**SECTION I** (50 MARKS)

** **Answer ALL the questions from this section.

- Find the reciprocals of 0.216 correct to 3 decimal places hence evaluate; (3 marks)

- Without using a calculator, evaluate; (4 marks)

- Three bells ring at intervals of 9 minutes, 15 minutes and 21 minutes. The bells will next ring together at 11.00pm. Find the time the bells had last rang together. (3 marks)

- Simplify the expression. (3 marks)

- Without using a calculator or mathematical tables, solve the equation. (4 marks)

2log_{10}x−3log_{10}2+log_{10}32=2

- A line L passes through point (3, 1) and is perpendicular to the line 2y = 4x + 5.

Determine the equation of line L. (3 marks)

- A forex bureau in Kenya buys and sells foreign currencies as shown below.
Buying Selling Currency Ksh Ksh Chinese Yuan 12.34 12.35 South African rand 11.28 11.37 - Calculate the amount of money in Kenya shillings that she received. (1 mark)
- While in Kenya, the businesswoman spent Ksh.1,258,000 and then converted the balance into South African Rand. Calculate the amount of money to the nearest Rand that she received. (3 marks)

- The seventh term of an A.P is 20 and the sum of the first 20 terms is 610. Find the first term and the common difference. (3 marks)
- The points P, Q and R lie on a straight line. The position vectors of P and R are 2
*i*+ 3*j*+ 13k and 5*i*– 3*j*+ 4k respectively. Q divides PR internally in the ratio 2 : 1. Find- The position vector of Q. (2 marks)
- Distance of Q from the origin. (1 mark)

- In the figure below, <MNO = 54
^{o}, <PLM = 50^{o}, PN = NM and PO is parallel to LM.

Find the value of <LPM.

(3 marks)

- Two matrices A and B are such that

and Given that the determinant of AB = 10, find the value of k. (3 marks)

- Two pipes A and B can fill an empty tank in 3 hours and 5 hours respectively. Pipe C can empty the full tank in 4 hours. If the three pipes A, B and C are opened at the same time, find how long they will take to fill the tank. (3 marks)
- Determine the equation of the normal to the curve y = x
^{2}– 3x + 1 at a point (−2, 3) giving your answer in the form ax + by = c. (3 marks)

- The size of each interior angle of a regular polygon is five times the size of exterior angle.

Find the number of sides of the regular polygon. (3 marks) - Find the integral values of x which satisfy the inequalities.

x + 8>4x – 6≥3(4 – x) (2 marks) - John had two bags A and B containing sugar. If he removed 2kg from bag A and added to bag B, the mass of sugar in bag B would be four times the mass of sugar in bag A. If he added 10kg of sugar to the original amount of sugar in each bag, the mass of sugar in B would be twice the mass of the sugar in bag A.

Calculate the original mass of sugar in each bag. (3 marks)

**SECTION II** (50 MARKS)

*Answer any FIVE questions from this section*

- The table below shows the height measured to the nearest cm of 101 pawpaw trees.
Height in cm 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 Frequency 2 15 18 25 30 6 3 2 - State the modal class. (1 mark)
- Calculate to 2 decimal places.
- The mean height (4 marks)
- The difference between the mean height and the median height. (5 marks)

- Three pegs R, S and T are on the vertices of a triangular plan field. R is 300m from S on a bearing of 300
^{o}and T is 450m directly South of R.- Using a scale of 1cm to represent 60m, draw a diagram to show the position of the pegs. (3 marks)

- Use the scale drawing to determine;
- The distance between T and S in metres. (2 marks)
- The bearing of T from S. (1 mark)

- Find the area of the field in hectares correct to one decimal place. (4 marks)

- Using a scale of 1cm to represent 60m, draw a diagram to show the position of the pegs. (3 marks)
- Mr. Mutuku owns a bicycle which he sometimes rides to go to work. Out of 21 working days in a month he only rides to work for 18 days. If he rides to work the probability that he is bitten by a rabid dog is
^{4}/_{15}otherwise it is^{1}/_{13}only. When he is bitten by the dog, the probability that he will get treatment is^{4}/_{5}and if he does not get treatment the probability that he will get rabies is^{5}/_{7}- Draw a tree diagram to show the events. (3 marks)
- Using the tree diagram above determine the probability that
- Mutuku will not be bitten by a rabid dog. (2 marks)
- He will get rabies. (2 marks)
- He will not get rabies. (3 marks)