Write the expression below in surd form and rationalize the denominator.

State the centre and the radius of the given equation of a circle.
x² – 6x + y² + 10y + 25 = 0

Evaluate

Find the standard deviation of the given data.

Marks out of 20	1 - 5	6 - 10	11 - 15	16 - 20
No.of students	3	7	6	4

Find the inverse of hence solve the simultaneous equations.

2x + 5y = 34
x + 2y = 21

The first four terms of a GP are 81, m, n, 3. Find the values of m and n.

Five people can build four huts in 28 days. Find the number of people working at the same rate that will build 10 similar huts in 16 days.

In the figure below ABCDE, AB = 2.5cm, AE = 10cm, ED = 5.2cm and DC = 6.9cm. Construct the locus of points equidistant from CD and CB.

Use 6371 km for the radius of the earth.
Find the distance from A (45^oN, 63^oW) to C (45^oN, 107^oE) in:
i) km (4 marks)

ii) nm (3 marks)

Two pilots X and Y started from A at the same time. X flew to C at a speed of 600km/h while
Y flew to B(60S,630W) at a speed of 400km/h. Who arrived first at their destination and by how
many hours? (4 marks)

a) Using a ruler and a pair of compass only, construct a triangle LMN where LM = 8cm,
MN = 6cm and LMN = 37.50. (3 marks)

b) i) Mark the two points P1 and P2 which are 5cm from M and equidistant from LN and LM.

(3 marks)
ii) Q is inside triangle LMN such that its distance from M is less than 5cm and it is nearer
to LN than to LM. Shade the region in which Q must lie. (4 marks)

a) x varies as the cube of y and inversely as the square root of z, and x = 6 when y = 3 and z = 35.
i) Find the equation connecting x, y and z. (2 marks)

ii) Find x when y = 7 and z = 9. (2 marks)

Find y when x = 8 and z = 16 (2 marks)

b) If y is increased by 20% and z decreased by 36%, find the % increase in x. (4 marks)

A married couple intends to have 3 children. They consult an expert who tells them that the probability of a male birth is 0.6.
(a) Draw a tree diagram to represent this occurrence. (2 marks)

(b) Find the probability that:
i) All the three children will be female. (2 marks)

ii) At least a male is born. (2 marks)

iii) At least 2 will be females. (4 marks)

The table below shows the analysis of examination marks scored by 160 candidates.

(b)Draw a cumulative frequency curve for the data. (4 marks)

(b) State the modal class. (1 mark)

(c) Use the graph to estimate:
(i)The quartile deviation.

(ii)How many candidates passed if a mark of 35% and above was a pass? (2 marks)

a) Complete the table below for y = sin 2x and y = (2x + 30⁰) giving values to 2dp.

b) Draw the graph of y = 2x and y = (2x + 30⁰) on the same axis. (4 marks)

c) Use your graph to solve sin (2x + 30⁰) – sin 2x = 0 (1 mark)

d) Describe the transformation which maps the wave sin 2x onto the wave of sin (2x + 30) (2 marks)

e) State the amplitude and period of y = a cos (bx + c) (1 mark)

Use the taxation rates table below to answer the questions that follow.

Taxable income in K£p.a	Rate % per K£
1 – 4500 4501 – 7500 7501 – 10500 10501 – 13500 13501 – 16500 Over 16500	10 15 20 25 30 40

A civil servant is entitled to a monthly personal relief of Ksh. 3000 and her tax (PAYE) is ksh. 9000 per month. She is deducted NHIF ksh. 350 per month. WCPS ksh. 800 and co-op shares ksh. 1200 per month. Calculate:
(a) The civil servant’s total deduction per month. (1 mark)

(b) Total tax per month. (1 mark)

(c) The civil servant’s annual gross salary (6 marks)

(d) The civil servant’s basic salary if her monthly house allowance and medical allowances are ksh.10000 and ksh. 2000 respectively. (2 marks)

An electronics dealer in Wote town wishes to purchase radios and TV sets. He can buy at most 30 of both items. On average, a radio and TV cost sh. 4000 and sh. 12000 respectively and he has sh. 240000 to spend. The number of TV sets should be at most twice the number of radios. He must buy more than 5 TV sets.
(a) Form all inequalities to represent above information. (4 marks)

(b) Graph the inequalities in (a) above. (4 marks)

(c) If the dealer makes a profit of sh.600 and sh.1000 per radio and TV set respectively, find the maximum possible profit. (2 marks)