Competency Based Questions Class 9 Maths

Curriculum Aligned
Competency Based Test Items
Mathematics
Class - 9
Central Board of Secondary Education

Table of Contents

Test Item
1 Number Systems .................................................................................................................03
2 Polynomials .........................................................................................................................06
3 Coordinate Geometry ..........................................................................................................09
4 Linear Equations in Two Variables......................................................................................12
5 Introduction to Euclid’s Geometry ......................................................................................14
6 Lines and Angles .................................................................................................................18
7 Triangles ..............................................................................................................................23
8 Quadrilaterals ......................................................................................................................27
9 Areas of Parallelograms and Triangles................................................................................30
10 Circles..................................................................................................................................33
11 Constructions.......................................................................................................................37
12 Heron’s Formula..................................................................................................................41
13 Surface Areas and Volumes .................................................................................................44
14 Statistics...............................................................................................................................48
15 Probability ...........................................................................................................................52

Scoring Key
1 Number Systems .................................................................................................................56
2 Polynomials .........................................................................................................................59
3 Coordinate Geometry ..........................................................................................................63
4 Linear Equations in Two Variables .....................................................................................66
5 Introduction to Euclid’s Geometry ......................................................................................69
6 Lines and Angles .................................................................................................................72
7 Triangles ..............................................................................................................................75
8 Quadrilaterals ......................................................................................................................78
9 Areas of Parallelograms and Triangles................................................................................81
10 Circles..................................................................................................................................84
11 Constructions.......................................................................................................................87
12 Heron’s Formula .................................................................................................................90
13 Surface Areas and Volumes .................................................................................................93
14 Statistics ..............................................................................................................................96
15 Probability ...........................................................................................................................99

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 02

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 1
Number System

SAS21M09Q0101
1 A number line consists of an in inite number of points. Points on it are associated with a rational
number.
Khushi says – ‘A point on the number line can represent different forms of a rational number.’
Akash says – ‘I think each point represents a unique rational number.’
Who is correct? Give an example to support your argument.

SAS21M09Q0102
2 Which of the following statements is true?

A. Every irrational number can be represented as a fraction.
B. Every irrational number can be represented with the help of decimals.
C. Every rational number can be represented as a terminating decimal.
D. Every rational number can be represented as an integer.

SAS21M09Q0103
3 Irrational numbers can provide more precision on measuring scale.
What can be the possible arguments in favour and against this statement?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 03

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 1

Deep draws the spiral of irrational numbers below on a paper.

SAS21M09Q0104

4 What is the length of OE in the spiral?

SAS21M09Q0105
5 Simplify:

A. -1
B. 3 -√5
C. -4+√15
D. 4-2√15

Vasu represents √4.5
4.5 on the number line PW. The length of TS = 1 unit. His representation is shown
below.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 04

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 1

SAS21M09Q0106
6 Which letter represent 0 of the number line?

A. P
B. R
C. X
D. S

SAS21M09Q0107
7 Between which two points does 5.2 lie on this number line?

A. U and V
B. T and U
C. S and T
D. V and W

SAS21M09Q0108

8 Screen size is de ined by the distance between two diagonally opposite corners of a screen. A
manufacturer can make rectangular display screens as per clients’ demands.
A client purchased a display screen of size 70 units from the manufacturer last year. For an upgrade, he
wants the same type of screen with a larger display.
What are the possible dimensions of the screen purchased by the client last year?

SAS21M09Q0109
9 The new screen size must be more than double, but it should be less than three times that of the
existing one.
Which of the following screen sizes meets the client’s requirement?

A. 145 units
B. 175 units
C. 2 70 units
D. 580 units

SAS21M09Q0110
10 The new display screen is to be installed in a space measuring 3 m × 3 m. To make the desired screen for
the client, what other information is required by the manufacturer?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 05

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 2
Polynomials

A shipment service provider uses three types of containers for shipping materials. The height and
width of the three containers are the same. The containers’ height is 0.15 m more than their width,
and the volume of the smallest container is 652 m³

SAS21M09C0201
1 Write a polynomial relating Container 1’s length, breadth and height with its volume.

SAS21M09C0202
2 Which of the following statements is true?

A. The volume of the three containers is the same.
B. The length of the three containers is the same.
C. The volume of Container 3 is 2,608 m³.
D. The length of Container 3 is 4 times the length of Container 2.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 06

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 2

SAS21M09C0203
3 What is the height of each container?

Hard plastic square shaped sheets are available in the.
The side length of sheets is as per requirement.
The price of a sheet is z per square meter.
Anuj requires two sheets – a smaller sheet with side length x m and a larger sheet with side length y
m. He has two choices:
Choice 1 – buy two separate sheets of side lengths x m and y m
Choice 2 – buy a single sheet with side length (x + y) m

SAS21M09C0204
4 What is the height of each container?

SAS21M09C0205
5 What is the difference in price between the two choices?

SAS21M09C0206
6 The area of a rectangle is (3 x2 + x – 2) square units. Its width is (1 + x) units. What is the length of the
rectangle?

SAS21M09C0207
7 3 2
A polynomial is expressed as x + bx + cx + d = 0 . The same polynomial can be written in factor form as
x + px + qx+ r = 0.
How is the constant term in the polynomial related to its factors p, q, and r?

A. d=p+q+r
B. d = (p + q) × r
C. d=p×q×r
D. d=pq+qr+pr
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 07

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 2

SAS21M09C0208
8 3 2
A polynomial is divided by (x – 1). The quotient obtained is 3 x – x – x – 4, and the remainder is – 5.
Which polynomial meets these conditions?
3 2
A. 3x – x – x – 9
3 2
B. 3x – x – x – 4
4 3
C. 3x – 4x – 3x + 4
D. 3x 4 – 4x 2 – 3x – 1
SAS21M09C0209
9 3 2 2
What is the common factor of x – x and – 22 x + 142 x – 120?

A. x
B. (x – 1)
2
C. x
D. 1
SAS21M09C0210
3 2
10 A polynomial is expressed as: p(x) = x + x – x – 1
At what values of x is the polynomial p(x) = 0?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 08

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 3
Coordinate Geometry

A forest ranger keeps track of bears in his area. He plotted their location on a graph. The origin
represents the ranger's control room’s location. To access and maintain equipment, Road x and
Road y have been laid and paved inside the forest. They pass through the control room.

One unit on the graph paper represents 1 km.

SAS21M09S0301
1 Which bear is nearest to a paved road?

A. Bear 389
B. Bear 415
C. Bear 425
D. Bear 467

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 09

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 3

SAS21M09S0302
2 Bear 467 has been injured. The forest rescue team starts from the control room and decides to use the
paved road as much as possible. Which road should they take?

SAS21M09S0303
3 How far is Bear 425 from Road x?

SAS21M09S0304
4 A tiger is at (11, 4). How far from it is the nearest bear?

A. 2 km
B. 4 km
C. 5 km
D. 7 km

SAS21M09S0305
5 In the forest, rain shelters are at an interval of 2 km along paved roads. A forest ranger is travelling on
Road x. He crosses a rain shelter located at (3, 0).
What is likely to be the location of the next shelter?

SAS21M09S0306
6 The control room receives a message about trespassers located at (–9, –8). The trespassers were seen
moving towards Road x on foot. The ranger immediately dispatches a team of guards in a jeep towards
them. The guards encounter the trespassers before crossing Road x.
Which of the following is most likely to be the location of the encounter?

A. (–9, –14)
B. (–9, –5)
C. (–9, 4)
D. (9, 5)
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 10

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 4

SAS21M09C0407
7 Ravi planted a red maple tree sapling. The height of the sapling is 0.25 m. The average growth rate of
the height of a red maple tree is 0.27 m per year.
The average life of a red maple tree is 80–100 years. Ravi estimated that his tree will grow up to 27 m.
What is the likely reason behind his estimation?

SAS21M09C0408
8 Which of the following equations represents the height (h) of the red maple tree after ‘t’ years of
planting?

A. h=0.25+0.27
B. h=0.25t+0.27
C. h=0.25+0.27t
D. h=0.25+0.27t

SAS21M09C0409
9 Which of the following is true for the line with equation: 1.x+0.y-4=0?

A. The distance of the line from the x-axis is 1.
B. The distance of the line from the Y-axis is 4.
C. The distance of the line from the Y-axis is –1.
D. The distance of the line from the x-axis changes from 1 to –4.

SAS21M09C0410
10 The equation of a line is ax+by+c=0.
What conditions ensure that the distance of the line from an axis is constant?

A. c = 0 and a, b ≠ 0
B. c < 0 and a, b ≠ 0
C. c, b ≠ 0 and a =1
D. c, b ≠ 0 and a = 0

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 11

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 4
Linear Equations in Two Variables

SAS21M09C0401
1 A soap manufacturer makes fragrant and non-fragrant liquid soaps. The liquid soaps are illed in
plastic bottles and packed in equal size cartons for transportation. Each carton contains 50 bottles.
The mass of a full bottle of soap is 220 gm and that of a half- illed bottle is 120 gm. What will be the
mass (gm) of the empty bottle?

A. 10
B. 20
C. 100
D. 110

SAS21M09C0402
2 A carton contains both fragrant and non-fragrant liquid soap bottles.
Write an equation representing the number of fragrant and non-fragrant bottles in the carton.

SAS21M09C0403
3 A carton is checked randomly. Which of the following cannot be the number of fragrant and non-
fragrant liquid bottles in the carton?

A. (5, 45)
B. (15, 35)
C. (20, 30)
D. (30, 40)

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 12

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 4

SAS21M09C0404
4 The soap bottles are available in small and large sizes.
A carton with 10 small and 40 large bottles weighs 10.8 kg. What is the mass of the carton with 50 large
bottles?

Sodium silicate is one of the constituents in liquid soap. The graph shows the amount of sodium
silicate in liquid soap.

SAS21M09C0405
5 How much sodium silicate (ml) is used for making 10 L of soap?

A. 100
B. 110
C. 1000
D. 10000

SAS21M09C0406
6 Write an equation to show the relation between quantities of sodium silicate and liquid soap.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 13

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 5
Introduction to Euclid's Geometry

SAS21M09G0501
1 Highways 20A and 56C run parallel to each other for 20 km in a state.
Which of the following statements is most likely to be true regarding them?

A. Both highways are of the same length.
B. There can be no link road between them.
C. The highways make an angle 90° with each other.
D. The distance between the two highways remains almost the same in the state.

Karan marks his city on the map as point A.

SAS21M09G0502
2 Savita says, ‘A dot is dimensionless, so your city is also dimensionless.’ Why is Savita wrong? Justify
your answer.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 14

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 5

SAS21M09G0503
3 Which of the following is not true?

A. A line has one dimension.
B. A plane has two dimensions.
C. A circle can be drawn with any radius and at any point.
D. Two distinct lines can pass through a point in the same direction.

The map shows three cities Conlen ©, Stratford (S), and Texhoma (T) on a straight highway.

SAS21M09G0504
4 Which of the following is true for the length of the highway between them?

A. The length of the highway between C and S is equal to the length of the highway between S and T.
B. The length of the highway between C and S is three-fourth of the length of the highway between
S and T.
C. The length of the highway between S and T is the sum of the lengths of the highway between CT
and CS.
D. The length of the highway between C and T is the sum of the lengths of the highway between CS
and ST.

SAS21M09G0505
5 A number Y is greater than a number X and another number Z < 0.
Which of the following relations can be true for a unique value of Z?

A. X×Z=Y×Z
B. X÷Z=Y÷Z
C. X–Z=Y
D. X+Z=Y

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 15

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 5

SAS21M09G0506
6 The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?

Raghvan claims that the magnitude of the angle ABC is greater than the magnitude of the area of the
right triangle PQR.

SAS21M09G0507
7 Is his claim correct? Why?

SAS21M09G0508
8 Two lines intersect at a point P.
Which of the following is true for the distance between the two lines as they travel beyond point P?

A. The distance becomes constant.
B. The distance increases continuously.
C. The distance decreases continuously.
D. The distance increases and decreases depending upon the intersection point.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 16

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 5

SAS21M09G0509
9 Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true?

A. The measure of an angle depends upon its orientation.
B. The measure of an angle depends upon the instrument used to measure it.
C. The measure of an angle depends on the length of its angle arms.
D. The measure of an angle depends upon the rotation of one arm on another.

SAS21M09G0510
10 TAB is a straight line. C is the mid-point of AB. D is the mid-point of AC.
Which of the following shows the relation between the line segments?

1
A. AD= 2 AB
1
B. AD= CB
2
C. AD=2AC
D. AD=2DC

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 17

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 6
Lines and Angles

The game of billiards is played with balls placed on a rectangular table. One ball is struck with the
end of a stick, called a cue. The ball bounces into other balls and re lects off the sides of the table. In
a real game, the ball may spin, but for mathematical purposes, it is considered that the ball travels
in a straight line with the same re lection and incidence angles.

On a billiard table ABCD, the ball placed at O is struck with the cue.

SAS21M09G0601
1 What is the value of ∠a + ∠d?

SAS21M09G0602
2 Why is the line OM parallel to PN?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 18

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 6

A parking lot for a city mall is shown below. The painted lines that separate the parking spaces are
parallel.

SAS21M09G0603
3 Parking space number 378 is inclined at 60° to the horizon line. At what angle is parking space 380
inclined to the horizontal line? Why?

Two equilateral triangles on a straight line are shown below.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 19

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 6

SAS21M09G0604
4 What is the measure of ‘x’?

A. 30
B. 40
C. 60
D. 65

The igure below shows an equilateral triangle bounded by two straight lines.

SAS21M09G0605
5 What is the sum of the four marked angles?

A. 180°
B. 240°
C. 270°
D. 360°

The igure below consists of a square and an equilateral triangle connected together with a
common side.

SAS21M09G0606
6 What is the measure of ‘x’?

A. 15
B. 30
C. 45
D. 60

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 20

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 6

In the igure below, BC = AC.

SAS21M09G0607
7 What is the measure of ∠BAD?

A. 30°
B. 60°
C. 75°
D. 90°

The igure below consists of a square and an equilateral triangle connected together with a
common side.

In the design, DF and IG are two iron rods perpendicular to BC. The measure of ∠BAC = 120°.

SAS21M09G0608
8 Which type of triangle is ABC? Why?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 21

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 6

SAS21M09G0609
9 The central triangle AFG is equilateral. What is the measure of ∠FDA?

A. 30°
B. 60°
C. 90°
D. 120°

SAS21M09G0610
10 The length of IG is half of the length of GC. Write a proof for the statement.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 22

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Assessment Items
Mathematical Literacy
Class 9 – Chapter 7
Triangles

In the given igure, ∆AFB ≅ ∆AFG, ∆ADE ≅ AGE and ∠EAF = 45°.

SAS21M10S0701
1 What is the measure of ∠DAB?

A. 60°
B. 90°
C. 120°
D. 135°

SAS21M10S0702
2 What is the length of AD?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 23

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 7

SAS21M10S0703
3 What is the area of the shaded region?

A. 12.5 cm²
B. 15 cm²
C. 20 cm²
D. 36 cm²

In the given igure, the isosceles triangle ABC ≅ EAD. The point E is equidistant from both A and B.

SAS21M09S0704
4 What is the value of x?

A. 40°
B. 60°
C. 70°
D. 80°

SAS21M09S0705
5 What is the value of y?

SAS21M09S0706
6 What is the value of ∠BDC?

A. 30°
B. 40°
C. 50°
D. 70°
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 24

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 7

The picture below shows a staircase outside a house. Each step of the staircase is congruent and
there are 25 steps in the staircase from the loor to the platform and 25 steps from the platform to
the roof.

SAS21M09S0707
7 What is the length of the staircase railing?

In a toy game, a robot starts from Home, picks an object from the Shop, delivers it to the Client and
goes back Home.

SAS21M09S0708
8 Which is the longest segment of the path travelled by the robot? Write the correct words.

______________________ to _______________________
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 25

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 7

SAS21M09S0709
9 Rita says, ‘For two triangles to be congruent, any three parameters of the six (3 sides and 3 angles)
should be equal.’
Give examples in favour of and against her statement.

SAS21M09S0710
10 ‘Two triangles with a pair of equal angles are congruent.’
Why is it necessary to have the side between the two angles be of the same length for both the
triangles?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 26

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Assessment Items
Mathematical Literacy
Class 9 – Chapter 8
Quadrilaterals

Atul likes to observe the stars with his telescope. He likes to track the movements of stars in the sky.
He took a picture of the night sky one day. On that day, Mars was equidistant from Saturn and Jupiter.

He draws a circle such that the dots showing the planets Mars (M), Jupiter (J), Saturn (S) and a star
Altair (A) lies on the boundary of a circle and ∠SMJ = 150°.

SAS21M09S0801
1 What is the measure of ∠SAJ?

A. 30°
B. 45°
C. 150°
D. 210°
SAS21M09S0802
2 Atul claims that the quadrilateral MJAS is a kite.
What additional information is required to con irm his claim?

A. Distance between Altair and Saturn is equal to the distance between Mars and Jupiter.
B. Distance between Altair and Jupiter is equal to the distance between Mars and Saturn.
C. Distance between Altair and Saturn is equal to the distance between Altair and Mars.
D. Distance between Altair and Saturn is equal to the distance between Altair and Jupiter.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 27

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 8

SAS21M09S0803
3 The adjacent sides of quadrilateral A are equal to corresponding sides of Quadrilateral B. All angles of
Quadrilateral A measure 90°. The angles of Quadrilateral B are 120°, 60°, 120° and 60° respectively.
Which quadrilateral has a greater area? Give reasons.

SAS21M09S0804
4 Sanya has a triangular piece of land. She wants to divide it into four equal areas. Suggest a way to do so.

SAS21M09S0805
5 Does joining four distinct points always produce a quadrilateral? Justify your answer.

The igure below shows the side view of a shopping trolley. The metal plate is ixed on the side by the
store keeper for advertisement.

SAS21M09S0806
6 Three angles of the basket are obtuse. Which type of angle is the fourth?

A. Acute
B. Obtuse
C. Right
D. Re lex
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 28

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 8

SAS21M09S0807
7 What is the shape of the metal plate?

A. Square
B. ectangle
C. Rhombus
D. Parallelogram

In the quadrilateral ABCD given below, ∠DAC = 90° and AB = AC = AD = DE = EB.

SAS21M09S0808
8 What is the value of ∠EAC?

A. 15°
B. 30°
C. 45°
D. 90°

SAS21M09S0809
9 Which type of quadrilateral is ABCE?

A. Rhombus
b. Kite
c. Trapezium
d. Parallelogram

SAS21M09S0810
10 What is the value of ∠ABE?

A. 20°
B. 30°
C. 45°
D. 60°

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 29

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Assessment Items
Mathematical Literacy
Class 9 – Chapter 9
Areas of Parallelograms and Triangles

In the igure given below, ABCD is a square of area 144 cm² andBECD is a parallelogram.

SAS21M09S0901
1 What is the length of CE?

A. 12 cm
B. 14.4 cm
C. 12√2 cm
D. 24 cm

SAS21M09S0902
2 What is the measure of ∠DCE?

A. 45°
B. 90°
C. 120°
D. 135°

SAS21M09S0903
3 Shashi claims that all parallelograms between two parallel lines and the same base are congruent.
Justify.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 30

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 9

SAS21M09S0904
4 The area of a triangle and a parallelogram are equal.
Which of the following statements is true for them?

A. The base length and the altitude of the triangle and the parallelogram are the same.
B. Both the triangle and the parallelogram lie between the same set of parallel lines and their
bases are the same.
C. The base length and the corresponding altitude of the triangle are two times the base length
and the corresponding altitude of the parallelogram.
D. Either the corresponding base length or the corresponding altitude of the triangle is the double
of the parallelogram’s base length or altitude.

SAS21M09S0905
5 Preeti wants to divide a scalene triangle into two triangles having equal areas. Suggest one way to do
so.

In the given igure, ABCD is a square with perimeter 8 cm. E is the mid-point of AD and AE = CF.

SAS21M09S0906
6 What is the measure of ∠EBF?

A. 60°
B. 75°
C. 90°
D. 135°

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 31

Curriculum Aligned Assessment Items Mathematical Literacy
Class 9 – Chapter 9

SAS21M09S0907
7 What is the area of ∆BCF?

A. 1 cm²
B. 2 cm²
C. 4 cm²
D. 8 cm²

In the igure given below, each small square represents an area of 1 cm².

SAS21M09S0908
8 What is the ratio between the area of the rectangle and the shaded region?

A. 1:1
B. 2:1
C. 3:1
D. 3:2

SAS21M09S0909
9 What is the area (in cm²) of the trapezium in the given igure?

A. 6 cm²
B. 8 cm²
C. 9 cm²
D. 12 cm²

The two parallelograms on a unit square grid are shown below.

SAS21M09S0910
10 Compare the areas of the two parallelograms.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 32

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 10
Circles

Given below is the map giving the position of four housing societies in a township connected by a
circular road A.

Society 2 and 3 are connected by straight road B, society 4 and 2 are connected by straight road C
and society 4 and 3 are connected by road D. Point P denotes the position of a park. The park is
equidistant to all four societies.
Rubina claims that it is not possible to construct another circular road connecting all four societies.

SAS21M09S1001
1 Which of the following options justi ies Rubina’s claim?

A. Equal chords of congruent circles subtend equal angles at the centre.
B. The perpendicular from the centre of a circle to a chord bisects the chord.
C. There is a unique circle passing through three non-collinear points.
D. Points equidistant from a given point will lie on a circle.

SAS21M09S1002
2 What is the position of the park P with respect to road A?

A. Chord
B. Centre
C. Sector
D. Segment

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 33

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 10

SAS21M09S1003
3 The length of Road B is equal to the length of Road D.
Which of the following options can be true for the roads in the township?

A. Road B bisects Road D.
B. Road B and Road make an acute angle.
C. Road B, Road C and Road D are of equal length.
D. Road B and Road D subtend equal angles at society 1.

SAS21M09S1004

4 Alex says, “The angle made by road B on road D is a right angle.”
Jai and Angad give different justi ications to support Alex’s claim.
Jai says, “Angles in the same segment of a circle are equal.”
Angad says, “The angle in a semicircle is a right angle.”
Who has given the correct justi ication?

Two new roads, Road E and Road F were constructed between society 4 and 1 and society 1 and 2.

SAS21M09S1005
5 What would be the measure of the sum of angles formed by the straight roads at society 1 and society
3?

A. 60°
B. 90°
C. 180°
D. 360°
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 34

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 10

SAS21M09S1006
6 Krish says, “The distance to go from society 4 to society 2 using Road D will be longer that the distance
using Road E”
Is Krish correct? Justify your answer with examples.

SAS21M09S1007
7 Road G, perpendicular to Road F was constructed to connect the park and Road F.
Which of the following is true for Road G and Road F?

A. Road G and road F are of same length.
B. Road F divides Road G into two equal parts.
C. Road G divides Road F into two equal parts.
D. The length of road G is one-fourth of the length of Road F.
SAS21M09S1008
8 Priya said, “Minor arc corresponding to Road B is congruent to minor arc corresponding to Road D.”
Do you agree with Priya? Give reason to support your answer.

_________________________________________________________________________________________________________________

Given below is the igure of a circle with centre O.
The measure of ∠BOC = 88°.

SAS21M09S1009
9 What is the measure of ∠BAC?

A. 44°
B. 60°
C. 88°
D. 176°
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 35

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 10

SAS21M09S1010
10 Priya claims, “The length of OB is equal to the length of OC.”
Siya and Aditi provide different justi ications for Priya’s claim.
Siya says, “OB and OC are radii of the same circle.”
Aditi says, “OC is the base of ∠BOC.”

Who has given the correct justi ication for Priya’s claim?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 36

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 11
Constructions

Pradeep bisects a given angle using a compass
and a ruler.
Here are some images of Pradeep’s work.

Step 1: With the vertex of the angle as centre and
any radius he draws two arcs intersecting the arms
of the angle.

Step 2: Without changing the radius from the
intersection of each arc and the leg of the angle,
mark arcs off in the angle’s interior so that they
intersect.

Step 3: Draw a line from point O to the intersection
of the arcs.

This is the output of Pradeep’s work after step 2

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 37

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 11

SAS21M09S1101
1 Which quadrilateral will be generated when the points Q, X, Y and Z are joined?

A. Square
B. Rectangle
C. Rhombus
D. Trapezium

SAS21M09S1102
2 Pradeep measures angle YQZ as 30°. He joined point Y with point P.
What is the measure of angle QYZ?

A. 30°
B. 60°
C. 120°
D. 150°

Here is a igure in which AB is a perpendicular bisector of line segment ST.
To construct the perpendicular bisector AB, Aditi marks A and B equidistant from S and T using a
compass.

SAS21M09S1103
3 Which of the following is not true for the igure shown above?

A. AT is equal to SB.
B. ∠SAO is greater than ∠TBO.
C. ∠AOS and ∠AOT forms a linear pair.
D. O is the mid-point of the line segment ST.
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 38

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 11

Anu Radha says, ‘You can get a perpendicular bisector of ST when the radii of arcs on one side of ST
is different from the radii of arcs on the other side of ST.
She draws this diagram to illustrate her point.

SAS21M09S1104
4 Zoya measures angle TLB =25° and angle LSB = 90°.
What is the measure of angle BTO?

A. 25°
B. 45°
C. 50°
D. 65°

Given below is the output of the construction of a 60 degree angle using a compass and a straight
edge.
Here, triangle ABJ is an equilateral triangle.

SAS21M09S1105
5 What is the sum of ∠IAB and ∠KBA?

A. 120°
B. 180°
C. 240°
D. 360°

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 39

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 11

SAS21M09S1106
6 Pradeep draws a line parallel to AB which joins point I and point K.
What kind of triangle is ABK?

A. Scalene
B. Isosceles
C. Equilateral
D. Right-angled
SAS21M09S1107
7 Jyoti wants to construct a triangle in which the measure of two angles are 45° and 60°, respectively and
the sum of all three sides is 15 cm.
He drew a line segment EF of length 15 cm.
Which of the following would be Jyoti’s next step to construct the triangle at point E?

A. Construct an angle of 15°.
B. Construct an angle of 30°.
C. Construct an angle of 60°.
D. Construct an angle of 120°.
SAS21M09S1108
8 A triangle whose base angles measure 70° and perimeter is 28 cm is drawn.
Which of the following options shows the side lengths of the triangle formed?

A. 7 cm, 14 cm and 7 cm
B. 8 cm, 12 cm and 8 cm
C. 9 cm, 10 cm and 9 cm
D. 10 cm, 8 cm and 10 cm
SAS21M09S1109
9 Paritosh wants to construct a triangle RST, in which angle S = 45°, ST= 10 cm long and RS-RT = 2 cm. He
has completed construction of some steps.
Step 1: Draw the base ST of the triangle
Step 2: At point S, make an angle RST of measure 45°.
What should be Paritosh’s next step?

A. Mark a point on RS at a distance of 2 cm from S.
B. Mark a point on RS at a distance of 8 cm from S.
C. Mark a point on RS at a distance of 2 cm from T.
D. Mark a point on RS at a distance of 8 cm from T.
SAS21M09S1110
10 Construct a triangle ABC in which BC = 7.5cm, ∠B = 46° and AB + AC = 13 cm.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 40

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 12
Heron’s Formula

Glass buildings can be strengthened using iron frames. A glass structure and its iron frame are
shown below.

The frame consists of equal triangles. The dimensions of a triangle are shown below.

SAS21M09S1201
1 How much area is enclosed by one triangle?

SAS21M09S1202
2 What is the area of part 1 of the frame?

A. 84 m²
B. 1680 m²
C. 3360 m²
D. 3696 m²

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 41

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 12

SAS21M09S1203
3 Is the area of part 1 equal to the area of part 2? Why?

SAS21M09S1204
4 Maintenance of the building’s exterior is done by a company. The company charges Rs 750 per square
meter per month.
Which of the following calculations represents the monthly maintenance charges?

A. 24 × 12
B. 750 × 24
C. 3024 × 750
D. 6720 × 750

The design on a tile is made of isosceles triangles.
The side lengths of the triangles are 6 cm, 6 cm and 8 cm.

SAS21M09S1205
5 How much area of the tile is black?

A. 24 cm²
B. 9√7 cm²
C. 90 cm²
D. 112√5 cm²

SAS21M09S1206
6 A tile is made by joining the vertices of four equilateral triangles. The side length of the triangles is 15
cm. What is the area of the tile?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 42

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 12

A zoo is in the shape of an isosceles trapezium.
It is divided into three zones – Zone 1, Zone 2 and Zone 3.
Animals are kept without cages in Zone 1. Zone 2 is for visitors and Zone 3 is reserved for park
authorities.

To avoid the entry of animals in zones 2 and 3, a 1.8 km long wired fencing is installed.
SAS21M09S1207
7 Which of the following calculations shows the area for animals?

A. √1.35×0.65×1.15
B. 2.15×0.35×0.65×1.15
C. √3.15×1.35×1.65×1.15
D. √4.30×1.35×0.65×1.15
SAS21M09S1208
8 “The area reserved for animals is twice the area reserved for the zoo authorities.” Do you have enough
information to support this statement? Explain your answer.

The outer boundary of Zone 1 is made of solid structures in the shape of isosceles triangles of the
same size and barbed wires.

The wall consists of 15 such solid structures.
SAS21M09S1209
9 Which of the following calculations shows the total area (in square meters) of the solid structures?

A. √50× 50 ×30
B. √130×50×50×30
C. 15√130×50×50×30
D. 15√260×180×180×16
SAS21M09S1210
10 What is the area of a triangle with side lengths 20 cm, 20 cm and 8 cm?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 43

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 13
Surface Area and Volume

Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The
top of the hut is a cone with radius 4 m and height 1 m. It is made of economical material. The loor
of the tent is covered with rugs.
The total height of the tent is 4.5 m. The cuboidal part of the tent is 6 m long and 5 m wide.

SAS21M09S1301
1 What is the outer surface area (in m²) of the hut?

A. 77
B. 77+4π√17
C. 137+4π√17
D. 137+4π(4+√17)

SAS21M09S1302
2 The length and width of a rug used for the loor are 2.6 m and 2 m respectively.
What is the minimum number of rugs required to cover the loor of the tent house?

This is the picture of a gas balloon illed with helium gas.

This balloon has 18 faces that are square in shape and 8 equilateral faces that are triangular.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 44

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 13

SAS21M09S1303
3 Which of the following is the net of the balloon?

A. C.

B. D.

SAS21M09S1304
4 The side length of the square is 20 cm. What is the total surface area of the balloon?

Raghav bought this planter.

The radius of the rim is 14 cm. The curved surface area of the planter is 1848 cm².

SAS21M09S1305
5 What is the height of the planter?

SAS21M09S1306
6 What is the volume of the planter?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 45

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 13

A company manufactures wooden boxes. Given below is the picture of an open wooden box.

The height of the box is 25 cm.

SAS21M09S1307
7 What is the surface area (in cm²) of the box?

A. 3500
B. 4700
C. 5900
D. 30000
SAS21M09S1308
8 A shopkeeper store cubes in it.
The side length of one cube is 9 cm.
What would be the maximum number of cubes the shopkeeper can store in a box? (All cubes should be
inside the box.)

SAS21M09S1309
9 Rajan packs a football into a cubical cardboard box. The radius of the football is 11 cm. Rajan keeps a
margin of 1 cm from all the sides of the box while packing.
What is the side length of the cardboard box?

A. 11 cm
B. 20 cm
C. 22 cm
D. 24 cm

This is the picture of an ice-cream cone.

The radius of the cone is 4 cm and the height is 15 cm.
An ice-cream seller keeps 1/4 of it empty.
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 46

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 13

SAS21M09S1310
10 What is the volume (in cm³) of the empty part of the cone?

A. 12π
B. 15π
C. 19π
D. 20π

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 47

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 14
Statistics

Five friends Anchal, Amisha, Mahi, Vaishu and Sahar are living in a hostel.
At the end of every month, they calculate the expenses on food and shopping.
The table given below shows their monthly expenses for the month of November.
Name Anchal Amisha Mahi Vishu Sahar
Expenditure (in Rs) 3000 5000 6000 4500 7000

SAS21M09D1401
1 Which graphical representation method would best represent the data given?

SAS21M09D1402
2 What is the average expense of the friends for the month of November?

SAS21M09D1403
3 Anchal says, “The difference between the median expenditures for October and November amounts to
10% of the November expense, and we have been able to reduce our median expense for November.”
What was their median expense for the month of October?

A. 12π
B. 15π
C. 19π
D. 20π
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 48

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 14

A charity surveys the people of a village for their haemoglobin counts. 25 out of 100 adult females
in the village were tested. The result is given in this table.
Haemoglobin (mg/dl) counts No. of females
5 3
6 3
7 2
8 5
9 1
10 1
11 3
12 4
13 2
14 1

SAS21M09D1404
4 A haemoglobin counts below 12 is considered de icient.
What proportion of females in the survey can be considered de icient?

A. 3
25

B. 4
25
C. 18
25
D. 22
25
SAS21M09D1405
5 What is the median haemoglobin counts (mg/dl) of the females in the survey?

A. 8
B. 9
C. 9.5
D. 12.5
SAS21M09D1406
6 Divya said that 8 and 12 are the most observed haemoglobin counts (mg/dl) among 25 females.
Krishna said that 8 and 12 are the most observed haemoglobin counts (mg/dl) among 100 females in
the village.
Who is correct? Explain your answer.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 49

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 14

In a school camp, 40 students were divided into two groups to play a game.
The table given below shows the scores of team A and team B.
Time(s) in minutes Cumulative Score of Team A Cumulative Score of Team A
0-5 14 20
5-10 35 27
10-15 30 31
15-20 35 31
20-25 44 37
25-30 52 50

SAS21M09D1407
7 How many score points did team A get between 10-15 minutes?

A. 6
B. 24
C. 30
D. 68
SAS21M09D1408
8 Which team scored more points during last 5 minutes? Justify your answer.

SAS21M09D1409
9 What is the mean number of score points obtained by team A in a 5-minute interval rounded to the
nearest whole number?

Draws a graphical representation of the points scored by team B.
His graphical representation is given below.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 50

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 14

SAS21M09D1410
10 Suman says, “Arun’s graphical representation is not appropriate.”
Do you agree with Suman? Mention YES or NO. Give reason to justify your choice.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 51

क ीय मा यिमक िश ा बोड
CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 9 – Chapter 15
Probability

The table given below shows the number of students in Sun Valley School.
Class Number of girls Number of boys
VI 18 22
VII 17 15
VIII 20 19
IX 15 19
X 17 21

SAS21M09D1501
1 Every year, one student is randomly chosen from Class X as the head student. The head student is
responsible for representing the school.
What is the probability of a girl being the head student?
17
A. 21
17
B.
38
17
C.
87
D. 17
183

SAS21M09D1502
2 All students of Class VI took part in a drawing competition. Aditi is a girl studying in Class VI.
The teacher says, “The winner of this year’s drawing competition is a boy from Class VI.”
What is Aditi’s probability of having won the competition?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 52

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 15

The school provides facility for after-school activities.
The table given below shows the number of students who take part in after-school activities.
Activity Number of girls participating Number of boys participating
Sports (any) 16 30
Classical dance 13 5
Aerobics 15 17
Musical Instruments 17 20
Arts and crafts 20 10
SAS21M09D1503

3 Of all the students participating in classical dance, one is randomly chosen for an annual day
performance. What is the probability of a boy being chosen?
1
A.
2
1
B.
5

C. 5
18
D. 5
82
SAS21M09D1504
4 Of all the students participating in classical dance, one is randomly chosen for an annual day
performance. What is the probability of a boy being chosen?
2
A. 16

2
B. 29

3
C.
10

D. 3
7
SAS21M09D1505
5 Salma is a girl and she has chosen to learn a musical instrument. The school choir wants to randomly
select a girl to play for them. What is the probability of Salma joining the choir?
1
A.
2
1
B.
17
1
C.
37
1
D.
63

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 53

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 15

SAS21M09D1506

6 Of all the students who have not participated in any after-school activities, one student is randomly
chosen to coordinate the annual day function. What is the probability of a boy being chosen?
1
A. 14
7
B. 10
14
C.
163

D. 14
183

Shyam made a die using a cuboid-shaped eraser.
He painted one face of the die with the number 2, two faces with the number 1 and three faces with
the number 4.
Shyam throws the die.

SAS21M09D1507

7 What is the probability of getting a 1?
1
A. 2
1
B. 3
1
C. 4
1
D. 6

SAS21M09D1508
8 What is the probability of getting a face showing an even number?
1
A.
2
1
B. 3
1
C. 6
2
D. 3

SAS21M09D1509
9 Find the probability of getting a face of the die showing number less than 5?

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 54

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 – Chapter 15

SAS21M09D1510
10 Shyam made another die identical to the one he made earlier. He throws both the dice together and
adds the number on the face of the two dice. Show the sample space of the experiment.

Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 55

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 − Chapter 1

Item Number Question 1
Question Code SAS21M09Q0101
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Interpret & Evaluate
Item Type Open Constructed Response
Full Credit (Full Score) Names both Khushi and Akash and provides a valid explanation with
examples

Ÿ Khushi is correct as numbers including 1/2, 2/4, 3/6, 4/8 and 0.5 can
be represented by the same point on the number line. Akash is
correct as each point on the number line represents a unique real
number.
Partial Credit (Partial Score) Names either Khushi or Akash, and supporting examples/arguments are
provided
No Credit (No Score) Any other response or missing response
Item Number Question 2
Question Code SAS21M09Q0102
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Interpret & Evaluate
Item Type Multiple Choice Question
Full Credit (Full Score) B. Every irrational number can be represented with the help of decimals.
No Credit (No Score) Any other response or missing response
Item Number Question 3
Question Code SAS21M09Q0103
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Open Constructed Response
Full Credit (Full Score) Uses the de inition of irrational numbers in the explanation and
identi ies the limitation of their placement on a measuring scale

Ÿ Irrational numbers are non-terminating with more number of
decimals so precision on measuring scale can be more. But they are
non-terminating, so ixing their exact location on a measuring scale is
not possible.
No Credit (No Score) Any other response or missing response
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 56

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 − Chapter 1

Item Number Question 4
Question Code SAS21M09Q0104
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Closed Constructed Response
Full Credit (Full Score) Writes √5 with or without the word ‘units’
Ÿ √5 units
Ÿ √5
No Credit (No Score) Any other response or missing response

Item Number Question 5
Question Code SAS21M09Q0105
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Multiple Choice Question
Full Credit (Full Score) C. -4+√15
No Credit (No Score) Any other response or missing response

Item Number Question 6
Question Code SAS21M09Q0106
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Interpret & Evaluate
Item Type Multiple Choice Question
Full Credit (Full Score) D. S
No Credit (No Score) Any other response or missing response

Item Number Question 7
Question Code SAS21M09Q0107
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Multiple Choice Question
Full Credit (Full Score) A. U and V
No Credit (No Score) Any other response or missing response
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 57

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 − Chapter 1

Item Number Question 8
Question Code SAS21M09Q0108
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Formulate
Item Type Closed Constructed Response
Full Credit (Full Score) Writes length and breadth, which are greater than zero and less than 70,
with or without the word ‘Chapter(s)’
Ÿ Length 21 and breadth 7
Ÿ 21 units and 7 units
Ÿ 69 units and 1 Chapter
No Credit (No Score) Any other response or missing response

Item Number Question 9
Question Code SAS21M09Q0109
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Multiple Choice Question
Full Credit (Full Score) D. 580 units
No Credit (No Score) Any other response or missing response

Item Number Question 10
Question Code SAS21M09Q0110
Grade & Chapter Name Grade 9 | Number System
Concept | Sub-concept Numbers | Irrational Numbers
Competency Employ
Item Type Open Constructed Response
Full Credit (Full Score) Due consideration is given to factors including display dimensions and
orientation (portrait/landscape) 2 x y z with or without the word ‘units’
Ÿ The manufacturer needs to know the space available for the screen
installation along with the screen size.
Ÿ Length and breadth, along with orientation, is to be considered.
Partial Credit (Partial Score) Only one factor associated with display dimensions or orientation
(portrait/ landscape) is considered.
Ÿ Length and breadth should be known.

No Credit (No Score) Any other response or missing response
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 58

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 − Chapter 2

Item Number Question 1
Question Code SAS21M09C0201
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Geometrical
Representation)
Competency Formulate
Item Type Closed Constructed Response
Full Credit (Full Score) Writes an equation relating length, breadth, height and volume.
Ÿ x³ + 2.15x² + 0.3x = 652
Ÿ x³ + 2.15x² + 0.3x - 652 = 0
Ÿ x(x + 2)(x + 0.15) = 652
Ÿ x(x + 2)(x + 0.15) - 652 = 0

No Credit (No Score) Any other response or missing response

Item Number Question 2
Question Code SAS21M09C0202
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Factorisation of
Polynomials)
Competency Interpret & Evaluate
Item Type Multiple Choice Question
Full Credit (Full Score) C. The volume of Container 3 is 2608 m³.
No Credit (No Score) Any other response or missing response

Item Number Question 3
Question Code SAS21M09C0203
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Factorisation of
Polynomials)
Competency Employ
Item Type Closed Constructed Response
Full Credit (Full Score) Write 8.15 with or without the Chapter
Ÿ 8.15 m
Ÿ 8.15
No Credit (No Score) Any other response or missing response
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 59

Curriculum Aligned Competency Based Test Items Mathematics
Class 9 − Chapter 2

Item Number Question 4
Question Code SAS21M09C0204
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Geometrical
Representation)
Competency Formulate
Item Type Closed Constructed Response
Full Credit (Full Score) Mentions Choice 1 OR 1
No Credit (No Score) Any other response or missing response

Item Number Question 5
Question Code SAS21M09C0205
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Factorisation of
Polynomials)
Competency Employ
Item Type Closed Constructed Response
Full Credit (Full Score) Writes 2 x y z with or without the word ‘units’
Ÿ 2xyz
Ÿ 2 x y z units

No Credit (No Score) Any other response or missing response

Item Number Question 6
Question Code SAS21M09C0206
Grade & Chapter Name Grade 9 | Polynomials
Concept | Sub-concept Algebra | Algebraic Expressions and Identities (Factorisation of
Polynomials)
Competency Interpret & Evaluate
Item Type Closed Constructed Response
Full Credit (Full Score) Writes 3x – 2 with or without the word ‘units’
Ÿ 3x – 2 units
Ÿ 3x – 2

No Credit (No Score) Any other response or missing response
Copyright (c) 2021 CBSE and Sri Aurobindo Society All Rights Reserved Page 60