NAIROBI SCHOOL

FORM TWO MATHEMATICS APRIL 2017, HOLIDAY HOMEWORK

1. Work out 25 ÷ -5 + 5 x 6

16 + 6 ÷ 2 - 34 (2marks)

2. Use mathematical tables to evaluate?

0.3 + 0.498

0.0351 (3 marks)

3. Express 46656 as a product of its prime factors and hence find the cube

root using factors. (3 marks)

4. Solve the equation 8x + 23x + 3 = 35 (3 marks)

5. Evaluate 1 ÷ 1 (3 marks)

6. Three points A(2,3) B(2K, 5) and C(-3, 6) line on a straight line. Find the value of K. (3 marks)

7. Find the x and y intercepts of a line whose equation is 4x – 3y = 9. Determine the equation of the perpendicular line 4x - 3y = 9, and passing through point P(4,3)

(4 marks)

8. Two similar conical solids made of the same material have masses 4000g and 500g respectively. If the base area of the smaller conical solid is 38.5cm², find the base area of the larger one. (3 marks)

9. The size of each interior angle of a regular polygon is eight times the size of the exterior angle. Find the number of sides the polygon has and the sum of the interior angles. (3 marks)

10. Solve the equation (3 marks)

x + 3 - x - 5 = 2

8 7

12. A library contain books which are either fiction biography or reference. There are 20 more fiction books than biography books, and there are three times more biography books than reference books. If there are 160 books in total, find how many are reference books. (4 marks)

13. Evaluate

‾2(5 + 3) – 9 ÷ 3 + 5

‾3 x ‾5 + -2 x 4 (3 marks)

14. A Kenyan company received US Dollars 100,000. The money was converted into Kenya shillings in a bank, which buys and sells foreign currencies as follows

Buying selling

(in Kenya Shillings) (in Kenya Shillings)

1 US dollar 77.24 7.44

1 sterling pound 121.93 122.27

(a) Calculate the amount of money, in Kenya Shillings, the company received. (2 marks)

(b) The Company exchanged the Kenya Shillings calculated in (a) above, into sterling pounds to buy a car from Britain. Calculate the cost of the car to the nearest sterling pound. (2 marks)

15. Evaluate 27⅔ x ‾¼

(3 marks)

16. Use logarithm tables to evaluate

142.7 x 62.3

22.84 x 17.31 (3 marks)

17. A Cube has a volume of 13824cm3. Find the radius of a cylinder which has the same volume and height as the cube. (3 marks)

18. Use reciprocal tables to evaluate

8 - 7

0.375  37.5 (3 marks)

19. Carol borrowed shs.150,000.00. She paid back shs.25000 in the first month, shs15000 in the second month and shs.34000 in the third month. She paid the rest in equal amounts for two months. How much did she pay for each of the last two months? (3 marks)

20. If r = 0.272727……. Find 100r. Hence find 99r. Express r as a fraction.(3 marks)

21. Simplify

⅔ (12p + 9q - 15r) -3 (p + q – r) (3 marks)

22. Juma bought a used car at shs.500,000. He spent a further shs.75000 on it for repairs and modifications. He then sold it at 20% profit. How much did he get from this sale. (3 marks)

23. The sum of the interior angles of a polygon is 1440°

Find ;-

(a) the number of sides of the polygon (2 marks

(b) the exterior angle of the polygon (2 marks)

24. Simplify

(3  marks)

25. A straight line L1 has a gradient - ½ and passes through the point P(-1, 3). Another straight line L2 passes through the point Q(1,-3) and R(4,5).

Find

(a) The equation of L1 (2 marks)

(b) The gradient of L2 (1 mark)

(c) The equation of L2 (2 marks)

(d)  The co-ordinates of the point of intersection of L1 and L2 (2 marks)

(e)  The equation of a line through R parallel to L1 (2 marks)

(f)  The equation of a line passing through a point S(0,5) and perpendicular to L2 (2 marks)

26. Using a ruler and a pair of compasses only

(a) Construct a triangle ABC in which AB=9cm, AC=6cm and angle BAC=37 ½° (4 marks)

(b) Drop a perpendicular from c to meet AB at D. Measure CD and hence find the area of the triangle ABC (4 marks)

(c) Point E divides BC in the ratio 2:3. Using a ruler and set square only, determine E, measure AE (2 marks)

27. The boundaries PQ, QR, RS and SP of a ranch are straight lines such that : Q is 16km on a bearing of 040° from P. R is directly south of Q and east of P and S is 12km on a bearing of 120° from R.

(a)  Using a scale of 1cm to represent 2km, show the above information in a scale drawing.

(b)  From the scale drawing determine ;

(i) the distance, in kilometers of P from S (2 marks)

(ii) the bearing of P from S (2 marks)

(c) Calculate the area of the ranch PQRS in square kilometers. (3 marks)

28. The triangle P¹¹Q¹¹R¹¹ with vertices P¹¹ (-2,3) Q¹¹(-1,2) and R¹¹(-4,1) is the image of PQR under certain transformation

(a)  Draw P¹¹Q¹¹R¹¹ and PQR and describe fully the transformation which maps triangle PQR onto triangle P¹¹Q¹¹R¹¹. (2 marks)

(b)  On the same plane, draw triangle P¹Q¹R¹, the image of triangle PQR, under reflection in line y=-x (2 marks)

(c)  Describe fully the transformation which maps triangle P¹Q¹R¹ onto triangle P¹¹Q¹¹R¹¹ (2 marks)

(d)  Draw triangle P¹¹¹¹Q¹¹R¹¹¹ such that it can be mapped onto triangle PQR by a positive quarter turn about (0,0). (2 marks)

(e)  State all pairs of triangles that are oppositely congruent (2 marks)

29. (a) Solve the equation

125x + 1 + 53x = 630 (3 marks)

(b) The masses of two similar containers are 2000g and 250g. if the area of the base of the smaller container is 100cm². find the area of the base of the larger container. (3 marks)

(c)  The sides of a right angled triangle are xcm, (2x – 1)cm and (2x + 1)cm. Use this information to find the value of x (4 marks)

30. Using a ruler and pair of compasses only

(a)  construct triangle ABC in which line BC=8.8cm, line AB=7.4cm and line CA=6.8cm. (3 marks)

(b)  Locate point D on line AB which is equal distant from lines CB and CA. (2 marks)

(c)  Locate point E inside triangle ABC which AEC=90° (4 marks)

(d)  Measure line DE (1 mark)

NOTE: In addition to the above work please do Revision Exercise 1.1, 1.2 and 1.3 in Advancing in Mathematics Book 2, pages 68 to 72

1.  Printed questions

2.  Revision exercise 1-1 – 1.2 – Advancing in Maths Book 2

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