## KNEC KCSE Mathematics Paper 1 – 2014 Gatundu Mock

### 2014 Gatundu Mock

#### Mathematics Paper 1

### SECTION 1 (50 Marks)

**ANSWER ALL QUESTIONS IN THIS SECTION IN THE SPACES PROVIDED BELOW EACH QUESTION.**

Using logarithms tables evaluate.

4 marks

A sum of money is divided between three people, Tom, Mary and Lucy in the ratio 5:3:1. If Mary

has sh.700 more than Lucy, calculate how much Tom has.

3 marks

Evaluate 3/8 of

3 marks

Express the following as fraction.

3 marks

In the figure below, O is the centre of the circle and OB bisects angel ABC. Given that <BAC= 40^{o}, find <ABO.

3 marks

Solve for x in the equation below:

125^{(x+1)}+5^{3x}=630

3 marks

Find the integral values of y of which satisfy the inequalities below.

3 marks

Use reciprocal and cube root tables to evaluate.

3 marks

The position vector of points A and B relative to the origin O are a and b respectively. Given that

a = 4**i** + 3**j** and b = **i** + 2**j**, find the modulus of the vector a + b.

3 marks

Tap A takes one hour to fill a tank with water. If tap B takes y hours to remove the same water and

both taps takes 1 ½ hours to fill the tank, find the value of y.

3 marks

Obenda weighed 120kg before he was taken ill of HIV/AIDs. After sometimes his weight decreased by

10% every week for 5 weeks. He was put on ARVs and his weight increased by 5% every week for 3

weeks. What is his weight at the end of eighth week?

4 marks

The mean age of 4 girls is 15 yeas. The first and second are aged 13 years and 18 years respectively.

The third girl is 3 years older than the first girl. Find the modal age.

2 marks

Solve the following simultaneous equations.

Log_{2}(4y + x) = 3

Log_{3}(4x + y) = 2

4 marks

The L.C.M of 15, 18 and a third number is 1260. Find the square of third number.

2 marks

Use the currency conversion table below to answer the questions that follow.

CURRENCY | BUYING | SELLING |

1 US DOLLAR | Ksh.78.4133 | Ksh.78.4744 |

1 EURO | Ksh.73.4226 | Ksh.73.5295 |

An American tourist came to Kenya with US dollar 10,000. He converted all his money to Kenya

shilling and used Ksh.32,000 while he was in Kenya. The tourist converted the remainder to Euros

because he wanted to visit Germany. How much did he get (give the answer to 4 decimal places)

3 marks

Find the length QR of the following triangle if PR=3.7cm PQ=4cm and <PQR = 63^{o}

4 marks

### SECTION II (50 Marks)

**ANSWER ANY 5 QUESTION FROM THIS SECTION**

Mr. Biwott operates two passenger service vehicles along Nakuru- Eldoret route. One is a 16 seater

Matatu and the other is 8-seater van. Each vehicle makes one route trip per day and the charges are ksh 250 and ksh 300 per passenger respectively (one way). The matatu uses diesel which costs ksh.48 per litre and the van uses regular petrol which costs ksh.52 per litre. The fuel consumption of the two vehicles is in the ratio of 4:3 respectively.

(a) If the matatu uses 80 litres for the round trip, determine the fuel consumption of the van for the

round trip. (2 marks)

(b) Calculate the daily collection for each vehicle. (2 marks)

(c) Determine which vehicle is more profitable (on daily basis) and by how much. (3 marks)

(d) If the price of both types of fuel goes up by 20% determine the percentage change in daily

collection. (3 marks)

10 marks

Two airports are such that B is 500km due East of A. Two planes P and Q take off from A and B

respectively and at the same time. Place P flies at 360km/h on a bearing of 030^{o}. Plane Q flies at

240km/h on a bearing of 315^{o}. The two planes land after 90 minutes. Using a scale of 1:10,000,000:

(a) Show the positions of the planes after 90 minutes. (7 marks)

(b) Find the distance between the planes after 90 minutes. (1 mark)

(c) Find:

(i) The bearing of plane P from plane Q after 90 minutes. (1 mark)

(ii) The bearing of plane Q from plane P after 90 minutes. (1 mark)

10 marks

The diagram which is not drawn to scale, shows an isosceles triangle XYZ in which XY=YZ. The

coordinates of x and y are (5,6) and (0, -4) respectively.

Given that the equation of line YZ is y=3/4x – 4 and that the perpendicular from X to YZ meet YZ at D, find.

(i) The equation of XD (2 marks)

(ii) The coordinate of D (2 marks)

(iii) The coordinates of Z (2 marks)

(iv) The area of triangle XYZ (4 marks)

10 marks

(a) On the grid provided plot the points A(1, 5) B(3, 1) C(4, 4) and D(3, 3). Join these points to form quadrilateral ABCD. (2 marks)

(b) The points A^{1}(2, 10) B^{1}(6, 2) C^{1}(8, 8) and D^{1}(6, 6) are the images of A, B, C and D under a certain enlargement. On the same grid draw the image A^{1}B^{1}C^{1}D^{1}(2 marks)

(c) Use the construction method to locate the centre of enlargement and state its coordinates. (2 marks)

(d) What is the scale factor of this enlargement? (1 mark)

(e) Determine the matrix of this enlargement. (3 marks)

10 marks

Draw the graph of the given function over the given range and use it to solve the given equation.

Range -4<x <4. y = 2x^{2} + x – 1 hence solve (5 marks)

(a) 2x^{2} + 5x + 4 = 0 ( 1 mark)

(b) 2x^{2} + 5x + 2 = 0 (2 marks)

(c) 2x^{2} + 4x + 3 = 0 (2 marks)

10 marks

The figure below shows a uniform cross-section of a swimming pool which is 4m wide. The depth of

the pool increase gently from 1.5m to 3.0m.

(a) How much water in litres does it hold when full? (3 marks)

(b) Calculate total internal surface area of the pool. (5 marks)

(c) Find the angle at which the bottom of the pool inclines to the horizontal. (2 marks)

10 marks

(a) Using a ruler and a pair of compasses only construct a rhombus A B C D such that AB = 6cm and

<ABC = 135^{o}. (4 marks)

(b) Drop a perpendicular from C to AB extended to meet AB at N. Measure BN and CN. (3 marks)

(c) Bisect <ABC and <DAB, let the two bisectors meet at M. Measure MA. (1 mark)

(d) Determine the area of triangle ABM. (2 marks)

10 marks

Two intersecting circles have centres P and Q as shown below. The circle centre P has radius 8cm and that of centre Q has radius 9cm.

The distance between the centres PQ = 14cm and PB:BQ = 3:4. Calculate

(i) Angles APC (2 marks)

(ii) Angle AQC (2 marks)

(iii) The area of the shaded region. (6 marks)

10 marks