Competency Based Questions Class 8 Maths

Curriculum Aligned
Competency Based Test Items
Mathematics
Class - 8
Central Board of Secondary Education

Table of Contents

Test Item
1 Rational Numbers ...............................................................................................................03
2 Linear Equations in One Variable .......................................................................................06
3 Understanding Quadrilaterals .............................................................................................10
4 Practical Geometry ..............................................................................................................14
5 Data Handling .....................................................................................................................17
6 Squares and Square Roots ..................................................................................................21
7 Cubes and Cube Roots ........................................................................................................24
8 Comparing Quantities ........................................................................................................27
9 Algebraic Expressions and Identities ..................................................................................30
10 Visualising Solid Shapes .....................................................................................................34
11 Mensuration ........................................................................................................................37
12 Exponents and Powers ........................................................................................................41
13 Direct and Inverse Proportions ...........................................................................................44
14 Factorisation ........................................................................................................................47
15 Introduction to Graphs ........................................................................................................50
16 Playing with Numbers ........................................................................................................54

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 1
Rational Numbers

An audit is an of icial checking of the inancial records of a company. It is done by an authorised
person who is not an employee of the company. The person who does the audit is called an auditor.
An auditor checks the expenses and income made by the company every year.
Mohit audited a company with 50 employees. The company records show its annual turnover
(annual income) is ₹100 million, and taxes have been paid according to government norms.

SAS21M08Q0101
1 Mohit observed that one- ifth of the employees have an annual salary of less than ₹ 400,000. How many
employees have an annual salary of less than ₹ 400,000?

SAS21M08Q0102
2 This year, the company spent 20% of their income on of ice maintenance, 40% on paying salaries to
their employees and 10% on miscellaneous things (including taxes). The rest of the amount is the pro it
gained by the company. How much pro it did the company earn this year?

SAS21M08Q0103
3 According to government norms, a company has to pay a tax of 6% of the total annual income.
Mohit said, ‘The tax amount paid by the company this year is one-third the amount paid last year.’
What was the tax amount paid last year?

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Class 8 – Chapter 1

Robin writes the properties of rational numbers as –
Property 1: For any two rational number x and y, x + y = y + x
Property 2: For any two rational number x and y, x - y = y - x
Property 3: For any two rational number x and y, x/y = y/x
Property 4: For any two rational number x and y, x × y = y × x

SAS21M09Q0104
4 Which properties written by Robin are incorrect? Why are they incorrect?

SAS21M08Q0105
5 Which of the following set of rational numbers lies between – 2 and 3?

-5 , 3 , 2 , 13
A. and
2 7 3 5
-4 , 3 , 2 , 20
B. and
2 7 3 5
-6 , 2 , 3 , 5
C. and
2 3 4 2
-1 , -6 , 8 , 10
D. and
3 5 7 9
SAS21M09Q0106
6 Is the statement ‘All integers are rational numbers but all rational numbers are not integers’ correct?
Give examples to support your answer.

SAS21M09Q0107
7 There is a two-digit odd number which is not a prime number. When the digits of the number are
reversed and added to the number itself, the resultant is a perfect square. What is the number?

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Class 8 – Chapter 1

SAS21M08Q0108
8 An integer is added to its multiplicative inverse. Which of the following statement is valid for the
resultant number?

A. It is an integer
B. It is a fraction
C. It is always one
D. It is a rational
SAS21M08Q0109
1
9 Which letter represents the approximate position of P + on the number line?
8

A. Q
B. R
C. S
D. T

SAS21M09Q0110
10 Simplify:
-8
9
x ( (
3 7
+
7 4

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 2
Linear Equations in One Variable

An event management company organises events for its clients. The company takes care of the
venue, decoration, and catering. The information used for the calculation of the cost for an event is
given in the tables below.

Venue Capacity (number of Size (in square Rate (in
people) metres) dollars )
Venue 1 (Closed space) 250 150 650
Venue 2 (Closed space) 250 - 500 200 1000
Venue 3 (Open courtyard) 500 - 2000 7500 3000

Decoration Charges (per square meter)
Basic 0.5 dollars
Standard 1 dollars
Premium 1.5 dollars

Catering service charges are 30 dollars per head. For organising an event for 250 guests in the
closed space with basic decoration and catering, the cost calculation equation is 725+30x.

SAS21M08C0201
1 Write an equation for the cost calculation of organising an event in Venue 2 with premium decoration
and catering.

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Class 8 – Chapter 2

SAS21M08C0202
2 The event management company makes a pro it of 40% on the venue, 50% on catering and 10% on
decoration. How much is t he pro it in organising an event for 200 guests at Venue 1 with basic
decoration?

SAS21M08C0203
3 What is the cost (in dollars) of organising an event for 300 people, in the open courtyard with standard
decoration and catering?

A. 1625
B. 10200
C. 15000
D. 19500

SAS21M08C0204
4 In an event with more than 1000 guests and standard decoration, a client gets a 20% deduction in
catering charges. He pays an amount of 39300 dollars for the event. How many guests did the client
invite?

In order to attract more customers, the event management company offers chauffeur driven cars.
They provide two services Elite and Premium. Below are the prices offered for the services.

Elite services Premium services
Fixed charges – 33 zeds Fixed charges – 22 zeds
Additional – 3 zeds per kilometre Additional – 4 zeds per kilometre

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Class 8 – Chapter 2

SAS21M08C0205
5 Which pair of linear equation shows the cost of Elite services (P) and Premium services (Q) for x
kilometres?

A. P = 33 dollars ; Q = 22 dollars
B. P = 33x dollars ; Q = 22x dollars
C. P = 33x + 3 dollars ; Q = 22x + 4 dollars
D. P = 33 + 3x dollars ; Q = 22 + 4x dollars

SAS21M08C0206
6 A client wants to avail car services for 24 kilometres (round trip). Which service would be economical?
Justify your choice.

Mohit is an entrepreneur. He started a start-up with an investment of 14,600 dollars. The monthly
operating cost of his start-up is given in the table.

Operations Expenses (in dollars)
Rent 1000
Electricity 100
Overheads (other expenses) 400
Average salary per person 500

He hired four people to run the operations. He was able to earn only operating cost in the irst two
months. From the third month onward, he earned an average of 1200 dollars per month above the
operating cost.

SAS21M08C0207
7 After how many months, did Mohit recover his investment?

SAS21M08C0208
8 Mohit hired some more employees once he recovered his investment. Write an algebraic expression to
show his operating cost after hiring.

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Class 8 – Chapter 2

SAS21M08C0209
9 A linear equation can be written as ax + b = 0, where a and b are constants.
Write the equation 3(x – 1) = 5(2x + 1) in the form of ax + b = 0.

Sasha solves a linear equation.
Her work is shown below.

x
2x - 3 = -5
2
2(2x - 3) = x - 5….. Step 1
4x - 6 = x - 5….. Step 2
4x - x = 6 - 5….. Step 3
3x = 1…..Step 4
1
x=
3

SAS21M08C0210
10 Is Sasha's solution correct? If not, in which step did Sasha make an error.

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 3
Understanding Quadrilaterals

The loor of a house can be made by laying wooden planks parallel to one another. Anuj uses planks
of length and width 150 cm and 30 cm, respectively, for making the loor of his house.

SAS21M08S0301
1 The loor of his study is rectangular, 4.5 m long and 3 m wide.
What is the minimum number of planks required to cover its loor?

Anuj lays a wooden loor for a kite-shaped room. He places the strips such that they are
perpendicular to the longest side of the room vertically. One strip is shown in the igure.
What is the minimum number of planks required to cover its loor?

SAS21M08S0302
2 What is the approximate length (in m) of the strip in the igure?

A. 10
B. 14.6
C. 15
D. 22.5
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Class 8 – Chapter 3

Another loor in Anuj’s house is in the shape of a trapezium.

SAS21M08S0303

3 The loor is divided into two parts having equal areas to lay planks. In each area, different colour planks
are used. Suggest a way in which it could be done.

SAS21M08S0304
4 Anuj has two pairs of planks of different lengths. Which geometric shape should he make with the four
planks to enclose the maximum area?

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Class 8 – Chapter 3

The igure below shows the layout of a rectangular stage in an auditorium. Two movable lexible
partitions of equal lengths mark the performance area. The shaded portion in the igure below
shows the performance area.

The movable partitions divide the back-wall into three equal parts.

SAS21M08S0305
5 Which of these is the angle between the movable partition and the back-wall?
A. 30°
B. 45°
C. 60°
D. 90°

SAS21M08S0306
6 The celling lights can turn by 90° along the vertical plane.
To cover only the performance area, what is the maximum angle the lights can turn along the horizontal
plane?

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Class 8 – Chapter 3

SAS21M08S0307
7 The performance area is in the shape of trapezium. The performance area can be divided into two
congruent halves.
Which property should the trapezium have to ensure congruent halves?

A. It should have four sides
B. It should have two parallel sides
C. It should have a pair of equal side lengths
D. It should have two parallel sides of unequal lengths
SAS21M08S0308
8 The dotted line representing Curtain 1 joins the mid-points of the movable partitions.
What is the length of the curtain line between the movable partitions?

SAS21M08S0309
9 Two laser light beams are lashed from the two ends of the Curtain 1 line. The beams intersect each
other at the mid-point of the Curtain 2 line.
At what angle to Curtain 1 line are the light beams lashed?

A. 0°
B. 45°
C. 60°
D. 120°

Vanita folds a rectangular sheet. The folded sheet is shown below.

SAS21M08S0310

10 What is the length of the sheet?

A. 8 cm
B. √10 cm
C. 10 cm
D. 12 cm
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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 4
Practical Geometry

To construct a quadrilateral using a straight edge and compass, information about the length of the
sides, angles or diagonal lengths are required.

SAS21M08S0401
1 Palak wants to construct a quadrilateral in which lengths of three different sides and one diagonal are
ixed. What other information does she require to construct a unique quadrilateral?

SAS21M08S0402
2 Which of the following quadrilaterals requires minimal measurement information along with
knowledge of quadrilateral properties for its construction?

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

Pradeep and Nadeem have been provided with the information below to construct a parallelogram.
The lengths of the sides of the parallelogram are 10 cm and 14 cm. The angle between the two
adjacent sides is 75°.

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Class 8 – Chapter 4

SAS21M08S0403
3 Are their parallelograms identical? Justify your answer.

SAS21M08S0404
4 Why do Pradeep and Nadeem’s parallelograms look different?

An architect draws a layout plan before actual construction. Layouts contain all of the components
of a inal map as graphical elements.
An architect wants to draw a layout plan for a rectangular stage. The stage is divided into multiple
sections. The performance section is created on the stage with the help of movable lexible
partitions. The performance section is in the shape of an isosceles trapezium.

SAS21M08S0405
5 What measurement information is required to draw the outer boundaries of the stage layout?

SAS21M08S0406
6 The length of the altitude of the performance section is at least 1 metre less than the smaller side of the
stage. Which of the following cannot be the rough sketch of the layout depicting the stage and the
performance area according to the given condition?

A. B.

C. D.

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Curriculum Aligned Competency Based Test Items Mathematics
Class 8 – Chapter 4

SAS21M08S0407
7 Which measurements are required to draw the performance section of the stage in the layout?

A. Lengths of the parallel sides and equal sides
B. Length of the non-parallel side and angle of inclination of parallel and non-parallel sides
C. Lengths of the parallel sides and angle of inclination of parallel and non-parallel sides
D. Lengths of one parallel side and diagonal

SAS21M08S0408
8 Anannya needs to calculate the length of the curtain to be installed between the mid-points of the two
moving partitions. Which of the following shows the process that can give the required length?

A. Calculate the average of the moving partition length
B. Calculate the average of all sides of the trapezium
C. Calculate the average of the lengths of the parallel sides
D. Calculate the average diagonal lengths

SAS21M08S0409
9 Venu wants to construct a quadrilateral ABCD, AB = 4 cm, BC = 5 cm, CD = 6.5 cm and ∠B = 105° and ∠C
= 80°. She made a rough sketch with the given information. Which of the following can be her next step?

A. Construct a triangle with the given lengths for the three sides.
B. Construct a triangle with the given lengths for the three sides and two included angles.
C. Draw one of the given lengths for a side as a base with the two given angles at the endpoints.
D. Draw a baseline of arbitrary length and construct given angles at its endpoints.

Kittu constructs a kite with sides 4 cm and 10 cm.

SAS21M08S0410

10 Which of the following statements is true for the kite?

A. 2 b > 14
B. a >10
C. a1 + b < 4
D. a1 + a2 < 14
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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 5
Data Handling

An online grocery delivery service records month-wise customer purchase details. A monthly
record for the number of customers according to order values is given in the table below.

Amount Number of Customer
500–999 100
1000–1499 250
1500–1999 150
2000–2499 300
2500–2999 225
3000–3499 175
3500–3999 50
More than 4000 25

SAS21M08D0501
1 The online grocery delivery service gives a 10% discount to the customers who order groceries for
more than Rs. 1999. How many customers were eligible for the 10% discount?

A. 725
B. 775
C. 925
D. 1275

SAS21M08D0502
2 A discount coupon worth Rs. 500 is offered on order values more than Rs. 3499 for the next purchase of
minimum value Rs. 1000. How much total discount is offered?

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Class 8 – Chapter 5

An eye camp is organised in a village. The graph below shows the number of people who came for
eye check-ups during the camp.

SAS21M08D0503
3 For which age group the most eye check-ups were done during the camp?

A. 20–30
B. 30–40
C. 40–50
D. 80–90

SAS21M08D0504
4 How many people got their eyes checked in the camp?

SAS21M08D0505
5 Rajneesh said that, ‘Lesser number of people from the 20–40 years age group got their eyes checked
than people from the 50–70 years age group’. Is Rajneesh correct? Justify your answer.

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Class 8 – Chapter 5

Spectacles were recommended for 80% people who got their eyes checked.
The graph given below shows the percentage of people with recommendations for different types of
spectacles.

SAS21M08D0506
6 How many people were recommended dual vision spectacles?

SAS21M08D0507

7 In the camp, a pair of spectacles is available for Rs. 200.
All the people who were recommended near vision spectacles bought it in the camp.
How much money was collected from the sale of near vision spectacles?

SAS21M08D0508
8 Which of the following conclusions can be drawn from the given data?

A. All the people of the village had their eyes checked in the camp.
B. More females had their eyes checked in the camp than males.
C. Most of the people who had their eyes checked in the camp had vision problems.
D. More people in the age group 30–40 had vision problems than in other age groups.

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Curriculum Aligned Competency Based Test Items Mathematics
Class 8 – Chapter 5

In an archery game, the points awarded for hitting a circular region on the board is shown in the
igure below.

No point is given when an arrow misses the board.

SAS21M08D0509
9 What is the probability of getting 6 points in a single shot?

A. 1
5
1
B. 6
3
C. 5
1
D. 2

SAS21M08D0510
10 What is his probability of scoring more than 14 in the next two shots?

A. 2
36
4
B. 36
6
C. 36
9
D. 36

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 6
Squares and Square Roots

For a school performance, an equal number of students are to be arranged in each row and column.
9 students can be arranged as shown in Arrangement 1.

Arrangement 1

SAS21M08N0601
1 How many students can be added in a row/column in Arrangement 1 for 625 students?

SAS21M08N0602
2 The teachers organising the performance think that it will be dif icult to arrange 625 students in one
group. They think of dividing the group into two square arrangements. How many students can be
there in each arrangement?

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Class 8 – Chapter 6

SAS21M08N0603
3 Which of the following symmetric arrangement cannot be used to represent a squared number?

A. B.

C. D.

SAS21M08N0604
4 What is the difference between squares of any two consecutive numbers? Justify your answer.

SAS21M08N0605
5 Which of the following is the odd one?

A. 100+20+20+4
B. 400+40+40+4
C. 900+60+60+4
D. 1400+80+80+4

The rectangle below is made of unit squares.

SAS21M08N0606

6 What are the possible ways of converting it into a square?

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Class 8 – Chapter 6

SAS21M08N0607
7 The sum of Geetha’s age and the square of her brother’s age is 54. What is Geetha’s age?

SAS21M08N0608
8 Which of the following is not a unit digit of a square number?

A. 0
B. 4
C. 6
D. 8

SAS21M08N0609
9 Are squares natural numbers? Explain.

SAS21M08N0610
10 How is the repeated subtraction method in dividing two numbers and inding square roots different?

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 7
Cubes and cube roots

Interlocking cubes come in different colours. Different shapes can be created by joining them.

Sasha is making a large cube using small interlocking cubes.
She starts with a yellow cube and then its one layer of red cubes around it to make the large cube.

SAS21M08N0701
1 What is the number of red cubes used?

A. 9
B. 18
C. 26
D. 27

SAS21M08N0702
2 Sasha considers the red layer as the irst layer on the yellow cube. Which equation can be used to ind
the number of red cubes?

A. 6x²
B. x³
C. x³ + 1
D. 2(x +2)² + 4x² + 4x
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Class 8 – Chapter 7

SAS21M08N0703
3 The red cube is surrounded by a layer of green cubes. The resulting igure is also a cube.
What is the number of green cubes used?

SAS21M08N0704
4 Shubham puts x layers around the yellow cube. How many small cubes did he use on the top-most face
of the large cube so formed?

SAS21M08N0705
5 Akshat has 35 interlocking cubes of the same colour.
He made two large cubes of different side lengths using up all the small cubes.
How many small cubes will be found along each side of the two large cubes made by him? Write in the
space provided below.

_________ cubes and __________ cubes

SAS21M08N0706
6 The cube of a number is divided by the number itself. The result is 36. What is the number?

A. 4
B. 6
C. 36
D. 216

SAS21M08N0707
7 What is the value of ?

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Class 8 – Chapter 7

SAS21M08N0708
8 For which value of x is the equation true?

A. 4
B. −64
C. −216
D. 216

SAS21M08N0709
9 What is the value of ?

A. 2
B. 3
C. 4
D. 9

SAS21M08N0710
10 Solve ?

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 8
Comparing Quantities

A cinema hall has a seating capacity of 350 people. On Monday, 200 seats were booked for a show.

SAS21M08N0801
1 What is the ratio of booked seats to the total number of seats?

SAS21M08N0802
2 What is the percentage of unbooked seats for the show on Monday?

SAS21M08N0803
3 A new movie was released on Friday, 150 seats were booked that day. The booking for the movie
increased to 300 seats on Saturday. What was the percent increase in the number of seats booked on
Saturday?

A. 2%
B. 100%
C. 150%
D. 200%
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Class 8 – Chapter 8

SAS21M08N0804
4 The cost of a ticket for the show is Rs. 250. Ayush got a 20% discount on buying a ticket through online
booking. How many rupees did Ayush pay for the ticket?

A. Rs. 25
B. Rs. 50
C. Rs. 200
D. Rs. 300

SAS21M08N0805
5 Outside the cinema hall, Neeraj has a stall that sells a pack of popcorn for Rs. 200.
The government charges 18% GST on selling of goods or services.
The price at which Neeraj sells popcorn includes GST.

How much GST (in rupees) is charged on selling one pack of popcorn? (Give your answer correct up to
one decimal place)

SAS21M08N0806
6 The cost price of raw materials used by Neeraj for making one pack of popcorn is Rs. 20, the cost of
packaging used to carry popcorn is Rs. 5 and the cost of preparation of popcorn Rs. 10 per pack.
What is Neeraj’s pro it percentage on selling popcorn?

SAS21M08N0807
7 Mayank deposited Rs. 50,000 in a bank for 5 years.
At the end of irst year, an amount of Rs. 3000 is added as interest in Mayank’s account.
At the end of ifth year, he had a sum of Rs. 66,911.27 in his account.

SAS21M08N0808
8 What is the rate of interest given by the bank on the sum of money in Mayank’s account?

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Class 8 – Chapter 8

SAS21M08N0809
9 At the end of one year, Riya gets Rs. 21,200 from the bank. She gets the same rate of interest on
deposited money as Mayank gets from the bank. What is the principal sum (in rupees) Riya deposited
with the bank?

A. Rs. 15,200
B. Rs. 18,200
C. Rs. 19,928
D. Rs. 20,000

SAS21M08N0810
10 Asha has some money to spare. She wants to deposit Rs. 15,000 for 3 years and Rs. 10,000 for 8 years in
a bank to earn interest. She has two banks to choose from. Bank A gives an interest of 6% per annum
compounded annually and bank B gives 7% per annum simple interest.
Which bank is a better choice for depositing Rs. 15,000? Justify your choice.

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 9
Algebraic expressions and identities

Restoration is a kind of repair process in which a house or a building is returned to its original
condition. Restoration normally involves repairing damages in walls, repairing or replacing old
equipment, removing old carpets and re inishing loors with materials and processes that were
used to make the original form.

SAS21M08N0901
1 Before itting a new carpet on the loor, the old carpet needs to be removed.
A contractor offers to remove the old carpet at a rate of Rs. 10 per m² from a room x m wide and y m
long.

Which expression gives the total cost of removing the old carpet from the room?

A. Total cost = 10xy
B. Total cost = 100xy
C. Total cost = 10(x + y)
D. Total cost = 10x + y

SAS21M07N0902
2 Ramya decided to replace the old carpet of her house with a new one.
Given below are the costs to it the carpet in the house.

Type of carpet

Type Cost per m²
Type 1 Rs. 20
Type 2 Rs. 25
Type 3 Rs. 30

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Class 8 – Chapter 9

Synthetic adhesive or glue costs Rs. 300 per bottle, each bottle can be used for itting a 2 m² carpet.
Labour charges for itting the carpet is Rs. 50 per m².
Ramya chooses the second type for the loor of her house.
Which calculation will the contractor use to correctly workout the cost of carpeting the loor of Ramya’s
house (given the length of the room is x m and breadth is y m)?

A. 25(x + y) + 50(x + y) + 300x(x + y)
B. 25x²y² + 50xy + 300
C. 25xy + 50xy + 600xy
D. 25xy + 50xy + 150xy

SAS21M08N0903
3 Ramya knows that the width of the loor is 3 m less than its length. Give the algebraic expression to
calculate the area of the loor.

SAS21M08N0904
4 The contractor offers a 5% discount on the total cost of removing the old carpet and 7% discount on the
total cost of itting the new carpet if they get the contract for both services.
What will be the cost to get both the jobs done to carpet a 20 m² loor with the third type of carpet?

Given below is the picture of a rectangular painting with a 5 cm wide black border.

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Class 8 – Chapter 9

SAS21M08N0905
5 The expression representing the breadth of the painting is a binomial expression. Do you agree? Give
reasons.

SAS21M08N0906
6 What is the area of the painting (excluding the border)?

The border of the painting has been made in such a way that the joints of the border are as shown in
the diagram below.

SAS21M08N0907

7 Shyam used a 5 cm wide piece of wood to make the border.
What is the length of the wood required by Shyam to make the border?

A. 2l – 2
B. 2l – 22
C. 8l – 8
D. 8l – 88

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Class 8 – Chapter 9

This is how Piyush made the border of the painting.

SAS21M08N0908

8 How many centimetres of wood did Piyush use?

SAS21M08N0909

9 Hemlata says, ‘the length of the diagonal of the painting along with the border is
Is Hemlata correct? Justify your answer.

SAS21M08N0910
10 Simplify the following algebraic expression.

(4g + h) (4h + g) – 2gh

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 10
Visualising Solid Shape

This map shows the location of the ATM machines in a metro city. The residential areas are divided
into sectors marked as ‘sec’, followed by the sector number.
Old residential areas have been marked by three letters.

SAS21M08S1001
1 Subramaniam’s bank card is accepted by some ATM machines and not by others. In which sector is he
more likely to ind an ATM which accepts his card?

A. Sector 1
B. Sector 18
C. Sector 26
D. Sector 54
SAS21M08S1002
2 Name the sectors surrounding the golf course.

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Class 8 – Chapter 10

SAS21M08S1003
3 Suchi lives in Sector 31. Her bank card works on all ATM machines. Where can she go to use the nearest
ATM?

A. Sector 25A
B. Sector 29
C. Sector 32
D. Sector 40

SAS21M08S1004
4 Ranbir is driving from the southwest corner of Sector 35 to the ilm city. Suggest a path guiding him to
the south of the ilm city.

The picture below shows a wire diagram of a multi-storey apartment building. There are 6 blocks in
the building. The blocks have either 9 loors or 13 loors other than a ground loor. The clubhouse,
the playrooms and the gym are on the ground loor. In each block, there is one apartment on each
loor. The size of the apartments vary in different blocks.

SAS21M08S1005
5 How many apartments are there in the building?

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Curriculum Aligned Competency Based Test Items Mathematics
Class 8 – Chapter 10

SAS21M08S1006
6 The height of the ground level of the building is 4.65 m. Other loors are of the height 3.7 m. What is the
height of the tallest block?

SAS21M08S1007
7 The builder claims that all the apartments of the building have three open sides. Do you agree with the
builder’s statement? Justify your answer.

SAS21M08S1008
8 Which of the following is not a polyhedron?

A. B. C. D.

SAS21M08S1009
9 To which of the given solids is Euler’s formula applicable?

A. B. C. D.

SAS21M08S1010
10 Is it possible to create a polyhedron with 8 faces, 12 vertices and 18 edges? Justify your answer.

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CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 11
Mensuration

The picture of a window is given below.

The length of side AB is 40 cm, side CE is 70 cm and side FE is 90 cm. AB is parallel to CE and E is the
midpoint of CD.

SAS21M08S1101
1 What shape does the window ABCD resembles?

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

SAS21M08S1102
2 Find the area of the window ABCD?
2
A. 270 cm
B. 5,950 cm2
C. 8,100 cm2
2
D. 16,200 cm
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Class 8 – Chapter 11

A wall decoration is in the shape given below.

Decoration is made of four congruent mirrors. The sides of a mirror are of the same length.

SAS21M08S1103
3 What is the area occupied by the decoration on the wall?
2
A. 25 cm
B. 30 cm2
C. 100 cm2
2
D. 200 cm

SAS21M08S1104
4 Rohan pasted four more mirrors congruent to the earlier ones.
What is the area of the new wall decoration?

The igure below shows a blueprint of a shower room of a club.

The walls of the shower room (inner boundary) is 0.1 m thick. The wall of outer boundary is 0.2 m
thick.
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Class 8 – Chapter 11

SAS21M08S1105
5 The inside wall and the loor of the shower room are covered with tiles. What area of the shower room
is covered with tiles?

A. 20.54 m2
2
B. 37.52 m
2
C. 58.06 m
D. 65.20 m2

SAS21M08S1106
6 Which of the following calculations shows the inside volume (in m3) of the shower room?

A. 7.9 × 2.6 × 1.76
B. 7.9 × 3.1 × 1.76
C. 8.2 × 3.1 × 1.76
D. 8.5 × 4.2 × 1.76

SAS21M08S1107
7 An area is marked for cupboards. How many cupboards with dimensions 1.5 × 0.6 × 1.76 (length x
breadth x height) can be built in the area?

SAS21M08S1108
8 One litre of paint is required to paint 12 square m. Approximately, how many litres of paint are required
to paint the outer boundary of the shower room?

A. 4
B. 5
C. 60
D. 89

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Class 8 – Chapter 11

Oil is transported through a special kind of truck with a cylindrical tank.

The radius of the cylindrical tank of one such tank is 1.4 m.

SAS21M08S1109
9 What is the total surface area of the tank?

SAS21M08S1110
10 The quantity of oil carried in the truck is measured in litres. The measurement in meters can be
converted into litres by using the conversion 1 cubic meter = 1000 litres.
2
What can be the maximum oil (in litres) stored in the tank? (Use π = 27 πÕ
)

A. 92.4
B. 132
C. 1000
D. 92,400

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CENTRAL BOARD OF SECONDARY EDUCATION

Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 12
Exponents and Power

The distance between planets varies depending on their position on their orbital path around Sun.
The table given below shows the average distance between two planets.

Planets Average distance between them

Venus to Earth 40,000,000 km

Earth to Mars 225,000,000 km

SAS21M08N1201
1 Which of the following options correctly represents the distance (in km) between Venus and Earth in
exponential form?
-6
A. 40×10
B. 4×106
C. 40×107
7
D. 4.0×10

SAS21M08N1202
2 How much further is Mars from Earth then Venus?

A. 1.85106
B. 1.95106
C. 1.75108
8
D. 1.8510
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Curriculum Aligned Competency Based Test Items Mathematics
Class 8 – Chapter 12

SAS21M08N1203
3 Divya inds the ratio of the distance between the Venus to the Earth and the distance between the Earth
to Mars. Which of the following cannot be the ratio?

A. 40:225
B. 4:22.5
C. 0.4:2.25
D. 0.4:22.5

SAS21M08N1204
4 The distance of planet Neptune from the Sun is 4495000000000000 km.
Which of the following can be another way of representing the distance (in km) between the Neptune
and the Sun?

A. 4.4 × 1014
15
B. 4.4 × 10
15
C. 44 × 10
17
D. 4.4 × 10

SAS21M08N1205
5 The mass of earth is 5.97 × 1024 kg, whereas Jupiter has a mass of 1.8986×1027 kg. About how many
times massive is Jupiter than Earth?

A. 3
B. 31
C. 300
D. 318

SAS21M08N1206
6 Rajat created an informative message. He forwards the message to 5 people. Each of the ive people
forward the message to next 5 people and the chain goes on. Rajat did not forward the message. How
many people have it?

A. 0
B. 1
C. 5
D. 10

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Class 8 – Chapter 12

SAS21M08N1207
7 The message is forwarded 5 times. Which of the following calculation can be used to ind number of
times message is forwarded?

A. 50 + 51+ 52+ 53+ 54
1 1 1 1 1
B. 5 +5 +5 +5 +5
0 5 10 15 20
C. 5 + 5 +5 + 5 + 5
D. 55+ 510+ 515+ 520 + 525

SAS21M08N1208
8 Which of the following represents the product of 1.08 × 1012 and 4.0 × 107?

A. 4 × 1.08 × 1012
19
B. 0.4 × 1.08 × 10
19
C. 4 × 1.0878 × 10
D. 0.4 × 1.0878 × 1084

SAS21M08N1209
9 Evaluate. 2
3 5
ìæ 9 ö æ 9 ö ü
íç ÷ ¸ ç ÷5ý
îè 5 ø è 5 ø þ

SAS21M08N1210
10 Which of the following shows the relation between mm and km?
-6
A. 1 mm = 10 km
-5
B. 1 mm =10 km
5
C. 1 mm =10 km
D. 1 mm =106 km

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 13
Direct and Inverse Proportion

Deepak and his family went on a road trip by car. They visited four cities. City 1 was 500 km from
their home. The petrol tank in their car has a capacity of 35 litres. The car runs 20 km on one litre.

City 1 City 2 City 3 City 4

Distance travelled by 500 1000 1500 2000
the car

From city 4, they travelled 500 km to reach home.

SAS21M08C1301
1 How many litres of petrol did they use to complete the road trip?

A. 100
B. 125
C. 200
D. 2500

SAS21M08C1302
2 The family travelled 500 km in a day. What is the smallest number of days in which the road trip can be
completed?

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Class 8 – Chapter 13

SAS21M08C1303
3 The car travelled at a uniform speed of 75 km/hr between city 3 and 4. How much distance did it travel
in 20 minutes?

SAS21M08C1304
4 The family started their journey from city 3 at 10 am. By what time will they reach half the distance to
City 4?

A. 12 noon
B. 1 pm
C. 1:30 pm
D. 3 pm

SAS21M08C1305
5 Deepak claims that the speed of the car and the time taken by it to cover the distance between the two
cities, 3 and 4, is inversely proportional.
Is Deepak correct? Why do you think so?

A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 hours
to clean all the rooms.

SAS21M08C1306

6 On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more than 2
hours? How can you say so?

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Class 8 – Chapter 13

SAS21M08C1307
7 Ishan says, “The number cleaners available in the hotel is directly proportional to the time taken by
them to clean the rooms.”
Mira says, “The number of cleaners available in the hotel is inversely proportional to the time taken by
them to clean the rooms.”
Who is correct? Give reason.

SAS21M08C1308
8 Equal number of rooms are allocated for each staff member for cleaning. How many rooms each
cleaner had to maintain?

SAS21M08C1309
9 The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by
each cleaner?

A. The total number of room increases by 2.
B. The total number of room decreases by 2.
C. The total number of room increases by 3.
D. The total number of room decreases by 3.

SAS21M08C1310
10 How many rooms has to be cleaned in an hour by each cleaner after the increase in the number of staff?

A. 1
B. 4
C. 8
D. 10

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 14
Factorisation

SAS21M08N1401
1 Which of the following is true for all the factors of 75?

A. They are odd numbers.
B. They are divisible by 3.
C. They are divisible by 5.
D. They are prime numbers.

SAS21M08N1402
2 2
2 Which of the following is not a factor of 18p q ?

A. 3
B. p2
C. pq
3
D. q

SAS21M08N1403
3 Factorise the following and ind its irreducible form.
2 4 2
15x y+6x y -9xy

SAS21M08N1404
4 4
4 Rajat factorises the given algebraic expression. a -r , Which of the following would be his next step?
4 4 2 2
A. a -r -2a r
B. (a+r) (a-r)
C. (a2)2-(r2)2
D. a2-r2
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Class 8 – Chapter 14

SAS21M08N1405
5 Satpal solved an algebraic equation as shown below.
Algebraic equation: (s+4)2=36+s2
Step 1: s2+16+8s=36+s2
Step 2: 8s = 52
Step 3: s = 528= 132

Did Satpal solve the equation correctly? Explain your answer.

SAS21M08N1406
6 “When a monomial is divided by a monomial, the quotient is a monomial.”
Siya disagrees with the statement as x2 divided by x2, is 1. Is Siya correct? Justify your answer.

SAS21M08N1407
2
7 When 5(6t +12t) is divided by a polynomial gives 30tas the quotient. What would be the divisor of the
polynomial?

A. t
B. 30t
2
C. t
D. t+2

SAS21M08N1408
8 Salma and Abid factorise the algebraic expression p + 9p + 18.
4 2

Salma:
p4 + 9p2+ 18 = p4 + 6p2+ 3p2+ 18
= p2 (p2+ 6) + 3(p2+ 6)
= (p2 + 3) (p2 + 6)
Abid:
4 2 4
p + 9p + 18 = p + 6p + 3p + 18
= p(p3+ 6) + 3(p + 6)
= ( p3+ 6) (p + 6)(p + 3)
Who is correct? Give a reason to justify your answer.

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Curriculum Aligned Competency Based Test Items Mathematics
Class 8 – Chapter 14

SAS21M08N1409
9 2x + 5 is divided by 5, What is the quotient?

A. 2x + 1
5
B. x+5
2
2
C. x+1
5
D. 2x + 5

SAS21M08N1410
10 2 2
Which of the following divides 25 (x y+y x) completely?

A. x2y
B. 5xy
C. 5x2y
2
D. 5y x

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 15
Introduction to Graph

Population projection is a scienti ic attempt to predict what a population will be in the future. The
prediction is based on past and current population, fertility rate, mortality rate and migration.
Based on population projection for 2011 - 2036, changes in the age structure of the Indian
population are shown in the graph below.

The population of the country is categorised into three broad age groups, 0-14 years, 15-59 years
and 60+years.

SAS21M08D1501
1 What percentage of the projected population will be in the age-group 15-59 in the year 2031?

A. 24
B. 60
C. 64
D. 70
SAS21M08D1502
2 What is the percent change in the projected population of the age group 60+ from 2021 to 2036?

A. 2
B. 6
C. 14
D. 26
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Class 8 – Chapter 15

SAS21M08D1503
3 The total population of the country in the year 2021 is 1300 million. How many people (in millions) are
in the age group 0-14 years?

SAS21M08D1504
4 Which of the following is not true for the graph shown above?

A. Most of the population is in the age group 15-59 years across all the years.
B. The projected population of age group 0-14 years increased in the year 2036 compared to the
year 2011.
C. The change in the population of the age group 60+ is less than 10 percent from 2011 to 2036.
D. The change in the population is the highest for the age group 0-14 years from 2021 to 2036.

The graph below shows the projected female population percentage of the country in the year 2036.

The total female population projected in the year 2036 is 775 million.

SAS21M08D1505
5 According to the projection, what percent of the female population will belong to the age group 11-40?

A. 13.2
B. 15.8
C. 43.2
D. 55.3

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Class 8 – Chapter 15

SAS21M08D1506
6 How many females (in millions) are in the age group 41-50?

SAS21M08S1507
7 If the total projected population for the year 2036 is 1518 million, what percentage of the total
projected population would be female?

A badminton academy charges fees on a per-hour basis for their badminton court. They also issue
monthly booking passes costing Rs 1500. The pass allows a user to play for 2 hours, 5 times a week.
Any extra time is charged on an hourly basis.
The graph shows the per hour cost of booking a badminton court.

The total female population projected in the year 2036 is 775 million.

SAS21M08S1508
8 Paul and his friends booked the badminton court for 7 hours. How much did the booking cost?

A. Rs 50
B. Rs 300
C. Rs 350
D. Rs 350

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Class 8 – Chapter 15

SAS21M08S1509
9 Rohan plays for 2 hours, 4 times a week. He pays on an hourly basis. Would using a monthly pass be
more economical for Rohan?

SAS21M08S1510
10 Pritam wants to be a badminton professional. He decided to practice at least 40 hours a month at the
academy. What is the minimum amount Pritam would be paying to the academy?

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Curriculum Aligned Competency Based Test Items
Mathematics
Class 8 – Chapter 16
Playing with Numbers

SAS21M08N1601
1 A housing society has 16 towers, named A, B, C and so on. Each tower has a different number of lats.
There are 720 fans installed in the tower A lats. Each lat has 9 fans. How many lats are there in tower
A?

A. 9
B. 80
C. 90
D. 729

SAS21M08N1602
2 A shopping complex in the housing society has shops of the same size. Each shop has 10 lights inside
the shop and two outside the shop. There are 360 lights itted in them. How many shops are there?

A. 12
B. 30
C. 36
D. 360

SAS21M08N1603
3 Tower J has some lats with 3 bedrooms and some with 2 bedrooms. Three-fourth of the lats have 3
bedrooms and the rest have 2 bedrooms. The total number of bedrooms is 385. How many two-
bedroom lats are there in tower J?

A. 30
B. 35
C. 105
D. 140

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Class 8 – Chapter 16

SAS21M08N1604
4 Priya plays a number game and follows the below steps.
Step 1: Choose a two-digit number between 20 and 100.
Step 2: Add digits together.
Step 3: Subtract the sum from the original number.

Which of the following statement is true of the resultant number in step 3?

A. It is a multiple of 2.
B. It is a multiple of 5.
C. It is a multiple of 7.
D. It is a multiple of 9.

SAS21M08N1605
5 Priya has two sets of three number cards 1, -3, 9 and – 27. Which of the following is the smallest number
she can make by adding the numbers on cards?

A. -30
B. -34
C. -60
D. -80

SAS21M08N1606
6 The general form of number 98 is 10×9 +8. Which of the following is the general form of number 1072?

A. 1+0+7+2
B. 1000+10×7+2
C. 1000+100×7+10×2
D. 1000+100+10×7+2

SAS21M08N1607
7 Rajesh works in the courier collection centre. He received ten boxes, with a total weight of 75 kg at his
centre. 15 kg, 13 kg, 11 kg, 10 kg, 9 kg, 8 kg, 4 kg, 2 kg, 2 kg, 1 kg
He wants to pack them into 3 crates. Each crate can carry a maximum of 25 kg.

How can Rajesh pack the boxes into the crates?

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Class 8 – Chapter 16

Kanika practised her math by solving the below questions

1
4 -3
2
1
5 -4
3
1
6 -5
4
1
7 -6
5
Manaya had done the same questions but she divides the two numbers instead of subtraction. Still,
Kanika and Manaya both get the same answer.

SAS21M08N1108
8 Why do both get the same answer?

SAS21M08N1609
9 A three-digit number can be written as 100x + 10y + z. A new number is formed by interchanging x and
z. What is the difference between the two numbers?

A. y
B. 99 (x – z)
C. x-y-z
D. 99 x - y - z

SAS21M08N1610
10 A two-digit number has different digits at the ones and tens place. The number is multiplied by 6. The
product is a three-digit number. Each digit of the product is ones digit of the original number. What is
the original number?

A. 16
B. 32
C. 66
D. 74

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