SESSION ENDING EXAMINATION Practice Exam-1
Grade: VIII Subject: Mathematics Max. Marks: 80 Duration: 180 +15 Minutes
General Instructions
All questions are compulsory
The duration of the paper is: 3 hrs 15 min (Reading time 15 min)
Read all the questions carefully before attempting.
The question paper consists of 40 questions divided into 4 Sections A, B, C, D
Section- A comprises 20 questions of I marks each.
Section- B comprises 8 questions of 2 marks each.
Section-C comprises 8 questions of 3 marks each
Section-D comprises 4 questions of 5 marks each.
SECTION-A (1 x 20 = 20)
1. Simplify the expression, (a22 × a−12) × (b−10 × b20)
(a) (ab)10 (b) a22 × b20 (c) (ab)12(ab)12 (d) a12 × b10
2. Express 81−2in the powers of 3
(a) 38 (b) (1/3)8 (c) 3−6 (d) (1/3)6
3. If sum of the length , breadth ,depth of the cuboid is 19 cm. and its diagonal is 5√5 cm and then its surface area is —
a) 216 cm2 b) 236 cm2 c) 256 cm2 d) 276 cm2
4. The volume of a cube is 64 cm3. Its surface area is
(a) 16 cm2 (b) 64 cm2 (c) 96 cm2 (d) 128 cm2
5.If the radius of a cylinder is tripled, but its curved surface area is unchanged, then its height will be
(a) tripled (b) constant (c) one-sixth (d) one third
6.Find the volume of the rectangular box whose length (l) = mn, breadth (b) = m2p, depth (d)= pmn2.
(a) m4n2p (b) m4n3p2 (c) m3n2p (d) m3n2p2
7. If n is odd, then (1+3+5+7+... to n terms) is equal to :
(a) n²+1 (b) n²-1 (c) n² (d) 2n²+1
8. In a quadrilateral ‘Rock’ which of the following is a diagonal?
(a) RO (b) OK (c) OC (d) KR
9.Which of the following shows three consecutive multiples of 8?
(a) 8x, (x +8), (x +16) (b) 8x, 8x +8, x +16 (c) 8x, 8(x +1), 8(x + 2) (d) x, (x + 8), (x +16)
10.Solve: 8x+4 = 3(x-1)+7
(a) x = 0 (b) x= 3/8 (c) x= 8/5 (d) x=1/5
11. Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm
12. Is 225 a perfect square? If so, find the number whose square is 225. Explain.
13. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively: (3mn,4np)
14.Find the value of (2-1 -4-1)2
15. Find the value of the expression 3x (4x – 5) + 3 for x = 3
16. The cost of 5 metres of a particular quality of cloth is Rs 210. Find the cost 2 metres of the same cloth.
17. If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2 ½ kilograms?
18. 5pq (p2 – q2) 2p (p + q)
19. Factorise x2 – 14x + 13
20. Find the highest common factor of 16x 3, -4x2, 32x
SECTION-B (2x8=16 marks)
21. Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
22. Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.
23. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
24. Write a Pythagorean triplets using when the smallest member is18 .
25. The length of the fence of a trapezium shaped field ABCD is 130 m and side AB is Perpendicular to each of the parallel sides AD and BC. If BC = 54 m, CD =19 m and AD = 42 , find the area of the field.
26. (a) Express Mass of Uranus = 86,800,000,000,000,000,000,000,000 kg in standard form.
(b) Find the value of m for which 5m÷5– 3 = 125.
27. 6 pipes are required to fill a tank in 1 hour 20 minutes. How long will it take if only 5 pipes of the same type are used?
28. Factorise: x4 – (y + z)4
SECTION-C (3x8=24 marks)
29. The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?
30. Solve:
31. There are 2401 students in a school. P.T. teacher wants them to stand in rows & columns such that the no. of rows to equal to the no. of columns. Find the number of rows.
32. Simplify: (a) Add: p ( p – q), q ( q – r) and r ( r – p)
(b) Subtract 5x2 – 4y2 + 6y – 3 from 7x2 – 4xy + 8y2 + 5x –3y.
33.In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m2.
34. Evaluate : (ii)
35. Factorise: (a) m4– 256 (b) x2+ xy + 8x + 8y
36. An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.
SECTION-D (5x4=20 marks)
37. (i) Find the least number which must be subtracted from 18265 to make it a perfect square. Also, find the square root of the resulting number.
OR
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20. (2 marks)
(ii)Simplify: (i) (5x – 6) (2 x – 3) + (3 x + 5)2
(ii ) (2x + 5y) (2 x + 3y) (3 marks)
38. (i)Find area of the below figure:(2 marks)
(ii) .A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form embankment. Find height embankment. (3 marks)
39. (i) Solve: (2 marks)
(ii) (a) If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
(b) A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle? (3 marks)
40.(i) Factorise then divide (3 marks) 156(36y²-64)y³ / 104(6y+8)y²
(ii) Find the value of x : ( 2 marks)
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