##### Mathematics Paper 1 Question Paper

### KCSE CLUSTER TESTS 25

#### Mathematics Paper 1

### SECTION A (50 Marks)

Evaluate without using tables or a calculator. Leave your answer as a fraction in its simplest.

3 marks

a) Find the LCM of

b) hence simplify

4 marks

Find the value of

10 marks

Solve the inequality and show the solution on the number line.

3 marks

Given that x is an acute angle and find without using tables or a

calculator tan

3 marks

The seven digit number 51y3183 is divisible by 11. Find the smallest value of y.

2 marks

The sum of all but one of the internal angles of a pentagon is Find the size of the remaining angle.

2 marks

Mariga on arrival in Kenya to play for his country converted 5000 euros into Ksh. During his three days stay he spent Ksh.250,000 and converted the remaining amount into U.S dollars. How many dollars did he get?

2 marks

Kutu withdrew some money from a bank. He spent of the money to pay for Mutua’s school fees and of the remainder on electricity and water bills. If the rest, which amounted to Ksh. 12330 was for food and savings, calculate the amount withdrawn from the bank.

3 marks

A triangle ABC whose vertices are A(1,1), B(4,1) and C(1,3) is rotated about (1,2) through .Find the coordinates of the image

2 marks

A cylindrical iron pipe is 2.1m long and 12cm in external diameter. The metal is 1cm thick and has a density 7.8g/cm3 .Taking pie as

4 marks

A two digit number is such that the difference between the ones digit and the tens digit is 2. If the two digits are interchanged, the sum of the new and original numbers is 132. Find the original number.

4 marks

The figure below shows a histogram.

4 marks

Construct a line PQ 7.5cm. Using a line inclined at at point P1 locate point R on PQ which divides line PQ in the ratio 2:3

3 marks

A father was three times as old as his son fifteen years ago and four times as old as his son nineteen years ago. What are their ages now?

4 marks

The position vectors of points A and B are respectively. Determine modulus

of AB if

3 marks

### SECTION B (50 Marks)

**Answer only five questions**

Amani, Umoja and Maendeleo contributed a total of Ksh. 8,041,950 for their joint campaigns a head of the 2013 general elections. The ratio of their contributions were Amani to Umoja 5:4 and Maendeleo to Umoja 2:3

a) How much did each contribute.

b) Amani further contributed Sh.875,000 towards the coalition kitty. In response, Umoja and Maendeleo increased their contributions in the ratios 10:9 and 11:6 respectively. How much more did Umoja and Maendeleo further their contributions.

c) The three agreed that if they win the elections they would share their 15 combined positions amongst themselves in the ratio of their contributions. How many cabinet positions did Maendeleo get?

10 marks

Two identical baskets A and B contain 5 white and 3 red balls each. A bag is chosen at random and 2 balls picked from one after another without replacement.

a) Illustrate this information using a tree diagram.

b) Find the probability that;

i) The two balls picked are of the same colour.

ii) The two balls picked are of different colours.

iii) None of the balls picked is red.

iv) At least one white ball is picked.

10 marks

The distance between Manchester and Barcelona is 600km. A car and a lorry travel from Manchester to Barcelona. The average speed of the lorry is 20km/h less than that of the car. The lorry takes hours more than the car to travel from Manchester to Barcelona.

a) If the speed of the lorry is xkm/h, find x

b) The lorry left Manchester town at 7.15 am, the car left Manchester later and overtook the lorry at 11.15am.

i) Calculate the time the car left Manchester city.

ii) Calculate the distance yet to be covered by the lorry as the car arrives at Barcelona.

10 marks

a) In the month of January an insurance salesman earned Sh.6750, which was a commission of 4.5% of the premiums paid to the company.

i) Calculate the premiums paid to the company.

ii) In February the rate of commission reduced by and the premiums reduced by 10%.

Calculate the amount earned by the salesman in the month of February.

b) During the month of March the company bought a lap top at the cost of sh.58,900 whose marked price was sh.62,000. Calculate the percentage discount.

10 marks

a) Find the equation of the perpendicular bisector of a line AB where A is (3,9) and B(7,5) in the form ax+by+c=0

b) The perpendicular bisector of line AB above intersects the line joining the points (2,4) and (-3,1) at C. Find the coordinates of C.

c) The line through (2,4) and (-3,1) make an angle Ѳ with the positive x-axis, find the value of angle Ѳ

10 marks

In the figure below, O is the centre of the circle. PQ and PR are tangents to the circle at Q and R respectively. Angle PQS=and angle PRS=

RTU is a straight line.

Find the following angles giving reasons in each case;

i) Angle QRS

ii) Angle RTQ

iii) Angle RPQ

iv) Reflex angle QOR

v) Angle TRO given that TR =TQ

10 marks

A rectangular tank whose internal dimensions are 2.04m by 1.68m by 26.4m is seven eighth full of milk.

a) If the tank is made of metal of thickness 3mm, Calculate the external volume of the tank in m3 when closed.

b) Calculate the volume of milk in the tank in m3.

c) The milk is to be packed in small packets. Each packet is in the shape of a right pyramid on an equilateral triangle base side 11.2cm. The height of each packet is 13.6cm, full packets obtained are sold at 35/= per packet.

Calculate;

i) The volume of milk in cm3 contained in each packet to 4 s.f. Hence find the number of full packets.

ii) The exact amount that will be realized from the sale of all the packets of milk.

10 marks

The vertices of a triangle PQR are P(0,0), Q(6,0) and R(2,4).

a) Plot these points on the grid provided.

b) Triangle 1 11 R QP is the image of PQR under an enlargement scale factor ½ and centre (2,2). Write down all coordinates of triangle P1Q1R1 and plot on the same grid.

c) Draw triangle P11Q11R11 the image of triangle 1 11 R QP under positive quarter turn about the point (1,1).

d) Draw triangle P111Q111R111 the image of triangle P11Q11R11 under reflection on the line y=1

e) Describe fully a single transformation which maps triangle P11Q11R11 onto triangle

10 marks