KNEC KCSEMathematics Paper 1 – 2014 Homa-Bay Mock

Evaluate without using a calculator 

Calculate the standard deviation for the data below.
5,8,13,12,7,10,8,15,3,14

A straight line L₁ is perpendicular to another line L₂ 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)

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.

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/cm³, find the radius of the cylinder. Take 

Simplify completely by factorization 

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)

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

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.

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.

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.

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

The diagram below shows the sketch of the curve y=x²-x-6.

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

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

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

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.

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)

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

(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)

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)

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)

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 m³(3mks)

The displacement of a particle S metres, t seconds after passing a fixed point O is given by
S=3+2t-5t².

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)

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)

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)