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# KNEC KCSE Mathematics Paper 2 Question Paper / 2014 Kakamega County Mock

## KNEC KCSE Mathematics Paper 2 Question Paper / 2014 Kakamega County Mock

### SECTION I (50 Marks)

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

1.

Use logarithms to evaluate:

3 marks

2.

Given that a2x2 +6ax + k is a perfect square, find k .

3 marks

3.

Make h the subject of the formula.

3 marks

4.

Given that P varies directly as V and inversely as the cube of R and that P = 12 when V = 3 and R = 2,
(i) Find an equation connecting P, V and R. (3 marks)
(ii) Find the value of V when P = 10 and R = 1.5 (1 mark)

4 marks

5.

The figure below shows a toy which consists of a conical top and a hemispherical base.

The hemispherical base has a radius of 5cm and the total height of the toy is 17cm. calculate the
volume of the toy. (Take π = 3.142)

3 marks

6.

a. Find the inverse of the matrix  1 mark)
b. Hence solve the following simultaneous equations using matrix method (3 marks)

3x – 4y = 2

3x + 5y = 13

4 marks

7.

The first term of an arithmetic sequence is (2x + 1) and the common difference is (x + 1). If the
product of the first and the second terms is zero, find the first three terms of the two possible
sequences.

4 marks

8.

Solve for x in the equation log5 -2 + log(2x + 10) = log(x – 4)

3 marks

9.

(a) Expand  (1 marks)
(b) Use the first three terms of the expansion in (a) to find the approximate value of (0.98)(2 marks)

3 marks

10.

Draw a line DF=4.6cm. Construct the locus of point K above DF such that angle DKF = 70o.

3 marks

11.

Machine A can complete a piece of work in 6 hours while machine B can complete the same work in
10 hours. If both machines start working together and machine A breaks down after 2 hours, how
long will it take machine B to complete the rest of the work?

3 marks

12.

Evaluate

3 marks

13.

The base and perpendicular height of a triangle measured to the nearest centimeter are 6cm and 4cm
respectively. Find
(a) The absolute error in calculating the area of the triangle. (2 marks)
(b) The percentage error in the area giving the answer to 1 decimal place. (1 mark)

3 marks

14.

Given that  , find the ratio x:y.

2 marks

15.

Complete the table below for the function y =3x2 -8x +10

 x 0 2 4 6 8 10 y 10 6 20 _ 138 _

Hence estimate the area bounded by the curve y =3x2 -8x +10 and the lines y = 0 , x = 0 and x = 10 using trapezoidal rule with 5 strips.

3 marks

16.

If  , find the value of a, b and c.

3 marks

17.

The table below shows the Kenya tax rates in a year

 Income (Ksh per annum) Tax rate (per £) 1 – 116,160 10% 116,161 – 225,600 15% 225,601 – 335,040 20% 335,041 – 444,480 25% Over 444,481 30%

In that year, Ushuru earned a basic salary of Ksh 30000 per month. In addition, he was entitled to a
medical allowance of Ksh 2,800 per month and a traveling allowance of Ksh 1800 per month. He is
housed by the employer and pays a nominal rent of 2000. He also claimed a monthly family relief of
Ksh 1056. Other monthly deductions were union dues Ksh 445, WCPS Ksh 490, NHIF Ksh 320,
COOP shares Ksh 1000 and risk fund Ksh 100.

Calculate:
(a) Ushuru’s annual taxable income. (2 marks)
(b) The tax paid by Ushuru in that year (5 marks)
(c) Ushuru’s net income in that year (3 marks)

10 marks

18.

(a)Complete the table for the function y=1/2 Sin2x , where 0o < x < 360 (2 marks)

 x 0o 30o 60o 90o 120o 150o 180o 210o 240o 270o 300o 330o 360o 2x 0o 60o 120o 180o 240o 300o 360o 420o 480o 540o 600o 660o 720o Sin2x 0o 0.866 _ _ 0o _ _ _ 0.866 _ -0.866 _ _ y=1/2 Sin2x 0o 0.433 _ _ 0o _ _ _ _ _ _ _ _

(b) On the grid provided, draw the graph of the function y=1/2 Sin2x , for 0o< x < 360 using the
scale 1cm for 30o on the horizontal axis and 4cm for 1 unit of y axis. (3 marks)

(c) Use your graph to determine the amplitude and period of the function y=1/2 Sin2x (2 marks)
(b) Use the graph to solve

(i)y=1/2 Sin2x = 0 (1 mark)
(ii) y=1/2 Sin2x – 0.5 = 0 (2 marks)

10 marks

19.

he following are marks out of 100 scored by 40 learners in a Mathematics contest.

 Marks 40 – 49 50 – 59 60 – 69 70 – 79 80 – 89 90 – 99 No. of learners 4 6 8 12 8 2

(a) (i) Using an assumed mean of 64.5, calculate the standard deviation of the data. (5marks)
(b) On the grid provided, draw a cumulative frequency curve. (3 marks)

(i) The median (1mark)
(ii) The interquartile range (1mark)

10 marks

20.

A triangle ABC with vertices at A (1,-1) B (3,-1) and C (1, 3) is mapped onto triangle A1B1C1 by a
transformation whose matrix is 

Triangle A1B1Cis then mapped onto A11B11C11 with vertices at A11 (2, 2) B11 (6, 2) and C11 (2,-6)
by a second transformation.
(i) Find the coordinates of A1B1C1(3 marks)
(ii) Find the matrix which maps A1B1C1 onto A11B11C11. (2 marks)
(iii) Determine the ratio of the area of triangle A1B1Cto triangle A11B11C11. (3 marks)
(iv) Find the transformation matrix which maps A11B11C11 onto ABC (2 marks)

10 marks

21.

In a form 2 class 2/3 are boys and the rest are girls. 4/5 of the boys and 9/10 of the girls are right handed; the rest are left handed. The probability that a right handed student will answer a question correctly is 1/10 and the corresponding probability for a left handed student is 3/10 irrespective of the sex.

By use of tree diagram; Determine

(a) The probability that a student chosen at random from the class is left handed. (5 marks)

(b) Given that getting a boy or a girl at any stage in a family of three children is equally likely;

(i) Use the letters B and G to show the possibility space for all families with three children
(1 mark)

(ii) Using the possibility space calculate the probability that a family of three children has at least one girl. (2 marks)

(iii)The oldest and the youngest are of the same sex. (2 marks)

10 marks

22.

In the figure below O is the centre of the circle. DEF is a straight line. FCX is a tangent at C.

DCX = 600 ,AFD = 5o andABC = 85o . FCX is the tangent to the circle and BAF = 10o

(a) Find the sizes of the following angles giving reasons.
(i) DFC (3 marks)
(ii) DAF (2 marks)
(iii)OCB (2 marks)
(b) If GF is 10 cm and the radius of the circle is 7 cm. Calculate GF (3 marks)

10 marks

23.

An aeroplane that moves at a constant speed of 600 knots flies from town A (14oN, 30oW)
southwards to town B (XoS, 30oW) taking 3 hrs 30 min. It then changes direction and flies along latitude to town C (XoS, 60oE). Given π = 3.142 and radius of the earth R= 6370 km
(a) Calculate
(i) The value of X (3 marks)
(ii) The distance between town B and town C along the parallel of latitude in km. (2 marks)
(b) D is an airport situated at (50N, 1200W), calculate
(i) The time the aeroplane would take to fly from C to D following a great circle through the
South Pole. (3 marks)
(ii) The local time at D when the local time at A is 12.20 p.m (2 marks)

10 marks

24.

A businessman wants to buy machines that make plastic chairs. There are two types of machines that can make these chairs, type A and type B. Type A makes 120 chairs a day, occupies 20 m2 of space and is operated by 5 men. Type B makes 80 chairs a day, occupies 24 m2 of space and is operated by 3men.The businessman has 200m2 of space and 40 men.
(a) List all inequalities representing the above information given that the business man
buys x machines of type A and y machines of type B. (3 marks)
(b) Represent the inequalities above on the grid provided. (3 marks)
(c) Using your graph find the number of machines of type A and those of type B that the business
man should buy to maximize the daily chair production. (2 marks)
(d) Given that the price of a chair is Ksh.250, determine the maximum daily sales the businessman
can make. (2 marks)

10 marks

### SECTION II (50 Marks)

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