##### Mathematics Paper 2 Question Paper

### KCSE CLUSTER TESTS 23

#### Mathematics Paper 2

### SECTION I (50 Marks)

**Answer all questions in this section**

Ngurumo had Turkeys, Ducks and Hens in his farm. The number of Turkeys was 48. Turkeys were eight times the number of Ducks. The number of Hens was five times the sum of Turkeys and Ducks. If he sold 30% of the Hens, find the number of Hens that remained.

3 marks

Simplify the logarithmic expression

3 marks

Find the area of quadrilateral PQRS below.

4 marks

Make x the subject of the equation

3 marks

Given that Find the values of a, b

and c.

3 marks

Find the co-ordinates of point Q which divides line AB externally in the ratio 5: 2. Take the

position vectors of A and B to be

4 marks

Find the absolute error in the expression

given that the measurements of p, q and r are

7cm, 2.5cm and 1.25cm respectively. Give your answer correct to 4 significant figures

4 marks

Use Binomial coefficients to obtain the value of (1.01)^{5}, correct to five decimal places

3 marks

The area of a sector of a circle, radius 5.6cm, is 6.93cm The arc of the sector subtends an angle , at the centre of the circle. Find the value of in radians correct to 3 decimal places

2 marks

Wabwile bought a saloon car for Ksh 580,000. After 5 years, the value of the car was Ksh 365,000. Determine the rate of depreciation per annum, correct to one decimal place.

3 marks

Expand and simplify

2 marks

The cost C, of producing n items varies partly as n and partly as the inverse of n. To produce two items it costs ksh 135 and to produce three items it costs ksh 140. Find the cost of producing 10 items.

4 marks

Given that

3 marks

Simplify

3 marks

In the figure below, AB is a tangent to the circle centre O and radius 20cm. The area of triangle ABO is 360cm2 and OCB is a straight line. Find the length of CB.

3 marks

. Tap P can fill an empty water tank in 3 hours while tap Q can fill the same tank in 6 hours. When the tank is full, it can be emptied by tap R in 8 hours. Tap P and Q are opened at the same time when the tank is empty. If one hour later, tap R is opened, find the total time taken to fill the tank

3 marks

### SECTION II (50 Marks)

**Answer only five questions**

An employee earns a basic salary of Ksh 28500 and is also given taxable allowance amounting to Ksh 11980.

The table of taxation is shown below.

Calculate

a) Taxable income for the employee

b) Total tax paid by the employee.

c) If the employee receives a 50% increase in his total income, calculate the corresponding percentage increase on taxes.

10 marks

. In the figure below, AB is parallel to CD. The lines AD and CB intersect at M. CB =12cm, CB : MB = 1:3, angle BAM = 38^{0 }and angle CMD = 75^{0 }

a) Find the length of MB.

b) Determine, the correct to 4 significant figures

i) The perpendicular distance between AB and CD.

ii) the length of MD.

c) Using the cosine rule, find the length of CD correct to 2 significant figures.

d) Calculate, correct to one decimal place, the area of triangle CDM.

10 marks

Kiprono is training to run in long distance races. In the first week he runs 50km and he intends to increase this speed by 10% each week.

a) Calculate how far he should run in the second week.

b) Show that the distance he runs each week form a geometric series, then list down the first four terms of the series. `

c) Find to the nearest kilometer, the total distance that he should run during the first 10 weeks.

10 marks

In the figure below OWJKL is a parallelogram in which

a) If A is a point on LK such that and a point B divides the line JK externally in the ratio 3 :1, express OB and AJ in terms of p and r.

b) Line OB intersects AJ at X such that OX = mOB and AX= nAJ.

i) Express OX in terms of p, r and m

ii) Express Ox in terms of p, r and n.

iii) Determine the values of m and n and hence the ratio in which point x divides line AJ.

10 marks

The circle given by equation passes through point (-3, -1).

Determine

a) The value of h.

b) The co-ordinates of the centre of the circle

c) The radius of the circle.

d) The co-ordinates of the other end of the diameter that passes through point (-3, -1)

10 marks

On a given day, the probability that it is windy is

3/5

. When it is windy, the probability that a kite

that is flown sticks on a tree is

3/4

, otherwise it is

1/5

.

a) Represent this information on a tree diagram.

b) Find the probability that the: i) Kite is flown on a windy day.

ii) Kite is flown

iii) Kite is not flown

10 marks

a) Complete the table below for the function

b) On the grid provided, draw the graph of

c) Use your graph to find the values of x which satisfy the simultaneous equations:

d) Write down and simplify a quadratic equation which is satisfied by the values of x where the graphs in (c) above intersect.

Use your graph in (b) above to solve:

10 marks

In the figure below, A, B,C and D are points on the circle centre O. ACT and SDTU are straight lines. Line SDTU is a tangent to the circle at D, angle CDT = 40^{0} and angle CTU =160^{0 }

10 marks