**SECTION I (50 Marks)**

- Use square roots, reciprocal and square root tables to evaluate to 4 significant figures the expression; (4 marks)

- Find the equation of the perpendicular bisector of line AB where A is (3, 9) and B (7, 5) giving your answer in the form ax+by+c = 0. (3 marks)

- It takes 40 road construction workers 8 days working 10 hours a day to complete a section of a road. How many days would 60 road construction workers working 8 hours a day take to complete the same section of the road working at the same rate? (3 marks)

- A solid cylinder with radius 7 cm and height 5 cm is melted down and recast into a spherical ball. Calculate to 2 decimal places the radius of the ball. (3 marks)

- The currency exchange rates of a given bank in Kenya are as follows;
Currency

Buying

Selling

1 Sterling pound

135.50

135.97

1 US dollar

72.23

72.65

- Find the value of n in 4
^{n+1}+2^{2n+1}= 384 . (3 marks)

- The exterior angle of a regular polygon is (x − 50)
^{0}and the interior angle is (2x+20)^{0}. Find the number of sides of the polygon. (3 marks)

- Find x if cos(3x − 30
^{0}) = sin(7x+50^{0}). (2 marks)

- The figure below shows the motion of a particle in 20 seconds. The particle starts off at a speed of 30 m/s and accelerates at 4 m/s
^{2}for 5 seconds. Calculate the total distance covered by the particle in 20 seconds. (4 marks)

- Construct triangle PQR such that PQ = 7 cm, QR = 5 cm and <RPQ = 30
^{0}. Construct the locus L_{1}of all points equidistant from P and Q to meet the locus L_{2}of points equidistant from Q and R at M. Measure PM. (4 marks)

- The surface areas of two cylindrical water tanks are 50 m
^{2}and 162 m^{2}Given that the volume of water in the second tank is 36 450 cm^{3}, find the volume of water in the first tank if it’s half full. (4 marks)

- Solve the inequalities below and represent the solutions on a single number line. (3 marks)

1-2x<5, 5-3x≥−10

- From the roof of a house, a boy can see an avocado tree which is 20 m away from the house. He measures the angle of elevation of the top of the tree as 21
^{0}and the angle of depression of the bottom of the tree as 31^{0}. Find the height of the avocado tree. (3 marks)

- Simplify (2 marks)

- The position vector of
**p**and**q**is 3i − 2j + k and 2i − j + 3k Determine the column vector PQ and hence calculate its length to 2 decimal places. (2 marks)

- The table below shows the height of 50 bean plants, six weeks after planting.
Height (h) in cm

Cumulative frequency

h≤4

4

h≤8

15

h≤12

31

h≤16

44

h≤20

50

**SECTION II (50 Marks)**

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