Evaluate:

The average lap time for 3 athletes in a long distance race is 36 seconds, 40 seconds and 48 seconds
respectively. If they all start the race at the same time, find the number of times the slowest runner
will have been overlapped by the fastest at the time they all cross the starting point together again.

Kamau toured Switerland from Germany. In Switzerland he bought his wife a present worth
72 Deutsche marks. Find the value of the present in
(a) Swiss Francs.
(b) Kenya shillings correct to the nearest sh, if
1 Swiss Franc = 1.25 Deutsche marks
1 Swiss Franc = 48.2 Kenya shillings

The equation of line AB in the figure below is y = 3 + 5 and A is the point (0, a). Line PQ is
parallel to AB and AP = 7 units.

(i) Find the value of a. (1mk)
(ii) Write down the equation of PQ.

Solve the equation 2x² + 3x = 5 by completing the square method.

Given that . Find the values of a, b and c.

The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number
is greater than the fourth by 8. Find the fifth number.

Show that the points P(3, 4), Q(4, 3) and R(1, 6) are collinear.

Solve the inequalities hence represent the solution on a number line.

Use the tables of squares, square roots and reciprocals only to find the value of

A circle of radius 7 units has it’s centre at the point of intersection between the lines
 x+ 2y + 1 = 0 and 2x + 3y – 3 = 0. Find the equation of the circle expressing it in the
form x² + y² + yx + fy + c = 0.

The gradient of a curve at any point (, y) is given by 3x² + 2. If the curve passes through
the point (-2, 1). Find its equation.

A solid metal cylinder with radius 7cm and height 5cm is melted down and recast into a spherical
ball. Calculate to 1 decimal place the surface area of this ball.

Sketch and label the net of the prism shown below.

The volume of two similar solid spheres are 4752cm³ and 1408cm³. If the surface area of the
small sphere is 352cm², find the surface area of the larger sphere.

A carpenter constructed a closed wooden box with internal measurements 1.5 metres long, 0.8
metres wide and 0.4 metres high. The wood used in constructing the box was 1.0cm thick and
has a density of 0.6g/cm³.
Determine the:
(i) volume in cm³ of the wood used in constructing the box. (3mks)
(ii) mass of the box in kilograms correct to 1 decimal place. (1mk)

Two aeroplanes, T and S leave an airport A at the same time. S flies on a bearing of 060ï‚° at
750km/h while T flies on a bearing of 210ï‚° at 900 km/h.
(a) Use a suitable scale, to draw a diagram showing the relative position of the aeroplanes
after two hours. (3mks)
(b) Use your diagram to determine:
(i) the distance between the two aeroplanes. (2mks)
(ii) the bearing of T from S. (1mk)
(c) Aeroplane T later flew to the East at the same speed for one hour. Show its final position
on the diagram in (a) above.
Determine:
(i) Its final distance from A. (2mks)
(ii) Its final bearing from S. (1mk)

The table below shows the income tax rates for a certain year.

That year Kazembe paid net tax of Ksh.5,512 per month. His total monthly taxable allowances
amounted to Ksh.15,220 and he was entitled to a monthly personal relief of Ksh.1,162.
Every month the following deductions were made:

- NHIF – Ksh. 320
- Union dues – Ksh.200
- Co-operative shares – Ksh.7,500
(a) Calculate Kazembe’s monthly basic salary in Ksh. (7mks)
(b) Calculate his monthly net salary. (3mks)

(a) On the grid provided below, draw the graph of y = (x + 4)(1 - 2x) for the range -5 < x < 2. (4mks)

(b) On the same grid draw the line y + 3x = 2. (2mks)

(c) Use your graph to solve the equations:
(i) (x + 4)(1 - 2x) = -5 (2mks)
(ii) -2 - 4x - 2x² = 0 (2mks)

A tetrahedron has equilateral triangular base ABC of side 10cm. The vertex V is such that
VA = VB = VC = 8cm. Calculate.
(a) The angle between the planes ABC and BCV. (5mks)
(b) The vertical height of the vertex V above the base ABC. (2mks)
(c) Volume of the tetrahedron. (3mks)

In the given figure, CAD = 50^o, BEC = 75^o and BDC = 25^o. BAF is a straight line.

Giving reasons where necessary, calculate the size of:-
(i) ∠ABC. (2mks)
(ii) ∠DEC. (2mks)
(iii) ∠ABD. (3mks)
(iv) ∠DAF. (3mks)

A bag contains 5 red, 4 white and 3 blue beads. Two beads are selected at random one after
another without replacement.
(a) Draw a tree diagram and show the probability space. (2mks)

(b) From the tree diagram, find the probability that:
(i) The last bead selected is red. (3mks)
(ii) The beads selected were of the same colour. (2mks)
(iii) At least one of selected beads is blue. (3mks)

A transformation represented by the matrix maps the points A(0, 0), B(2, 0), C(2, 3) and
D(0, 3) of the quad ABCD onto A¹B¹C¹D¹ respectively.
(a) Draw the quadrilateral ABCD and its image A¹B¹C¹D¹. (3mks)
(b) Hence or otherwise determine the area of A¹B¹C¹D¹. (2mks)
(c) Another transformation maps A¹B¹C¹D¹ onto A¹¹B¹¹C¹¹D¹¹.
Draw the image A¹¹B¹¹C¹¹D¹¹. (2mks)
(d) Determine the single matrix which maps A¹¹B¹¹C¹¹D¹¹ back to ABCD. (3mks)

The distance from town A to town B is 360km. A bus left town A and traveled towards town B
at an average speed of 60km/h. After 1½ hours, a car left town A and traveled along the same
road at an average speed of 100km/h.
(a) (Determine
(i) The distance of the bus from town A when the car took off. (2mks)
(ii) The distance the car traveled to catch up with the bus. (4mks)
(b) The distance from P to Q is 160km. If an express train was 16km/h slower it would take
20 minutes longer on the journey. Find the average speed of the express train. (4mks)