ANSWER KEY SESSION ENDING EXAMINATION Model Exam -1

 ANSWER KEY   SESSION ENDING EXAMINATION   Model Exam  -1

Grade: VIII                 Subject: Mathematics      Max.Marks: 50    Duration: 120 +15 Min

Chapters : Algebraic Expressions, Factorization, Exponents and Powers & Direct and Inverse proportions

SECTION-A (1 x 10 = 10)

1.(a) 12a3bc2              

2.c) Rs. 13.00

3.d) 2x(1-4)(1+4x)

4.d) 7(a-3b)(a+3b)

5. c) 34/24

6.0.000532

7. 6

8. 240 MIN

9.(pq-1)(q+1)

10. 2x (3x + 5xy) =6x²+10x²y

SECTION-B (2x5=10 marks)

11. Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y , –3xz + 5x – 2xy.

12. State whether or not 2x + 3 is a factor of 6x3 +19x2 +13x – 3 

2x+3=0

x=-3/2

Yes. 6(-3/2)³  -3 +19 (-3/2)² + 13(-3/2)

13. A train is moving at a uniform speed of 75 km/hour. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km. 

14. Evaluate : (6-1 – 7-1 )-1 – (5-1 – 4-1 )-1.  ‘

= (⅙-1/7)^-1 x (⅕-¼)^-1= (1/42)x(1/-20) = (-840)

15. Find the factors of 16l2 + 24lm + 9m2.  = (4l+3m)²

SECTION-C (3x5=15 marks)

16.  Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c ) 

Or

 Simplify: 3y(2y – 7) – 3(y – 4) – 63 and evaluate for y = – 2. 

17. Factorize the following expressions: a)  x4 – (x – z)4  b) a4 – 2a²b² + b4 

18.The vertical pole 5 m 60 cm high  casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5m long

19. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same? 

20.Express the number appearing in the following statements in standard form. 

  (i) Sun is located 300,000,000,000,000,000,000 m from the centre of our Milky Way.  

3x 10^20 m

 (ii) The distance between Sun and Saturn is 1,433,500,000,000 m = 1.4335 x 10^12

SECTION-D  (5x3=15 marks)

21. Simplify:

 (i) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd) (3 marks)

 (ii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y (2 marks)

22. (i) Factorise the expressions and divide them as directed.  (3 marks)

(a) (5p2 – 25p + 20) ÷ (p – 1)  

 

(b) 4yz(z2 + 6z – 16) ÷ 2y(z + 8) 

(ii) Find the value of x for which    

(2 marks)

23. (i) By what number should be divided that quotient is ? (2 marks)

(ii)  Ramesh is making a wheel using spokes. He wants to  x equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table:   (3 marks)

a) Are the number of spokes and the angles formed between the pair of consecutive spokes in inverse proportion? 

b) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. 

c) How many spokes would be needed if the angle between a pair of consecutive spokes is 40o?