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Mathematics Paper 2

SECTION A (50 Marks)

Answer all the questions

Using logarithms evaluate

4 marks


are the solutions of a quadratic equation. Write the equation in the form

3 marks


A student correctedDetermine the percentage error in the estimation.

3 marks


The figure below represents a scale drawing of a rectangular piece of land, RSTU. RS=18cm and ST=14cm.

An electric post P, is to be erected inside the piece of land. On the scale drawing, shade the possible region in which P would lie such that PU> PT and PS = 14cm.

3 marks


Two points A and B have coordinates (-2, 3) and (1, 3) respectively. A translation maps point A to A’(10,10). a) Find the coordinates of B’, the image of B under the translation.

2 marks


Solve the inequalityand show the solution on a number line.

3 marks


Without using tables evaluate

3 marks


Konango invested Ksh 8000 compounded quarterly at a rate of r% p.a. The value of the money after 2 ¼ years is Kshs 18000. Determine the value of r.

3 marks


The figure below shows a circle with chords AB and CD produced and meeting externally at T. Chords AD and BC intersect internally at x. If BT= 4cm, AB=2cm and DT=3cm

a) Find CT

b) Show that triangles ADT and CBT are similar.

3 marks



4 marks


Make P the subject of the formula

3 marks


A varies as a constant and partly inversely as the cube root of P. When A=8, P=8, when A=7, P= 27. Find the law connecting A and P Hence find A when P=125.

3 marks


a) Expand

b) Use your expansion to give the coefficient of

3 marks


The table below shows values of x and y for the function

a) On the grid provided, Draw the graph of

b) From the graph determine the period.

3 marks

SECTION B (50 Marks)


The table below shows income tax rates for all income earned.

Owenga pays a monthly tax of Kshs 4600. His monthly relief is Ksh 1200. He gets medical allowance of Ksh 3500 monthly. He is housed by the employer and pays a nominal rent of Ksh.960 per month.


a) His gross tax per annum.

b) His taxable income in Kshs. per month.

c) His basic salary per month in Kshs.

10 marks


The diagram below shows the speed- time for a train travelling between two stations. The train starts from rest and accelerates uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds.

Given that the distance between the two stations is 10450m, calculate the;

a) Maximum speed , Km/h, the train attained;

b) Acceleration;

c) Distance the train travelled during the last 100 seconds;

d) Time the train takes to travel the first half of the journey.

10 marks


a) Draw a tree diagram to represent the information.

b) Find the probability that i) A student goes to school by bus.

ii) A student is late for school.

iii) A student walks to school and arrives in time.

10 marks


b) A plane leaves A going to B and takes 5 hours to arrive at B travelling along a parallel of latitude at 400km/hr. Find

i) the maximum time the plane could have taken to travel from A to B.

ii) the radius of the circle of latitude on which towns A and B are situated.

iii) The latitude of the two towns

10 marks


A water vendor has a tank of capacity 18,900 litres. The tank is being filled with water from two pipes A and B which are closed immediately when the tank is full. Water flows at the rate of 150000cm3/ minute through pipe B.

a) If the tank is empty and the two pipes are opened at the same time, calculate the time it takes to fill the tank.

b) On a certain day the vendor opened the two pipes A and B to fill the empty tank. After 25 minutes he opened the outlet tap to supply water to his customers at an average rate of 20 litres per minute.

i) Calculate the time it took to fill the tank on that day.

ii) The vendor supplied a total of 542 jerricans, each containing 25 litres of water, on that day. If the water that remained in the tank was 6 300 litres, calculate, in litres, the amount of water that was wasted.

10 marks


The table below shows the marks scored by students in a chemistry exam.

a) Calculate the interquartile range

b) Using an assumed mean of 47;

i) Determine the variance of the distribution.

ii) Hence determine the standard deviation.

10 marks


The product of the first three terms of a geometric progression is 64. If the first term is a, and the common ratio is r.

a) Express r in terms of a.

b) Given that the sum of the three terms is 14

i) Find the values of a and r and hence write down two possible sequences each up to the 4th term

10 marks


a) Draw a graph of

b) Estimate the area bounded by the y-axis and the line x=4 using trapezium rule with 8 trapezia.

c) Determine the actual area by integration.

d) Calculate the error in the area obtained by applying the trapezoidal rule.

10 marks

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