JKBOSE 8th Class Model Paper Maths

19

Class 8th Mathematics Model Paper for Summative
Assessment 2023-24
Chapters and the Distribution of Questions as per Cognitive
Level for final Summative Assessment 2023-24
Chapter CL-1 CL-2 CL-3 Total
Marks
Practical 1 0 5 6
Geometry
Square and 2 0 2+1 5
Square roots
Cube and 2 0 2+1 5
Cube roots
Algebraic 3 1+1 3 8
Expressions
Mensuration 1+1 2 3 7
Exponents 1 2 3 6
and powers
Introduction 5 1 1 7
to Graphs
Playing with 1+1 3 1 6
Numbers
Total 18 10 22 50
Note:
A) CL-1 (Cognitive level-1, which includes memorized and
understanding of the concepts). These questions are
purely based on LOTS
B) CL-2 (Cognitive Level-2, which includes application of the
learnt concepts). These questions are mostly based on
LOTS
C) CL-3 (Cognitive Level-3, where a student sometimes
needs multiple concepts to solve a problem and has also
opportunity to develop new rules and innovative ideas).
These questions are mostly based on HOTS
LOTS= Lower Order Thinking Skills
HOTS=Higher Order Thinking Skills

20

Model Paper 2023-24
Section (A) Objective Type Questions (Each of 1 Mark)
Q.1. Which one of the following is a binomial?
a) 2𝑥(𝑥 + 1) b) 2𝑥(𝑥𝑦𝑧)
c) 2 + 𝑥 + 𝑦 d) (𝑥 − 1) + 𝑦

Q.2. If a natural number is divisible by both 5 and 10, then its
unit digit must be:
a) 0 b) Any digit 0 to 5
c) Either 5 or 0 d) 5

Q.3. Which formula can be applied to calculate the surface area
of a cuboid, if 𝐿 is (Length), 𝐵 is (breadth), 𝐻 is (Height)
a) 𝐿 × 𝐵 × 𝐻 b) 2(𝐿 + 𝐵 + 𝐻)
c) 2(𝐿𝐵 + 𝐿𝐻 + 𝐵𝐻) d) (𝐿𝐵 + 𝐵𝐻 + 𝐿𝐻)

Q.4. Every even number is divisible by:
a) 5 b) 4
c) 2 d) 3

Q.5. The value of 5−1 𝑖𝑠 (CL-1)
a) 4 b) −5
1 1
c) d)
5−1 5

21

Q.6. How do we calculate the area of given figure?

a) 2(10 + 5) b) (10 + 5)2
c) 10 × 5 d) 10 + 5

Q.7. If the area of a square shaped field is (16𝑎4 ) 𝑚2 , what is
the length of its side?
a) (256𝑎4 )𝑚2 b) (256𝑎16 )𝑚2
c) (4𝑎2 )𝑚 d) (4𝑎)𝑚2 (CL-2)

Q.8. We know that: 2 × 2 × 2 × 5 × 5 × 5 × 3 × 3 × 𝑎2 = 9000𝑎2 .
What least number should be multiplied to 9000𝑎2 so that
is will become it perfect cube?
a) 𝑎 b) 3
c) 3𝑎 d) 3𝑎2 (CL-2)
Q.9. The value of {[(−𝑎3 × 𝑏 −5 ) ÷ 2−4 ]0 }−100 − 1 is ……
(CL-2)
a) 1 b) −101
c) −𝑎−300 𝑏 500 2400 d) 0
Q.10.Observe the given rectangle and identify the situation in
1
which its area will increase by 2 𝑥 square units
2

1
a) If its length is increased by units
2
1
b) If its breadth is increased by units
2

c) If its length is increased by 2𝑥 units and breadth
1
increased by 𝑥 units.
2
1
d) If its breadth is increased by 2 units (CL-3)
2

22

Q.11. In which of the given situations, an isosceles triangle can
be constructed uniquely?
a) If the measures of all its three angles are given.
b) If the length of one of its sides and one of its angles is given.
c) If the measure of one of its equal sides and the
measures of one of its equal angles is given.
d) If the lengths of both the equal sides is given.

Q.12. If 𝑥 2 + 2𝑥 2 + 3𝑥 2 + 4𝑥 2 + 5𝑥 2 = 60, then the value of ′𝑥′ is
a) 60 b) 15
c) 4 d) 2 (CL-3)

Q.13. A number ′𝑦 ′ is 5 more than one of the multiples of 12.
What least number should we add to the number ′𝑦′ to
become it multiple of multiple of 4?
a) 7 b) 3
c) 0 d) 5 (CL-3)

Section (B) Very Short Answer Type Questions
(Each of 2 Marks)
Q.14. Find the square of: −52

Q.15. Estimate the cube root of 4096

Q.16. Calculate the area of the given quadrilateral:
(CL-2)

23

Q.17. Given below is the data of three kinds of fruits sold by a
shopkeeper during a week. Represent it by some suitable
chart/graph.
Fruit Quantity sold
Kashmiri Apple 300kgs
Mangoes 300kgs (CL-2)
Bananas 600kgs

Q.18. Determining the square root of a number with more than
two digits, a systematic approach involves pairing the digits
from the right side and proceeding with the division
process.
For the following, under which circumstances does the
result is same/different as to the authentic result when
pairing digits from the left side. In case the result is
different from the authentic result, will it be more or less
than the authentic result.
Case 1. When there are even number of digits in the number.
Case 2. When there are odd number of digits in the number.
Q.19.To find the least number by which 57,600 is to be
multiplied so that it will become a perfect cube, we
proceed as follows:
We factorize the given number as:
57600 = 2 × 2 × 3 × 3 × 4 × 4 × 4 × 5 × 5
We observed that 30 is the least number which is to be
multiplied to 57600 so that it will become a perfect cube.
Questions:
a) Why did we factorize the given number into prime
factors?
b) How did we come to know that 30 is the only least
number needed to multiply 57600 to become it a perfect
cube? (CL-3)

24

Section (C) Short Answer Type Questions
(Each of 3 Marks)
Q.20. Simplify 𝑎(𝑎2 + 𝑎 + 1) + 5 and find its value when 𝑎 = −1
1
Q.21. Express: 9−4 with the base and positive exponent
3

(CL-2)
Q.22. In the given pattern of figures, each shape in the figure
is a square of side 𝑥 + 1 units. What is the area of figure
number 76 when the same pattern is continued.

Q.23. A milk woman sold milk to her customers by using the
vessel marked as 1𝑙 capacity. After one month (30days),
she came to know that the vessel actually contains 900𝑚𝑙.
She decided to give the leftover milk to her customers
without letting them know about. She brought another
cylindrical measuring vessel of radius 5𝑐𝑚 and height 14𝑐𝑚.
For how many days she needs to use the new
measuring vessel so that the customers will get exact
quantity of leftover milk. (Remember there is no change in
the quantity of milk from customer side) (𝑇𝑎𝑘𝑒 1𝑐𝑚3 = 1𝑚𝑙)

Q.24. When we divide 100000, 10000, 1000 and 100 by 7, we
get remainders 5, 4, 6 and 2 respectively. Without actually
dividing, fide the remainder when 111107 is divided by 7,
also show your working.

25

Section (D) Long Answer Type Questions
(Each of 5 Marks)

Q.25.The given graph shows 10
days actual and forecasted
temperature of a locality.
Observe the it carefully and
answer:

a) When did the weather forecast
come 100% true?
b) When there was fall in actual-
Temperature observed?
c) If the actual temperature is
represented by the dotted line, What modifications in the
legend is/are required?
d) There is a break in temperature axis (vertical axis)
between origin and 26, Why?
e) Can this information be represented by some other type
of graph? If yes, mention the name of the graph. If no,
give reason.
Or
Compare the given information graphically, mark an
average line for each category, (if possible).
Class Boys Girls
8th 20 30
7th 15 25
6th 20 25

26

Q.26.Given below is the rough drawing of a quadrilateral in which
𝐴𝐵 ∣∣ 𝐶𝐷, observe it carefully and construct it in your
notebook using compass and straight edge:

Or
Construct a rhombus who’s each diagonal is of length 6𝑐𝑚.
Is this a special type of rhombus, If yes give reason.