##### Mathematics Paper 2 Question Paper

### KCSE CLUSTER TESTS 20

#### Mathematics Paper 2

### SECTION I (50 Marks)

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

Use logarithm tables only to evaluate

4 marks

Make x the subject of the equation

3 marks

Two brands of dairy meal A and B cost ksh 720 and ksh 864 per 70kg bag respectively. An animal feed dealer mixes the two brands and sells the mixture at sh. 1008 per 70kg bag, making a profit of 20%. Find the ratio in which he mixes them.

3 marks

Solve for x :-

2 marks

Solve for x in the equation :-

4 marks

R divides PQ for P(3,2,4) and Q(1,-1,0) in the ratio 1:2 . Find the co-ordinate of R.

2 marks

The gradient function of a curve is given by

Determine,

a) the equation of the curve given that it passes through the point (0,5) (2mks)

b) the co-ordinates of the turning point of the curve. (2mks)

4 marks

Find the equation of a circle whose diameter has the end points (-2,5) and (4,1)

4 marks

Using the figure below, answer the questions that follows.

a) Construct the locus of the points inside the triangle that are equidistant from PR and QR (1mk)

b) Construct the locus of the points inside the triangle that are 4cm from Q (1mk)

c) A point K is nearer to PR than to RQ, and not more than 4cm from Q. Shade the region within which K can be found (1mk)

4 marks

The data below shows the ages of 10 students picked at random in a secondary school 6,11,13,14,8,7,12,20,P and 9. If âˆ‘f^{x2}=1360. Determine the value of P, hence find the standard deviation to 2 decimal places.

3 marks

Find the percentage error in evaluating

4 marks

The period of a function of the form

2 marks

(1 mark)

b) Use your expansion in (a) above to estimate the values of (2.01)^{6} to 4 decimal places. (2mks)

3 marks

Find the shortest distance between X(0^{0},16^{0}W) and Y(0^{0},20^{0}E) in kilometers

3 marks

Simplify:-

3 marks

A plot of land was valued at Ksh. 150,000 at the start of 1994. It appreciated by 25% during 1994. Thereafter, every year, it appreciated by 15% of its previous yearâ€™s value. Find

a) the value of land at the start of 1995 (1mk)

b) the value of land at the end of 1997 (2mks)

3 marks

### SECTION II (50 Marks)

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

The density of juice and water are 2g/cm^{3} and 1g/cm^{3} respectively. Passion fruit drink is prepared by mixing the juice and water to give a suspension of density 1.5g/cm^{3}

a) If the volume of a glass of passion fruit juice made is Â½ litre and is sold for sh.10 and that the juice was served to 100 people; a glass per person. Find the profit made on this day if the cost of a litre of juice is ksh.15. (Assume that no cost for water and sugar used in the passion fruit preparation) (6mks)

b) If the total cost of producing a glass of passion fruit drink, water juice and labour is considered is to be sh. 7.50, what is the cost of the sugar in the glass. (1mk)

c) A patient was required by his doctor to take a litre of passion fruit drink whose ratio of juice to water is 3:2. What is the density of the drink? (3mks)

10 marks

Complete the table below, giving the values correct to 2 decimal places.

10 marks

a) A quantity C varies partly as x^{2} and partly as x when x=1, c=4 and when x=2, c=6.

i) Find the equation connecting c and x. (4mks)

ii) Find the value of x if c=6 (3 mks)

iii) A variable P varies inversely as square root of Q and directly as the square of R. If Q is increased by 44% and R decreased by 40%, determine the percentage change in P and state the nature of the change. (3 mks)

10 marks

A school organized inter house ball game competition in football, volleyball and basket ball among other games. The probability of a house winning in football was found to be

. If it won or lost in football then the probability of winning in volleyball is

. If a

team lost in volleyball, then it would win in basket ball with a probability of

, but if it

wins in volleyball then the probability of winning basket ball is

a) Show the above information on a tree diagram. (2mks)

b) Use the tree diagram to calculate the probability that:-

i) A house won all the three games (2mks)

ii) A house lost in atmost two games (2mks)

iii) A house won two games (2mks)

iv) A house lost all the three games (2 mks)

10 marks

The table shows the marks scored by some candidates in a mathematics test.

a) Using the information above, draw a cumulative frequency curve. (4mks)

b) Use your graph to estimate

i) Median (1mk)

ii) The semi-interquartile range (3mks)

iii) the pass mark if 40% of the candidates failed. (1mk)

iv) the probability of candidates being between 43.5 marks and 68 marks. (1mk)

10 marks

The figure below shows a pyramid VABCD with a square base of 8cm and each of its slanting edges 12cm long. O is the centre of the base. Calculate:

a) the length OB (2mks)

b) the height VO (2mks)

c) the angle between VB and the base (2mks)

d) the angle between the plane VAB and the base (2mks)

e) the angle between the planes VBC and VAD (2mks)

10 marks

The 2nd , 4th and 7th terms of an A.P are the first 3 consecutive terms of a G.P. Find:

a) common ratio (4mks)

b) the sum of the first 10 terms of:

i) the G.P if the common difference of the A.P is 2. (4mks)

ii) the arithmetic progression (AP) (2mks)

10 marks

A particle moves in a straight line between two points P and Q such that the velocity V in t seconds from P is given by V=ht-t^{2} When t=6 the particle is at rest momentarily at Q.

i) Find the value of h (2mks)

ii) Find the distance between P and Q (3mks)

iii) Find the average speed of the particle between P and Q (2mks)

iv) Find the acceleration of the particle at P (3mks)

10 marks