**SECTION I** (50 marks)

*Answer all the questions in this section in the spaces provided.*

1. The length and width of a rectangular piece of paper were measured as 60 cm and 12 cm respectively. Determine the relative error in the calculation of its area. (4 marks)

2. Simplify

(2 marks)

3. An arc ll cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle. (4 marks)

4. In the ﬁgure below, O is the centre of the circle. A, B, C and D are points on the circumference of the circle. Line AB is parallel to line DC and angle ADC = 55°.

Determine the size of angle ACB. (3 marks)

5. Eleven people can complete of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate can take to complete the remaining job. (3 marks)

6 The length and width of a rectangular signboard are (3x +12) cm and (x — 4) cm respectively. If the diagonal of the signboard is 200 cm, determine its area. (4 marks)

8. Use the expansion of (x — y)5 to evaluate (9.8)5 correct to 4 decimal places. (3 marks)

9. The diameter of a circle, centre O has its end points at M(— 1, 6) and N(5, —2). Find the equation of the circle in the form x2 + yl + ax + by = c where a, b and c are constants. (4 marks)

Find the value of x given that log (x — 1) + 2 = log (3x + 2) + log 25. (3 marks)

10. Below is a line AB and a point X. Determine the locus of a point P equidistant from points A and B and 4 cm from X.(3 marks)

11. In a nomination for a committee, two people were to be selected at random ﬁ’0m a group of 3 men and 5 women. Find the probability that a man and a woman were selected. (2 marks)

12. A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. (4 marks)

13. Evaluate

(3 marks)

14. The positions of two points P and Q, on the surface of the earth are P(45 °N, 36 °E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place. (3 marks)

15. Solve the equation sin (½x — 30°) = cos x for 0 < x < 90°. (2 marks)

16. The position vectors of points P, Q and R are

Show that P, Q and R are collinear. (3 marks)

**SECTION II **(50 marks)

*Answer any ﬁve questions from this section in the spaces provided.*

17. In a retail shop, the marked price of a cooker Was Ksh 36 000. Wanandi bought the cooker on hire purchase tenns. She paid Ksh 6400 as deposit followed by 20 equal monthly instalments of Ksh 1750.

(a) Calculate:

(i) the total amount of money she paid for the cooker. (2 marks)

(ii) the extra amount of money she paid above the marked price. (l mark)

(b) The total amount of money paid on hire purchase terms was calculated at a compound interest rate on the marked price for 20 months. Determine the rate, per annum, of the compound interest correct to 1 decimal place. (4 marks)

(c) Kaloki borrowed Ksh 36 000 from a ﬁnancial institution to purchase a similar cooker. The ﬁnancial institution charged a compound interest rate equal to the rate in (b) above for 24 months. Calculate the interest Kaloki paid correct to the nearest shilling. (3 marks)

18. Mute cycled to raise funds for a charitable organisation. On the ﬁrst day, he cycled 40 km. For the ﬁrst 10 days, he cycled 3 km less on each subsequent day. Thereafter, he cycled 2 km less on each subsequent day.

(a) Calculate:

(i) the distance cycled on the 10th day; (2 marks)

(ii) the distance cycled on the 16th day. (3 marks)

(b) If Mute raised Ksh 200 per km, calculate the amount of money collected. (5 marks)

19. The equation of a curve is given by y = 1 + 3 sin x. (a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place (2 marks)

(b) (i) On the grid provided, draw the graph of (3 marks)

(ii)State the amplitude of the curve y = 1 + 3 sin x. (1 mark)

(d) Use the graphs to solve the equation (l mark)

(c) On the same grid draw the graph of y = tan x for 90° 5x 5 270° (3 marks)

20. The ﬁgure below represents a cuboid EFGHJKLM in which EF = 40 cm, FG = 9 cm and GM = 30 cm. N is the midpoint of LM.

Calculate correct to 4 signiﬁcant ﬁgures:

(a) the length of GL; (1 mark)

(b) the length of F]; (2 marks)

(c) the angle between EM and the plane EFGH; (3 marks)

(d) the angle between the planes EFGH and ENH; (2 marks)

(e) the angle between the lines EH and GL. (2 marks)

21. A quantity P varies partly as the square of m and partly as n. When P = 3.8, m = 2 and n = -3. When P = -0.2,m = 3 and n = 2.

(a) Find:

(i) the equation that connects P, m and n; (4 marks)

(ii) the value of P when m = 10 and n = 4. (1 mark)

(b) Express m in terms of P and n. (2 marks)

(c) If P and n are each increased by 10%, ﬁnd the percentage increase in m correct to 2 decimal places. (3 marks)

22. A particle was moving along a straight line. The acceleration of the particle after t seconds was given by . The initial velocity of the particle was 7 .

Find:

(a) the velocity (v) of the paiticle at any given time (t); (4 marks)

(b) the maximum velocity of the particle; (3 marks)

(c) the distance covered by the particle by the time it attained maximum velocity. (3 marks)

23. The marks scored by 40 students in a mathematics test were as shown in the table below.

(a) Find the lower class boundary of the modal class. (1 mark)

(b) Using an assumed mean of 64, calculate the mean mark. (3 marks)

(C) (i) On the grid provided, draw the cumulative frequency curve for the data. (3 marks)

(ii) use the graph to estimate the semi—interquartile range (3 marks)

24. A quadrilateral with vertices at K(1, 1), L(4, 1), M(2, 3) and N(1, 3) is transformed by a matrix

to quadrilateral K’L’M’N’

(a) Determine the coordinates of the image (3 marks)

(b) On the grid provided draw the object and the image. (2 marks)

(c) (i) Describe fully the transformation which maps KLMN onto K’ L’ M’N’. (2 marks)

(ii) Determine the area of the image; (1 mark)

(d) Find a matrix which maps K’ L’M’N’ onto KLMN. (2 marks)