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E:\Working\Focus_Learning\Math_Genius-8\Open_Files\00_Prelims\Prelims
\ 07-Jan-2025 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Life Skills—include the ability to manage your
maths fun
emotions, school performance, health, finances,
Play this Tic-Tac-T oe game, with your friends.
3 216 behaviour, relationships, etc.
the box. 1296 3 10648
Take the turns alternatively, solve the given problem and acquire
3
2 3 1728 3 3
3
The player who marks three of their boxes in a line (horizontal,
vertical, or diagonal) is the winner. 3 8 3 + 4 + 5 3
3 512
(2 × 3) 2
36
Life Skills
Maths Fun—make math practice more It is believed that architecture containing the golden ratio in its design looks beautiful.
ab
+
, where a is the longer length and b is
a
engaging by running these fun with math The two numbers a and b are said to be golden ratio = b = a
activities. the shorter length. The Taj Mahal’s design uses a golden ratio of approximately 1.618. If the height of the
dome (a) is 80 feet, find the length of the base of the dome (b).
Learning by Doing—for creating interest
of the learners in the subject and help them
Mental Maths
draw conclusions on their own or sometimes
the pit.
1. A cubical pit of side length 6 m is dug in a field and soil is taken out. Find the surface area of
to verify the concepts with hands-on practice.
2. If the volume of two cubes are in the ratio 27 : 8, find the ratio of their sides.
3. Find the percentage increase in the volume of a cube if its edge is doubled.
4. Find the percentage decrease in the area of a square if its side length is halved.
Mental Maths—to focus on 21st
Century skills in teaching, learning Learning by Doing
and assessment.
Objective: To reiterate the concept that multiplication of rational numbers
is commutative.
Materials Required: White chart paper, pencil, geometry box, coloured
pencils, scissors 3 5 E B
Procedure: A
• Draw two identical squares of suitable side length (say 2
www
MAths connect ABCD and PQRS each of side 10 cm). 7 G I H
• Divide the 1st square ABCD into 7 equal parts horizontally
and colour its parts yellow. Again, divide the square into
2
Do you know about the use of scale given at the bottom of a map in your atlas?
7
A map is a miniature representation of a large region. A map scale is the ratio between the distance on a map
5 equal parts vertically and colour its 3 5 parts red. What
and the corresponding distance on the ground. This scale of a map is based on the concept of direct proportion.
distances between major cities. does the double-shaded part (rectangle AEIG) represent? F C
Look at the map of India in your atlas and consider the scale given there. Using the scale, find the actual
• Divide the 2nd square PQRS into 5 equal parts horizontally D 2
and colour its parts red. Again, divide the square into 7 P 7 T Q
3
5
equal parts vertically and colour its 2 7 parts yellow. What 3
does the double-shaded part (rectangle PTXV) represent?
• Cut the rectangles AEIG and PTXV from both squares. Try 5
Maths Connect—for enhancing the logical/critical to superimpose one another. V X W
thinking skills and encouraging the child to apply Observation:
the knowledge in handling real life situations. We observe that: 2 3 S U R
The rectangle AEIG represents 7 3 × 5 2 . A(T) E(X)
5
The rectangle PTXV represents × 7 .
Model Test papers—for self-testing the
Chapter Assessment—the process of interpreting, After superimposing, the two figures cover each other G(P) I(V)
completely.
preparation before the semester-end exam.
recording and using information about a student’s Therefore, 2 × 3 = 3 × 2 .
responses. Conclusion: 7 5 5 7 a c c a
a c are two rational numbers, then b × d = d × b , i.e., multiplication is
If b and MODEL TEST PAPER – 1
d
commutative.
A. Choose the correct option in Questions 1 to 10.
1. –5.5 can be expressed as a rational number in standard form as .................
34
Mathematics-8
−55 (b) –55 (c) −11 (d) –5.5
2
(a)
Chapter assessment
A. Choose the correct option. 10 0
2. Multiplicative inverse of is
1. The standard form of 0 is ............... 5 (c) –5 (d) Not defined
(a) 0 (a) 5 (b) 0
(b) 1 1
(c) 5x
0 (d) Does not exist 3. If 3x 2 −= 13 − 2 , then x is (d) 6
7
−15
2. –1.5 can be expressed as a rational number in standard form as ............... (a) 0 (b) 1 (c) 5
(a)

10 (b) –15 (c) 15 −3 4. If Sumit present age is twice of her younger sister. If his sister age 5 years ago is 3 years,
10 (d)
2 then Sumit present age is (d) 16 years
3. How many rational numbers are there between 1 and 3?
(a) 1 (b) 12 years (c) 14 years
(b) 0 (a) 11 years
(c) unlimited
5 (d) 100 5. Sum of interior angles of a hexagon is (d) 1080°
4. Additive inverse of 1 is (c) 720°
10 (a) 360° (b) 540°
(a) 15 −3 6. Two angles of a quadrilateral are of measure 70˚ and the other two angles are equal. What
As per the new assessment practices, questions in is the measure of each of the equal angles? (d) 140°

10
(b)
10
(c) 1
10

2
(d) –1
5
the examination will be competency-based in the (a) 100° (b) 110° (c) 120°
5
5
−6

−  1
5. The numerical expression 
+
=
 shows that
 7
14
2

form of multiple choice questions (MCQs), 7. The value of 500 2 – 499 2 is (c) 999 (d) 1001
(a) rational numbers are closed under addition.
(b) 900

(a) 899
case-based questions and source-based questions. 8. Which of the following number has same ones digit as its cubes? (d) 82
(b) rational numbers are not closed under addition.
(c) rational numbers are closed under multiplication.
(d) addition of rational numbers is not commutative. (a) 33 (b) 66 (c) 77
9. 40% of [100 – 30% of 300] is equal to
6. Which of the following is not true? (c) 30 (d) 40
(a) 3 (b) 4
(a) Rational numbers are closed under division. 10. If the selling price of a toy car at 5% profit is ₹840, then its cost price is
(d) `815
(b) Rational numbers are closed under subtraction. (a) `800 (b) `770 (c) `779
(c) Rational numbers are closed under multiplication.
(d) Non-zero rational numbers are closed under division. Directions. (For Qs 11–12): In the following questions, a statement of Assertion (A) is followed
by a statement of Reason (R). Choose the correct option.
a
7. If a be the reciprocal of rational number b, then the reciprocal of the reciprocal of b will be (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of
(a)

b
b (b) Assertion (A).
a (c) a (d) b (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation
1 of Assertion (A).
4 2
8. Karan works at Pizza Hut. In morning, he chopped 1 kg of white onions and 8 kg of red onions.
3
How much onions did Karan chop in all? (c) Assertion (A) is true but Reason (R) is false.
(a) 9 11 kg 11 (d) Assertion (A) is false but Reason (R) is true.
12 (b) 11 kg 11 11. Assertion (A): Natural numbers lie between 12 2 and 13 2 are 24.
12 (c) 10 kg (d) 12 11 Natural numbers are the positive integers are non negative integers which
−5 −9 8 12 12 kg
9. The product of × × × −1 is Reason (R):
3 10 21 6 start from 1 and ends at infinity.
(a) 2 4 191
21 (b) (c) −2
21 21 (d) −4
3 21
10. The multiplicative inverse of is
10
(a) −3 10
10 (b) (c) −10
3 (d) 3
3
10
31