DELHI PUBLIC SCHOOL TAPI CLASS VIII

SUMMATIVE ASSESSMENT 1

SUBJECT: MATHEMATICS

DATE: 30/09/14 TOTAL MARKS: 90

DURATION: Reading – 15 Mins. + Writing – 2 Hrs. 45 Mins. + Revision – 15 Mins.

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General Instructions: a) All questions are compulsory. b) The question paper consists of 34 questions divided into four sections A, B, C and D. Section A comprises of 8 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each. c) Question numbers 1 to 8 in Section A are multiple choice questions where you are to select one correct option out of the given four. d) There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. e) Use of calculators is not permitted. f) Draw a rough column on the right hand side for rough calculations. g) Do not write anything on the question paper. SECTION A

Question numbers 1 to 8 carry 1 mark each. 1. The reciprocal of a negative rational number is

a. A positive rational number

b. A negative rational number

c. Can be either a positive or a negative rational number

d. Does not exist

2. If 3x – 1 = 5, then x is equal to

a. 43

b. -2 c. 2 d. 6

3. Two consecutive natural numbers whose sum is 85 are

a. 32, 53 b. 42, 43 c. 41, 44 d. 40, 45

4. Which of the following is true?

a. Sum of interior angles of a quadrilateral is 540°

b. Sum of interior angles of a pentagon is 720°

c. Sum of measures of the exterior angles of any polygon is 360°

d. None of these

5. A bag contains 3 white and 2 red balls. One ball is drawn at random. What is the probability that the

ball drawn is red?

 

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a. 12

b. 23

c. 15

d. 25

6. Which of the following numbers is not a perfect square?

a. 3600 b. 6400 c. 81000 d. 2500

7. The largest four digit number which is a perfect cube is:

a. 9999 b. 9261 c. 8000 d. 9899

8. x % of Rs. 400 = 60. What is the value of x?

a. 6 b. 12 c. 15 d. 20

.

SECTION B

Question numbers 9 to 14 carry 2 marks each.

9. Find four rational numbers between -13

and 12

.

10. Solve 3x5x + 2

= −4 .

11. Construct a rhombus whose diagonals are 6 cm and 8 cm respectively. Steps of construction are not

required.

12. The weekly pocket expenses (in rupees) of 30 students of a class are given below:

62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103,

96, 64, 94, 87, 85, 105, 115

Construct a frequency table with class intervals 60-70 and so on.

13. Which of the following triplets are Pythagorean?

A. (1, 2, 3)

B. (3, 4, 5)

C. (6, 8, 10)

D. (2, 2, 3)

OR

13. Find the value of (86)2, using the diagonal method.

14. An article marked at Rs. 500 is sold at Rs. 470. Find the discount %?

SECTION C

Question numbers 15 to 24 carry 3 marks each.

15. Subtract the sum of −23

and 13

from the sum of 53

and −43

.

16. Simplify 23

+ −56

"

#$

%

&' -

−35

"

#$

%

&' + 7

15

 

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17. Solve: 5− 7y2+ 4y

=−87

18. The denominator of a rational number is greater than its numerator by 7. If the numerator is increased

by 17 and the denominator is decreased by 6, the new number becomes 2. Find the original number.

19. In a parallelogram PQRS ∠R = (5y)°, ∠S = (2y +19)°. Find the value of y.

OR

19. Find the number of sides of a polygon, the sum of whose interior angles is 1620°.

20. From a well-shuffled deck of 52 cards, one card is drawn at random. Find the probability of getting

A. a red card

B. a 10 of black cards

C. a face card

21. Find the greatest number of five digits, which is a perfect square. Also find the square root of the

number so obtained.

OR

21. Find the smallest number by which the number 3645 must be divided so that it becomes the perfect

square. Also find the square root of the resulting number.

22. Find the square root of the given numbers by long division method:

A. 9801

B. 72.25

23. Find the smallest number which when multiplied by 3600 will make the product a perfect cube. Find

the cube root of the product.

24. In how many years will Rs. 1800 amount to Rs. 2178 at 10% per annum when compounded annually.

OR

24. Find the compound interest on Rs. 5000 at 6% p.a. for 2 12

years, interest being payable annually.

SECTION D

Question numbers 25 to 34 carry 4 marks each.

25. Find:

A. The area of a rectangular park, which is 1835

m long and 503

m broad.

B. The distance covered by a car in 152

hours which is moving at an average speed of 2025

km/hr.

 

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26. Three prizes are to be distributed in a quiz contest. The value of the second prize is five-sixths the

value of the first prize and the value of the third prize is four-fifths that of second prize. If the total

value of the three prizes is Rs.150, find the value of each prize.

27. A sum of Rs. 90,000 is to be divided between three business partners A, B and C in the ratio 5:6:7.

How much money will each partner get?

28. Find x, y, z in the given parallelogram ABCD.

29. Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4.1cm, CD = 4.4 cm, AD =3.3 cm and ∠A = 75°. Steps of construction are not required.

30. The monthly savings (in rupees) of 32 salaried persons are:

420, 400, 600, 500, 460, 400, 500, 520, 620, 720, 620, 660, 460, 560, 520, 580, 520, 700, 600, 660,

560, 400, 500, 420, 420, 800, 600, 500, 860, 700, 620, 520

Construct a frequency distribution table with class intervals such as 400 - 500.

Draw a histogram for this distribution.

31. By selling a T- shirt for Rs. 432, a shopkeeper loses 4%. For how much should he sell it to gain 6%?

OR

31. Price of a DVD player including 12% VAT is Rs. 4480. Find the price of DVD player before VAT is

added.

32. Savita invested Rs. 1,000 in a finance company and received Rs. 1331 after 3 years. Find the rate of

interest percent per annum compounded annually.

OR

32. Find the difference between compound interest and the simple interest on Rs 50,000 at 10% per

annum for 2 years.

33. Ram buys two fans for Rs. 220 and Rs. 280 respectively. He sells first fan at the profit of 10% and the

second at the loss 10%. Find his gain or loss per cent on the whole transaction.

34. Out of her total monthly salary, Mrs. Gupta spends 20% on house rent and 60% of the rest on house

hold expenditure. If she saves Rs. 2800, what is her total monthly salary?

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