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Analytic Geometry B Accelerated Week 5 Page 39 of 5.docxLynellBull52
Analytic Geometry B Accelerated Week 5 Page 39 of 51
Analytic Geometry B Accelerated Week 5
Lesson 12.2 Combining Functions by Arithmetic Operations
Lesson 12.3 Combining Functions by Composition
Lesson 13.1 Transformations of Quadratic Functions
Lesson 13.2 Even/Odd Functions
Lesson 14.1 Writing Equations of Circles
Lesson 14.2 Writing Equations of Parabolas
Before working the problems, study the lesson listed above each problem set.
Record the answers on the answer sheet. Turn in the answer sheet to be
graded.
For some problem sets, answer boxes are given. Choices may be used more than
once if necessary.
Lesson 12.2 Combining Functions by Arithmetic Operations
Given , , and find each function.
1. 2. 3. .
4. • 5. 6. •
Choices for 1‐6
A) 2 14 24 B) 2 9 14 C) 3 9 27 D) 6
E) 8 15 AB) 9 12 AC) 12 AD) 9 12
AE) 5 12 BC) 6 9 BD) 12 BE) 7 15
CD) 9 12 CE ) DE ) ABC)
ABD) ABE) 27 ACD) 2 6 ACE ) 2 5
ADE) 3 3 BCD) 3 BCE) 3 CDE) 4
Analytic Geometry B Accelerated Week 5 Page 40 of 51
Given , , and find each function.
7. 8. 9.
10. 11. 12.
Given and indicate the restrictions in the domain. Choose all
restrictions that apply (there may be more than one answer). If there are no restrictions,
select “none”.
13.
14.
15. •
16.
17.
Choices for 7‐12
A) 2 14 24 B) 2 9 14 C) 3 9 27 D) 6
E) 8 15 AB) 9 12 AC) 12 AD) 9 12
AE) 5 12 BC) 6 9 BD) 12 BE) 7 15
CD ) 9 12 CE) DE) ABC)
ABD) ABE) 27 ACD) 2 6 ACE) 2 5
ADE) 3 3 BCD) 3 BCE) 3 CDE ) 4
Choices for 13‐17
A) x ≠ 0 B) x ≠ 4 C) x ≠ –4 D) x ≠3
E) x ≠ –3 CD) x ≠ 9 CE) x ≠ –2 CDE) None
Analytic Geometry B Accelerated Week 5 Page 41 of 51
Lesson 12.3 Combining Functions by Composition
Given and find each composition.
18. ∘ 19. ∘
Given and find each composition.
20. ∘ 21. ∘
Given and find each composition.
22. ∘ 23. ∘
Given and find each composition.
24. ∘ 25. ∘
Choices for 18‐25
A) 2 8 8 AE) 4 6
B) 4 4 2 BC)
C) 4 6 BD) 4 18
D) 2 7 6 BE) 3
E) 4 4 CD) 16 16
AB) 4 2 CE)
AC) 8 DE) 2
AD) ABC) 4
Analytic Geometry B Accelerated Week 5 Page 42 of 51
Lesson 13.1 Transformations of Quadratic Functions
What effect on the quadratic parent graph does each of the following have?
26. 2( ) ( )f x x h if 0h Choices for 26‐32
27. 2( )f x x k if 0k
28. 2(.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
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Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
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.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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.
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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!
1. Annexure - ‘ E ’
SYLLABUS/CURRICULUM
MATHEMATICS (041)
S.A.-II (2012-13)
CLASS-X
Second Term
Marks : 90
UNITS
MARKS
II.
ALGEBRA (Contd.)
23
III.
GEOMETRY (Contd.)
17
IV.
TRIGONOMETRY (Contd.)
08
V.
PROBABILITY
08
VI.
COORDINATE GEOMETRY
11
VII. MENSU RATION
23
TOTAL
90
The Question Paper will include value based question(s) to the extent of 3-5 marks.
UNIT II : ALGEBRA (Contd.)
3.
QUADRATIC EQUATIONS
(15) Periods
Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of the quadratic equations
(only real roots) by factorization, by completing the square and by using quadratic formula. Relationship
between discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
4.
ARITHMETIC PROGRESSIONS
(8) Periods
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms and
their application in solving daily life problems.
UNIT III : GEOMETRY (Contd.)
2.
CIRCLES
(8) Periods
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
1.
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2.
(Prove) The lengths of tangents drawn from an external point to circle are equal.
95
2. 3.
CONSTRUCTIONS
(8) Periods
1.
Division of a line segment in a given ratio (internally)
2.
Tangent to a circle from a point outside it.
3.
Construction of a triangle similar to a given triangle.
UNIT IV : TRIGONOMETRY
3.
HEIGHTS AND DISTANCES
(8) Periods
Simple and believable problems on heights and distances. Problems should not involve more than two right
triangles. Angles of elevation / depression should be only 30o, 45o, 60o.
UNIT V : STATISTICS AND PROBABILITY
2.
PROBABILITY
(10) Periods
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on
single events, not using set notation.
UNIT VI : COORDINATE GEOMETRY
1.
LINES (In two-dimensions)
(14) Periods
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of
geometrical representation of quadratic polynomials. Distance between two points and section formula
(internal). Area of a triangle.
UNIT VII : MENSURATION
1.
AREAS RELATED TO CIRCLES
(12) Periods
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and
perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems
should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)
2.
SURFACE AREAS AND VOLUMES
(i)
(12) Periods
Problems on finding surface areas and volumes of combinations of any two of the following: cubes,
cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems
with combination of not more than two different solids be taken.)
96
3. RECOMMENDED BOOKS
1.
Mathematics - Textbook for class IX - NCERT Publication
2.
Mathematics - Textbook for class X - NCERT Publication
3.
Guidelines for Mathematics laboratory in schools, class IX - CBSE Publication
4.
Guidelines for Mathematics laboratory in schools, class X - CBSE Publication
5.
A hand book for designing mathematics laboratory in schools - NCERT Publication
6.
Laboratory manual - Mathematics, secondary stage - NCERT Publication.
97
4. Design of Sample Question Paper
Mathematics (047)
Summative Assessment-II
Class X- (2013)
Type of Question
Marks per question
M.C.Q
SA-I
SA-II
LA
TOTAL
Total no. of Questions
1
2
3
4
Total Marks
8
6
10
10
34
8
12
30
40
90
The Question Paper will include value based question(s)
to the extent of 3-5 marks
Weightage
S.No.
Unit No.
Topic
Weightage
1
II
23
2
III
Algebra (contd.)
[Quadratic Equations A.P.]
Geometry (contd.) [Circles, Constructions]
3
IV
08
4
V
Trigonometry (contd.)
[Height and Distances]
Probability
5
VI
Coordinate Geometry
11
6
VII
Mensuration
23
Total
90
98
17
08
5. SAMPLE QUESTIONS
MATHEMATICS (047)
S.A.-II (2012-13)
CLASS-X
MCQ- 1 Mark
Q.1
The tenth term of an A.P. 1.0, 1.5, 2.0, ............... is
(a)
3.5
(b)
5.5
(c)
5.5
(d)
6.5
Q.2
A sphere and a cone of height ‘h’ have the same radius and same volume, then r: h is
(a)
4:1
(b)
1:4
(c)
16:1
(d)
1:16
SA-II - 2 Marks
Q.3
9 K.M.
JUNGLE
6.5 K.M.
2 K.M.
12 K.M.
A helicopter has to make an emergency landing as shown in the figure. What is the
probability of a safe landing?
Q.4.
In the figure, quadrilateral ABCD circumscribes the circle. Find the length of the side CD.
99
6. SA-III - 3 Marks
Q.5
The sum of first, third and seventeen term of an A.P. is 216. Find the sum of the first
13 terms of the A.P.
Q.6
The point R (p-3q, q) divides the line segment joining the points A (3, 5) and B (6, 8)
in the ratio 2:1. Find the co-ordinates of R.
Q.7
Draw a triangle ABC with side BC= 7cm, AB= 6cm and ABC = 60°. Construct a
triangle whose sides are
of the corresponding sides of ∆ ABC. Also write steps of
construction.
LA - 4 Marks
Q.8
A cone of height 3.25 cm is surmounted by a hemisphere having same base. If the
diameter of the base is 3.5 cm, then find the curved surface area. (Take π =
Q.9
If the sum of the roots of the equation
Kx² 2
is
Q.10
+1=0
, then find the roots of the equation.
A
D
100 m
600
B
80 m
θ
E
C
In ∆ DCE
tan θ – tan (90 θ) = 0
Also AE = 100 m and DC = 80 m.
Find BC.
100
)
7. ANSWER KEY
1. (c)
2. (b)
3. Length of a Jungle = (12 – 9) km = 3 km
Breadth of a Jungle = (6.5 –2) km = 4.5 km
Area of Jungle = 13.5 sq. km
Area of Total field = 12 x 6.5 = 78 sq. km
P (Safe landing) =
=
=
(1)
4. AE = AH (length of tangents from external points are equal)
x =4–x
2x = 4
x =2
DH = (5 – 2) = 3 cm
DH = DG = 3 cm
CF = CG
(1)
2y – 3 = y
y=3
DC = DG + GC = 3 + 3 = 6 cm
5. a + a + 2d + a + 16d = 216
3a + 18d = 216
(1)
a + 6d = 72
S13 =
=
2a + (13 – 1) d
2a + 12d
101
8. =
x 2 a + 6d
= 13 x 72
= 936
(1)
6. p – 3q =
p – 3q =
p – 3q = 5
(1)
(1 mark)
Also q =
q=
=
=7
(2)
(1 mark)
Substituting (2) in (1) we get
p–3x7=5
p = 26
(1 mark)
7. correct construction
Steps of construction
(2 marks)
(1 mark)
8.
Curved surface area of the hemisphere =
(4πr2)
= (2 x
102
x
x
) cm2 (1 mark)
9. Slant height of the cone (l) =
=
= 3.7 cm (approx.)
CSA of cone = πrl =
x
x 3.7 cm2
Total Curved Surface Area =
=
x
(1 mark)
(1 mark)
(3.5 + 3.7) cm2
x 7.2 = 39.6 cm2 (approx.)
(1 mark)
9. Sum of the roots =
=
K =2
(1)
Now the quadratic equation is
2x2 2
x+1=0
D = b2 4ac = 8 8 = 0
(1)
Roots are real and equal
x=
=
=
Roots are
,
(2)
10. tan θ = tan (90 θ)
tan θ = cot θ
→ θ = 45°
(1)
In ∆ DCE
tan 45° =
103
10. EC = 80 m
(1)
In ∆ ABE
= cos 60°
=
BE = 50
(1)
BC = BE + EC
= 50 + 80
= 130 m
(1)
104
11. VALUE BASED QUESTIONS
MATHEMATICS (047)
S.A.-II (2012-13)
CLASS-X
Ramesh, a juice seller has set up his juice shop. He has three types of glasses of inner
diameter 5 cm to serve the customers. The height of the glasses is 10 cm.(use π =3.14)
-
A glass with a plane bottom.
-
A glass with hemispherical raised bottom.
-
A glass with conical raised bottom of height 1.5 cm.
Type A
Type B
Type C
He decided to serve the customer in “A” type of glasses.
1.
2.
3.
4.
Find the volume of glass of type A.
Which glass has the minimum capacity?
Which mathematical concept is used in above problem?
By choosing a glass of type A, which value is depicted by juice seller Ramesh?
105
12. ANSWER KEY
1. Diameter = 5 cm
radius = 2.5 cm
height = 10 cm
Volume of glass of type A = πr2h
= 3.14 x 2.5 x 2.5 x 10
= 196.25 cm3
Volume of hemisphere = πr3
= x 3.14 x 2.5 x 2.5 x 2.5
= 32.71 cm3
Volume of glass of type B = 163.54 cm3
Volume of cone = πr2h
= x 3.14 x 2.5 x 2.5 x 1.5
= 3.14 x 2.5 x 2.5 x 0.5
= 9.81 cm3
Volume of glass of type C = 196.25 – 9.81
= 186. 44 cm3
(1) The volume of glass of type A = 196.25 cm3.
(2) The glass of type B has the minimum capacity of 163.54 cm3.
(3) Volume of solid figures (Mensuration)
(4) Honesty
106