## KNEC KCSE Mathematics Paper 2 Question Paper / 2015 KCSE Kirinyaga West

### 2015 KCSE Kirinyaga West

#### Mathematics Paper 2

### SECTION 1 (50 Marks)

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

The length of two similar iron bars A and B were given as 10.5m and 8.2m. Calculate the maximum possible difference in length between the two bars.

3 marks

The first term of an arithmetic sequence is 5 and the common difference is 2.

a) List the first six terms of the sequence. (1 mark)

b) Determine the sum of the first 40 terms of the sequence. (2 marks)

3 marks

In the figure below PQR is the diameter of the circle centre O. Angle QPR = 20^{o} and angle QTR = 80^{o}

Determine the size of

a) Reflex angle POS (2 marks)

b) Angle OSQ (1 mark)

3 marks

The quantities P, Q and R are such that P varies directly as Q and inversely as the square of R. Given that P = 2 when Q = 12 and R = 6. Determine the equation connecting the three.

3 marks

The table shows the frequency distribution of marks scored by students in a test.

Marks | Frequency |

21 – 30 31 – 40 41 – 50 51 – 60 61 – 70 |
2 4 11 5 3 |

Determine the median mark correct to one decimal point.

4 marks

Determine the amplitude and period of the function 3y = 6sin (2x – 30).

2 marks

In a transformation, an object with area 9cm^{2} is mapped onto an image whose area is 54cm^{2}. Given that the matrix of transformation is find the value of x

2 marks

Expand (4 – x)^{7} upto to the term in x^{4}. Hence find the appropriate value of (3.8)^{7}.

3 marks

Solve for x without using mathematical tables or calculators.

Log_{2}(x^{2} – 9) = 3 Log_{2}2 + 1

4 marks

The figure below represent a square based right pyramid ABCDV. AB = 10cm,

AV = BV = CV = DV = 15cm

Calculate the angle between AV and the base ABCD to the decimal place.

3 marks

Solve the simultaneous equations.

2x – y = 3

xy – y2 = 0

4 marks

Francis bought a vehicle at ksh. 2 800 000. After three years he sold the vehicle at Kshs. 1,500,000. Determine the average rate of depreciation per annum correct to one decimal place.

3 marks

A plane flies from point P (400N, 500E) towards West to a point Q. Given that the plane covers a distance of 10,000km what is the position of Q.

(Take 𝜋𝜋= 22/7, radius of the earth 6370km)

3 marks

Given and . Find

3 marks

The gradient function of a curve is x^{3} – 4. If the curve passes through point (2, 3). Find the equation of the curve.

3 marks

A vehicle initially moving at a velocity of 80m/s had breaks applied. The table below shows how velocity changed in the next 14 seconds.

Time (seconds) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 |

Velocity (m/s) | 80 | 60 | 46 | 34 | 26 | 20 | 16 | 14 |

Determine the average rate of deceleration between the fourth and the twelfth second.

3 marks

### SECTION 2 (50 Marks)

**(ATTEMPT ANY FIVE)**

A businesswoman mixes three types of rice A, B and C in the ratio A : B = 1 : 2 and B : C = 4 : 5. The mixture is to contain 60 bags of type B.

a) Find the ratio A : B : C (2 marks)

b) Find the required number of bags of type C. (2 marks)

c) The cost per bag of type A is Kshs. 7,500, type B Kshs. 5,000 and type C Kshs. 4,000.

i) Calculate the cost per bag of the mixture. (2 marks)

ii) Find the percentage profit if the selling price of the mixture is Ksh. 6,500 per bag. (2 marks)

iii) Find the selling price of a bag of the mixture if the businesswoman makes a profit of 25%. (2 marks)

10 marks

The figure below shows the pulleys with centres A and B and radii 13cm and 6cm respectively. The distance between the centres is 25cm.

A belt PRSTUP goes round the two pulleys. PQ and TS are also tangents.

a) Calculate

i) Length PQ (3 marks)

ii) Angle BAP (3marks)

b) Hence or otherwise calculate the length of the belt. (4 marks)

10 marks

The table below shows income tax rates for a certain year.

Monthly income in Kenya shilling | (Ksh) Tax rate in each shilling |

0 – 10164 10165 – 19740 19741 – 29316 29317 – 38892 Over 38892 |
10% 15% 20% 25% 30% |

A secondary school teacher was earning a monthly basic salary of Ksh. 55,480 house allowance of Kshs. 12,000 and a commuter allowance of ksh. 8000. He was entitled to a personal relief of Kshs. 1162 per month.

a) Calculate

i) The teacher’s taxable income. (2 marks)

ii) The teacher’s net monthly tax. (6 marks)

b) In addition to the tax the other deductions were per month as follows:

– Cooperative loan Ksh. 10,000

– Co-operative shares Ksh. 2,000

– Window and children’s pensions scheme at 2% of the basic salary.

Calculate the teacher’s net monthly pay.

10 marks

A farmer wishes to keep some chicks and ducks. Chicks cost Ksh. 60 each while ducks costs Kshs. 80 each. She finds its uneconomical to keep less than 250 birds. She also wishes to keep more chicks than ducks but the chicks must be less

than 200. She cannot afford to spend more than ksh. 24,000.

a) Taking x and y to be the number of chicks and ducks respectively rite down all the inequalities that satisfy the above conditions. (4 marks)

b) Represent the inequalities graphically shading out the unwanted region. (4 marks)

c) If the farmer makes a profit of ksh. 200 per chicks and ksh. 250 per duck, find the number of chicks and ducks she must keep in order to maximize her profit. State the profit. (2 marks)

10 marks

Three pupils Irene, Mary and Atieno applied for a form one vacancy. The probability of Irene, Mary and Margaret getting the chance in the school are 0.5, 0.4 and 0.9 respectively. Determine the probability that

a) None gets the chance (2 marks)

b) Only one gets the chance. (2 marks)

c) At most one of the three gets the chance. (3 marks)

d) At least one of the three gets the chance. (3 marks)

10 marks

The figure shows triangle OPQ in which QN : NP = 1 : 2, OT : TN = 3 : 2 and M is the mid – point of OQ.

OP = p and OQ = q

a) Express the following in terms of p and q.

i) PQ (1 mark)

ii) ON (2 marks)

iii) PT (2 marks)

iv) PM (2 marks)

b) Hence show that P, T and M are collinear. (3 marks)

10 marks

Using a ruler and compasses only, construct triangle ABC such that AB = AC = 3.9cm and angle ABC = 300(3marks)

b) Measure BC. (1 mark)

c) A point P is always on the same side of BC as A. Draw the locks of P such that angle BAC is always twice angle BPC.(3 marks)

d) Drop a perpendicular from A to meet BC to D. Measure AD. (3 marks)

10 marks

The relationship between two variables X and Y is known to be of the form y = ax2 + b where a and b are constants. In an experiment, for some fixed values of x, corresponding values of y were recorded as in the table below.

a) Fill the missing values of x2. (2 marks)

b) Draw the graph of Y against x2. (3 marks)

c) Using the graph find the value of a and b. (4 marks)

d) State the relationship between y and x. (1 mark)

10 marks