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

### 2014 Kakamega County Mock

#### Mathematics Paper 2

### SECTION I (50 Marks)

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

Use logarithms to evaluate:

3 marks

Given that a^{2}*x*^{2} +6a*x +* k is a perfect square, find k .

3 marks

Make h the subject of the formula.

3 marks

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

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

a. Find the inverse of the matrix 1 mark)

b. Hence solve the following simultaneous equations using matrix method (3 marks)

3*x* – 4*y* = 2

3*x* + 5*y* = 13

4 marks

The first term of an arithmetic sequence is (2*x* + 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

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

3 marks

(a) Expand (1 marks)

(b) Use the first three terms of the expansion in (a) to find the approximate value of (0.98)^{4 }(2 marks)

3 marks

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

3 marks

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

Evaluate

3 marks

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

Given that , find the ratio x:y.

2 marks

Complete the table below for the function *y* =3*x*^{2} -8*x* +10

x | 0 | 2 | 4 | 6 | 8 | 10 |

y | 10 | 6 | 20 | _ | 138 | _ |

Hence estimate the area bounded by the curve *y* =3*x*^{2} -8*x* +10 and the lines y = 0 , x = 0 and x = 10 using trapezoidal rule with 5 strips.

3 marks

If , find the value of a, b and c.

3 marks

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

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

x | 0^{o} |
30^{o} |
60^{o} |
90^{o} |
120^{o} |
150^{o} |
180^{o} |
210^{o} |
240^{o} |
270^{o} |
300^{o} |
330^{o} |
360^{o} |

2x | 0^{o} |
60^{o} |
120^{o} |
180^{o} |
240^{o} |
300^{o} |
360^{o} |
420^{o} |
480^{o} |
540^{o} |
600^{o} |
660^{o} |
720^{o} |

Sin2x | 0^{o} |
0.866 | _ | _ | 0^{o} |
_ | _ | _ | 0.866 | _ | -0.866 | _ | _ |

y=1/2 Sin2x | 0^{o} |
0.433 | _ | _ | 0^{o} |
_ | _ | _ | _ | _ | _ | _ | _ |

(b) On the grid provided, draw the graph of the function y=1/2 Sin2x , for 0^{o}__<__ x __<__ 360 using the

scale 1cm for 30^{o} 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

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)

From your graph, determine;

(i) The median (1mark)

(ii) The interquartile range (1mark)

10 marks

A triangle ABC with vertices at A (1,-1) B (3,-1) and C (1, 3) is mapped onto triangle A^{1}B^{1}C^{1} by a

transformation whose matrix is

Triangle A^{1}B^{1}C^{1 }is then mapped onto A^{11}B^{11}C^{11} with vertices at A^{11} (2, 2) B^{11} (6, 2) and C^{11} (2,-6)

by a second transformation.

(i) Find the coordinates of A^{1}B^{1}C^{1}(3 marks)

(ii) Find the matrix which maps A^{1}B^{1}C^{1} onto A^{11}B^{11}C^{11}. (2 marks)

(iii) Determine the ratio of the area of triangle A^{1}B^{1}C^{1 }to triangle A^{11}B^{11}C^{11}. (3 marks)

(iv) Find the transformation matrix which maps A^{11}B^{11}C^{11} onto ABC (2 marks)

10 marks

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

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

DCX = 60^{0} ,AFD = 5^{o} andABC = 85^{o} . FCX is the tangent to the circle and BAF = 10^{o}

(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

An aeroplane that moves at a constant speed of 600 knots flies from town A (14^{o}N, 30^{o}W)

southwards to town B (X^{o}S, 30^{o}W) taking 3 hrs 30 min. It then changes direction and flies along latitude to town C (X^{o}S, 60^{o}E). 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 (5^{0}N, 120^{0}W), 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

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 m^{2} of space and is operated by 5 men. Type B makes 80 chairs a day, occupies 24 m^{2} of space and is operated by 3men.The businessman has 200m^{2} 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.**