ܽ
a)
ଵ
log௫ ቀ
భబ
య
ቁ
b)
ଵ
ଵ
log௫ ቀ
భబ
ల ቁ
c)
ଵ
log௫ ቀ
ల
భబ
ቁ
d)
ଵ
ଵ
log௫ ቀ
భబ
ଷ
ቁ
4. Solve for x: ln ݔ − 1 = ln(2ݔ + 1)
a) The equality never exist
b) 0
c) ݁
d) 1
5. Solve for x satisfying ݁୪୭భబ ௫
− 10୪୬ ଶ௫
= 0.
a) ݔ ≈ 2.546
b) ݔ ≈ 1.232
c) ݔ ≈ 4.915
d) ݔ ≈ 0.246
2. 2
3333----GEOMETRY(7GEOMETRY(7GEOMETRY(7GEOMETRY(7THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Find the area of the region enclosed by the graph ||ݔ + ||ݕ = 16.
a) 648 b) 256 c) 768 d) 512
2. A barber pole is a revolving cylinder 25ߨ inches tall with a diameter of 12 inches. The red stripe
make 5 complete turns around the cylinder as it goes from the bottom to the top. How long is the
stripe?
a) 25ߨ b) 60ߨ c) 65ߨ d) 100ߨ
3. A quadrilateral has vertices at A (-5,4), B (8,6), C (12,0) and D (-1,-2). What type of quadrilateral is
ABCD?
a) Parallelogram
b) Trapezoid
c) Square
d) Kite
4. Given a 4 m by 4 m square, form a new square by connecting each vertex to the midpoint of the
opposite side. What is the area of the new square?
a) 4.5 sq. meters
b) 3.2 sq. meters
c) 2.8 sq. meters
d) 16 sq. meters
5. The perimeter of a right triangle is 15 + 20√22 units. The sum of the squares of all its sides is 396.
Find the area of the triangle.
a) ܣ ≈ 3 448 .ݍݏ ݏݐ݅݊ݑ
b) ܣ ≈ 2 392 .ݍݏ ݏݐ݅݊ݑ
c) ܣ ≈ 6 385 .ݍݏ ݏݐ݅݊ݑ
d) ܣ ≈ 2 194 .ݍݏ ݏݐ݅݊ݑ
6. What is the ratio of the area of a square that is inscribed in a regular octagon to tha area of the
regular octagon?
a)
ඥଶା√ଶ
ଶ
b)
√ଶ
ଶ
c)
√ଶିଵ
ଶ
d)
√ଶ
ସ
7. Suppose we draw 200 horizontal lines and 200 vertical lines in a plane. How many “pieces” of the
plane are formed by cutting among all of these lines?
a) 40 401 b) 40 000 c) 48 400 d) 44 100
8. A 5 in by 6 in by 12 in box is to have an equal increase to each edge to increase its capacity by
1080cubic inches. Find the increase.
a) 1 inch
b) 2 inches
c) 4 inches
d) 8 inches
9. What is the area of the square whose diagonal is two units longer than the length of its side?
a) 8√2 b) 2√2 c) √2 d) 4√2
10. A certain chord of a circle is 12 inches and is the perpendicular bisector of a radius of the circle.
Determine the area of the circles in terms of pi.
a)
గ
ଵ
sq. inches
b) 4ߨ sq. inches
c) 36ߨ sq. inches
d) 27ߨ sq. inches
4444----COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Find the equation of the circle with a center at (2, -5) and is tangent to the line x=7.
a) 10ݔଶ
− ݕଶ
− 4ݔ + 4ݕ + 5 = 0
b) ݔଶ
+ 2ݕଶ
− 4ݔ + 10ݕ + 5 = 0
c) ݔଶ
+ ݕଶ
− 4ݔ + 10ݕ + 4 = 0
d) ݔଶ
+ ݕଶ
+ 4ݔ − 4ݕ + 10 = 0
3. 3
2. All ordered pairs below are positive integers (x,y) that can satisfy the equation: ݕ௫మିଵଵ௫ାଶସ
= 1, ݔ +
ݕ = 11 ݁ݐ݁ܿݔ
a) (8,3) b) (3,8) c) (1, 8) d) (1,7)
3. Find the area bounded by 2ݔଶ
+ 4ݔ + ݕ = 0 ܽ݊݀ ݐℎ݁ ݈݅݊݁ ݕ = 2ݔ
a) 3√3 .ݍݏ ݏݐ݅݊ݑ
b) 9 sq. units
c) 12 sq. units
d) 6 + 2√2 sq. units
5555----ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Find the equation of the hyperbola whose transverse axis is parallel to the y-axis, its y-intercepts
are 3 and -1, and asymptotes having equations ݕ − ݔ − 1 = 0 ܽ݊݀ ݕ + ݔ − 1 = 0.
a)
(௬ିଵ)మ
ସ
−
(௫ି)మ
ଶ
= 1
b)
(௬ାଵ)మ
ସ
−
(௫ିଵ)మ
ସ
= 1
c)
(௬ିଵ)మ
ସ
+
(௫ିଵ)మ
ଶ
= 1
d)
(௬ିଵ)మ
ଶ
−
(௫ା)మ
ଶ
= 1
2. Convert the polar equation of the cardioid ݎ = 2(1 − cos ߠ) into the equivalent equation in
rectangular coordinates.
a) (ݔଶ
− ݕଶ
+ 2ݔ)ଶ
= 4(ݔଶ
+ ݕଶ)
b) (ݔଶ
+ 2ݕଶ
+ ݔ)ଶ
= (ݔଶ
− ݕଶ)
c) (2ݔଶ
+ ݕଶ
+ ݔ)ଶ
= 2(4ݔଶ
+ ݕଶ)
d) (ݔଶ
+ ݕଶ
+ 2ݔ)ଶ
= 4(ݔଶ
+ ݕଶ)
6666----PROBABILITY(8PROBABILITY(8PROBABILITY(8PROBABILITY(8THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Two balls are picked randomly at a time from a jar containing 5 balls that are numbered 2, 3, 6, 9
and 10. What is the probability that the selected balls are both prime numbered balls?
a)
ଵ
ଶ
b)
ଵ
ଵ
c)
ଶ
ହ
d)
ଵ
2. Three sticks are chosen from a set of nine sticks whose lengths are 1 dm, 2 dm, 3 dm …, 9 dm. What
is the probability that the three sticks, placed end to end will form a triangle?
a)
ଽ
ଷସ
b)
ଷ
ଶ଼
c)
଼
ଽ
d)
ଵ
ସଶ
7777----FUNCTIONFUNCTIONFUNCTIONFUNCTION (10(10(10(10THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. If ݂()ݔ =
ଷ௫ି
ହ௫ି
for any real positive number a and b. If ݂(0) = 0 and
݂(1) ݅ݏ .݂݀݁݊݅݁݀݊ݑ ܹℎܽݐ ݅ݏ ݂ ቀ
ଷ
ହ
ቁ ?
a)
ଷ
ହ
b) −
ଽ
ଵ
c) −
ଷ
ହ
d)
ଽ
ଵ
2. For which values of x does ݂(ݔ + 3) = ݂(ݔ) + 1 ?
a) (0,1) b) (1,1) c) (1,-1) d) (0,-1)
3. If ݂(݊ + 1) =
()
for all positive integers n and ݂(1) = 2. ݀݊݅ܨ ݂(8).
a)
ଵ
ଷ
b)
ଵହ
ଵ
c)
ଵହ
ଷଶ
d)
ଷହ
ଷଶ
8888----ARITHMETICARITHMETICARITHMETICARITHMETIC (7(7(7(7THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. Reversing the digits of Anna’s age gives her mother’s age with difference of eighteen years. If the
sum of the digits of each are 6, how old is Anna?
a) 15 y.o. b) 24 y.o. c) 42 y.o. d) 33 y.o.
4. 4
2. Two brothers go up the 60-step escalators. The older brother rides up the escalators, but can only
take 20 steps up during the ride since it is quite crowded. His younger brother runs up the empty
down escalator, arriving the top at the same time as his brother. How many steps does the younger
brother take, assuming that both escalator have the same rate?
a) 100 steps
b) 60 steps
c) 40 steps
d) 150 steps
3. The positive integers 24, 56 and A have the property that the product of any two of them is divisible
by the third. What is the smallest possible value of A ?
a) 21 b) 24 c) 8 d) 18
4. Today is Monday, 1 July 2002. What day of the week will be 2ଽ଼ଷଷ
days from now?
a) Wednesday
b) Sunday
c) Tuesday
d) Friday
5. Find the smallest positive integer that has exactly 15 positive integral divisors.
a) 144 b) 36 c) 324 d) 81
6. Find the sum of 1ଷ
+ 2ଷ
+ 3ଷ
+ ⋯ + 100ଷ
a) 25 205 050
b) 25 502 500
c) 25 520 500
d) 25 025 050
7. The sum of three geometric progression is 52. If 8 is added to the middle term, the other two are
left unchanged, the progression becomes arithmetic. What is the original middle term?
a) 20 b) 12 c) 16 d) 36
8. The sum of the squares of the digits in a three place number is 84. The square of the middle digit is
equal to the product of the two numbers. If the digit are reversed in order, the number is decreased
by 594. What is the number?
a) 631 b) 284 c) 402 d) 842
9. My watch is 2 seconds fast each hour and my seatmate’s is 3 seconds slow each hour. Right now
they show the same time. In how many days will they show the same time again?
a) 200 days
b) 360 days
c) 640 days
d) 400 days
10. Melissa’s credit card number consists of nine nonrepeated, nonzero digits. By examining the digits
from left to right, she found that 1 divides the 1st digit, 2 divided the first 2 digits, 3 divides the first
three, and so on, until 9 divides the entire number. If the number begins with 3816, what is her
complete credit card number?
a) 381 627 945
b) 381 692 574
c) 381 654 729
d) 381 697 542
9999----POLYNOMIALS (10POLYNOMIALS (10POLYNOMIALS (10POLYNOMIALS (10THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. What should be the value/s of k such that the expression ݇ݔଶ
+ 24ݔ + 9݇ become a perfect square
trinomial?
a) ±2 b) ±6 c) ±4 d) ±1
2. The quadratic equation ݔଶ
+ ܽݔ + ܾ = 0, has roots c and d. The quadratic equation ݔଶ
+ ܿݔ + ݀ = 0
has roots a and b. Give all the possible values of the sum a+b+c+d.
a) 1 and 0 b) -2 and 0
5. 5
c) -2 and 1 d) -1 and 1
3. Evaluate the following sum: ݅!
+ ݅ଵ!
+ ݅ଶ!
+ ݅ଷ!
+ ⋯ + ݅ଵ!
a) 97 b) 90+i c) 95+2i d) 96+4i
4. Find the term in ൫3 + √ݔ൯
ଵଵ
that has ݔସ
as its variable.
a) 1 472 ݔସ
b) 2 591 ݔସ
c) 3 545 ݔସ
d) 4 455 ݔସ
5. The quadratic polynomial has the following properties ܲ()ݔ ≥ 0 for all real numbers x, ܲ(6) =
0, ܽ݊݀ ܲ(10) = 10. What is the value of
(ଶ)ା (ି)
ଶ
?
a) 125 b) 170 c) 45 d) 295
10101010----ALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIES (9(9(9(9THTHTHTH GRADE)GRADE)GRADE)GRADE)
1. The numbers x, y and z satisfy the equation |ݔ + 3| + |ݕ + 5| + |ݖ − 8| = 1. Which of the following
could be the value of |ݔ + ݕ + ?|ݖ
a) 8 b) 3 c) 5 d) 0
2. Find the value of ݔ −
ଵ
௫
, given that √ݔ +
ଵ
√௫
= 5 ݓℎ݁݁ݎ ݔ ≠ 0.
a) 25 b) 21√5 c) 21 d) 5√21
3. Find the value of ݔଶ
+ ݕଶ
, ݂݅
ଵ
௫ା௬
+
ଵ
௫ି௬
=
ଵ
ସ
for any positive integers x and y, where x > y ?
4. For which value of x satisfying
௫
|௫ିଵ|
> 9 is true
a) ݔ ≠ 0 b) ݔ >
ଽ
ଵ
c) ݔ >
ଽ
଼
d) ݔ = 1
5. Solve the equation for x: ݕ =
ଵି √௫మయ
ଵା √௫మయ
a) ݔ = ටቀ
ଵି௬
ଵା௬
ቁ
ଷ
b) ݔ = ට1 −
௬
௬ାଵ
య
c) ݔ = (1 − )ݕ(ଵା௬)
d) ݔ = ටቀ
ଵି௬
ଵା௬
ቁ
ଶయ
THANK YOU FOR CONSIDERING YOUR TIME TAKING THIS TEST!
ASSESMENT EVALUATIONASSESMENT EVALUATIONASSESMENT EVALUATIONASSESMENT EVALUATION
TRIGONOMETRYTRIGONOMETRYTRIGONOMETRYTRIGONOMETRY 4/5 4/5 2/5 2/5
LOGARITHMSLOGARITHMSLOGARITHMSLOGARITHMS 4/5 4/5 2/5 2/5
GEOMETRYGEOMETRYGEOMETRYGEOMETRY 8/10 7/10 6/10 4/10
CORRDINATE GEOMETRYCORRDINATE GEOMETRYCORRDINATE GEOMETRYCORRDINATE GEOMETRY 3/3 2/3 2/3 1/3
ANALYTICAL GEOMETRYANALYTICAL GEOMETRYANALYTICAL GEOMETRYANALYTICAL GEOMETRY 2/2 1 /2 1 /2 1 /2
PROBABILITYPROBABILITYPROBABILITYPROBABILITY 2/2 1/2 1/2 1 /2
FUNCTIONSFUNCTIONSFUNCTIONSFUNCTIONS 3/3 2/3 2/3 1 / 3
ARITHMETICARITHMETICARITHMETICARITHMETIC 8/10 7/10 6/10 4/10
POLYNOMIALSPOLYNOMIALSPOLYNOMIALSPOLYNOMIALS 4/5 3/5 3/5 2/5
ALGEBRAALGEBRAALGEBRAALGEBRA 4/5 4/5 3/5 2/5
RATINGS:RATINGS:RATINGS:RATINGS: 42424242----50505050 EXCELLENTEXCELLENTEXCELLENTEXCELLENT 35353535----41414141 EFFICIENTEFFICIENTEFFICIENTEFFICIENT 28282828----34343434 SATISFACTORYSATISFACTORYSATISFACTORYSATISFACTORY 0000----28282828 PROFICIENTPROFICIENTPROFICIENTPROFICIENT
6. 6
Excellence – You excel in different branch of Mathematics. Keep it going!
Efficient – You are diligent in finding solutions and efficient in aiming high scores
Satisfactory – You are a “middle-class” Math student that satisfies a good highschool math enthusiast
Proficient – You are on your way to open some improvements! Math is hard but sure is fun
ANSWER KEYANSWER KEYANSWER KEYANSWER KEY
TRIGONOMETRY
1. D
2. A
3. D
4. C
5. C
LOGARITHMS
1. D
2. B
3. A
4. A
5. D
GEOMETRY
1. D
2. C
3. A
4. B
5. D
6. B
7. A
8. C
9. A
10. D
COORDINATE GEOMETRY
1. C
2. C
3. B
ANALYTICAL GEOMETRY
1. A
2. D
PROBABILITY
1. B
2. D
FUNCTIONS
1. B
2. C
3. D
ARITHMETIC
1. B
2. A
3. A
4. D
5. A
6. B
7. C
8. D
9. B
10. C
POLYNOMIALS
1. A
2. B
3. C
4. D
5. B
ALGEBRA
1. D
2. D
3. C
4. B
5. A