**SECTION I** (50 marks)

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

- Without using a calculator evaluate, (3marks)

- Simplify (4 marks)

- The external length, width and height of an open rectangular container are 41 cm, 21cm and 15.5 cm respectively. The thickness of the materials making the container is 5 mm. If the container has 8 litres of water, calculate the internal height above the water level. (4 marks)

- The figure below shows a net of a solid (measurements are in centimetres).

Below is a part of the sketch of the solid whose net is shown above. Complete the sketch of the solid, showing the hidden edges with broken lines. (3 marks)

- Given that OA = 2i + 3j and OB = 3i — 2j, find the magnitude of AB to one decimal place. (3 marks)

- A bus travelling at an average speed of 63 km/h left a station at 8:15 a.m. A car later left the same station at 9:00 a.m. and caught up with the bus at 10:45 a.m. Find the average speed of the car. (3 marks)

- Given that x is an acute angle and cos x
^{°}=^{ 2}/_{5}√5 find, without using mathematical tables or a calculator, tan (90 — x)°. (2 marks)

- Without using mathematical tables or a calculator, evaluate (3 marks)

- A minor arc of a circle subtends an angle of 105° at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc. (Take π it = 22/7). (3 marks)

- The gradient of the tangent to the curve y= — ax
^{3}+ bx at the point (1,1) is —5. Calculate the values of a and b. (4 marks)

- A line with gradient of —3 passes through the points (3, k) and (k, 8). Find the value of k and hence express the equation of theline in the form ax + by — c, where a, b and c are constants. (3 marks)

- Points L and M are equidistant from another point K. The bearing of L from K is 330°. The bearing of M from K is 220°. Calculate the bearing of M from L. (3 marks)

- In this question, mathematical tables should not be used.

A Kenyan bank buys and sells foreign currencies as shown below:

A tourist arrived in Kenya with 105 000 Hong Kong Dollars and changed the whole amount to Kenya Shillings. While in Kenya, she spent Sh 403 879 and changed the balance to South African Rands before leaving for South Africa. Calculate the amount in South African Rand, that she received. (3 marks)

- A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm3, find the volume of the frustum. (3 marks)

- The production of milk, in litres, of 14 cows on a certain day was recorded as follows:

22, 26, 15, 19, 20, 16, 27, 15, 19, 22, 21, 20, 22 and 28.

Determine:- the mode: (1 mark)
- the median. (2 marks)

- Given that Log 4 = 0.6021 and Log 6 = 0.7782, without using mathematical tables or a calculator, evaluate log 0.096. (3 marks)

**SECTION II** (50 marks)