## KNEC KCSE Mathematics Paper 1 – 2014 Homa-Bay Mock

### 2014 Homa-Bay Mock

#### Mathematics Paper 1

### SECTION 1 (50 Marks)

**Answer all questions in the spaces provided.**

Evaluate without using a calculator

3 marks

Calculate the standard deviation for the data below.

5,8,13,12,7,10,8,15,3,14

3 marks

A straight line L_{1} is perpendicular to another line L_{2 }whose equation is 3y+4x=12. If the two lines

meet at point P which lines on the x-axis, find:

(i) The co-ordinate of point P (1mk)

(ii) The equation of line L1 in the form y=mx+c (3mks)

4 marks

Mr. Ochuodho who deals in electronics sells a radio to a customer at Kshs. 1,440 after giving him a

discount of 10% but finds that he still makes a 20% profit. Find the profit Mr. Ochuodho would

make if he does not give a discount.

3 marks

A solid block in the shape of a cylinder has a height of 14cm and weighs 22kg. If it is made of

material of density 5g/cm^{3}, find the radius of the cylinder. Take

3 marks

Simplify completely by factorization

3 marks

The figure below shows a triangle ABC not drawn to scale, D is a point on line AC. Given that

BC=14cm, DC=7cm and ABC=BDC. Find the length of AD (3mks)

3 marks

Solve the simultaneous inequalities given below and list all the integral values of x.

3 marks

In the circle drawn to scale below A,B,C and D are points on its circumference, Chord BC=AC and

angle ADC=138^{o}.

Giving reasons calculate the angle ACB.

3 marks

The figure below shows a triangular prism ABCDEF. AF=CD=BE=18cm, The ends ABC and EDF

are equilateral triangles of side 8cm. calculate the angle plane ABD makes with the lie CD.

3 marks

Patricia a student at Ongeti mixed Secondary bought 5 pens and 3 exercise books from Solving

supermarket at Kshs. 135, at the same time Jane her class mate also bought 4 pens and 5 exercise

books and spent Ksh. 25 more than Patricia. Find the cost of each pen and exercise book.

4 marks

Evaluate using mathematical tables only expressing your answer to 4 significant figures.

3 marks

The diagram below shows the sketch of the curve y=x^{2}-x-6.

Using the mid-ordinate rule with five rectangles, calculate the area of the shaded region

4 marks

Given that sin (3x-35)^{o} – cos (x+20)^{o}= 0 and x is an acute angle, find its value.

2 marks

A train of length 80m crosses a bridge 20 m long in 5 seconds. Calculate the average speed of the

train in km/h.

3 marks

Mr. Ombogo the principal of Chiga secondary would wish to cover the floor of the new administration block using the square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of each of the largest tiles which can be used to fit exactly without breaking.

3 marks

### SECTION B (50 Marks)

**Answer ONLY FIVE questions in this section in the spaces provided**

Four schools Wiobiero, Asumbi, Nyawita and Angiro are such that Wiobiero is 15km from Asumbi

on a bearing of 158^{o}, Nyawita is to the west of Asumbi and 20km away while An’giro is to the South

of Nyawita and on a bearing of 240^{o} from Wiobiero.

(a) Using a scale of 1:400,000 draw a scale diagram showing the relative positions of the four

schools. (5mks)

(b) Using your diagram determine the distance and bearing of Ang’iro from Asumbi (2mks)

(c) A mast is to be erected so that its equidistant from Asumbi and Nyawita and 20km from Ang’iro

on the same diagram show the position of the mast and find its distance from Wiobiero (3mks)

10 marks

The table shows the marks obtained by 40 candidates in an examination

Marks | 5-14 | 15-29 | 30-34 | 35-44 | 45-49 |

Frequency | 2 | 12 | 7 | 15 | x |

(a) Find the value of x (2mks)

(b) On the grid provided below draw a histogram to represent the data (5mks)

(c) By drawing a straight line on the graph above determine the median mark (3mks)

10 marks

A matatu left Oyugis for Homabay town 51km away at an average speed of 48km/h at 7.00am. At

7.30am a Boda boda left Homabay for Oyugis travelling along the same route at an average speed of

60km/h.

(a) The time when Boda boda meet the matatu (3mks)

(b) How far from Oyugis did the Boda boda meet the matatu (3mks)

(c) After meeting the Boda boda the matatu stopped for fifteen minutes before resuming the journey.

At what speed should it travel then to reach Homabay at the same time when the Boda boda reached

Oyugis (4mks)

10 marks

A group of people planned to contribute equally towards a water project which needed Ksh.2,000,000 to complete. However 40 members of the group withdrew from the project. As a result each of the remaining members were to contribute Kshs.2,500 more

(a) Find the original number of members in the group (5mks)

(b) Forty five percent of the value of the project was funded by constituency development fund(CDF). Calculate the amount of contribution that would be made by each of the remaining members. (3mks)

(c) Members contribution were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contribution was 6:9. Calculate the total amount of money contributed by the members (2mks)

10 marks

The figure below shows a prism whose cross section is a regular pentagon of side 6cm and whose

length is 20cm joined to a cylinder of radius 14cm and height 6cm to form a the model of a solid

(a) Calculate the cross section area of the pentagon (3mks)

(b) Calculate the total volume of the solid (4mks)

(c) The model represents a pillar of total height 5.2m, calculate the volume of the actual solid

in m^{3}(3mks)

10 marks

The displacement of a particle S metres, t seconds after passing a fixed point O is given by

S=3+2t-5t^{2}.

Calculate:

(a) The displacement of the particle 2 seconds later (2mks)

(b) The time taken for the particle to return to O (2mks)

(c) The maximum displacement of the particle (3mks)

(d) The initial velocity of the particle (2mks)

(e) The acceleration of the particle after t seconds (1mk)

10 marks

The diagram below shows a circle ABC with AB=12cm, BC=15cm, and AC=14cm

Calculate to 4 significance figures:

(a) The angle ACB (3mks)

(b) The radius of the circle (3mks)

(c) The area of the shaded region (4mks)

10 marks

OABC is a trapezium such that the coordinates of O,A,B and C are (0,0),(2,-1) (4,3) and (0,y)

(a) Find the value of y (2mks)

(b) M is the mid-point of AB and N is the mid point of OM. Find in column form

(i) The vector AN (3mks

(ii) The vector NC (2mks)

(iii) Vector AC (1mk)

(c) Hence show that A, N and C are collinear (2mks)

10 marks