## KNEC KCSE Mathematics Paper 2 Question Paper / 2016 KCSE KAMDARA JET Examination

### 2016 KCSE KAMDARA JET Examination

#### Mathematics Paper 2

### SECTION I (50 Marks)

**Answer all the questions in this section in the spaces provided below each question.**

Using an assumed mean of 50 , calculate the standard deviation of the marks obtained in a test recorded as follows: 50, 52, 45, 40, 55, 51 56, 48, 55, 60

2 marks

Make x the subject of the formula

3 marks

Find the value of x in the equation

Log_{3} X – 4log_{X}3 = -3

4 marks

a) Expand the binomial (2 – ¼ x)^{5}(2 marks)

b) Using the first 4 terms of the binomial above solve for 1.755 (2 marks)

4 marks

a) Find the inverse of the matrix (1 mark)

b) Hence determine the point of intersection of the lines (2 marks)

x + y = 7

3x + y = 15

3 marks

Rationalise the denominator and simplify the answer completely.

3 marks

Solve for x in the trigonometric equation 4cos^{2}*x* + 4sin^{2} *x* = 16sin^{2}*x*cos^{2}*x *in 0^{o} ≤x≤360^{o}

5 marks

The mass of a cylinder of a small material varies jointly as the square of the radius and as the

height. If the radius is increased by 20% and the height by 10%. Find the percentage increase in

mass. (3 marks)

3 marks

Given that the dimensions of a rectangle are 20.0cm and 25.0. Find the percentage error in calculating the area.

3 marks

Maina bought a new laptop on hire purchase. The cash value of the laptop was Ksh. 56,000. He paid a deposit of Ksh. 14,000 followed by 24 equal monthly installments of Ksh. 3500 each. Calculate the

monthly rate at which the compound interest was charged.

3 marks

Find the equation of tangent to a curve x^{2} = 4y+1 at the point (2, 0.75)

3 marks

Object A of area 12cm^{2} is mapped onto its image B of area 72cm2 by a transformation. Whose matrix is given by . Find the positive values of x.

3 marks

In the figure below, AB is a tangent, meeting chord CDE at B. AD = 5cm, CD = 4cm, DF = 2cm, EB =

7.5cm and DE = x cm.

Determine:

(a) The value of x (1mark)

(b) The length of AB. (2 marks

3 marks

A ship covers 60km on a bearing of 230^{o}. If then it changes course and heads due west for

80km, determine its direct distance from the starting point.

3 marks

Find the centre and the radius of the circle whose equation is x^{2} + y^{2} – 7x + 6 + 11y = 0

3 marks

The 2nd, 4th and 7th terms of A.P are the first 3 consecutive terms of a G.P. Find:

(a) The common ratio (2Marks)

(b) The sum of the first eight terms of the G.P if the common difference of the A.P is 2.

(2Marks)

4 marks

### SECTION II (50 Marks)

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

In the figure above, M divides line OB in the ratio 1:2 and N divides in the ratio 2:3 and

intersect at X. Given and

a) Find in terms of a and b :

(i) (1 mark)

(ii) (1 mark)

(iii) (1 mark)

b) If and where h and k are scalars

(i) Express in two ways.

Hence find the value of h and k (4 marks)

c) Find the ratio of (1 mark)

(i) Express OX in two ways. ( 2 marks)

10 marks

The figure below shows a right pyramid with a rectangular base. The length of the rectangular base is

15cm and the width is 8cm. The slant edges are all equal to 20cm.

Calculate

a) The volume of the pyramid. (3 marks)

b) The angle VAB makes with ABCD (3 marks)

c) The angle plane XBD makes with VBD given that point X lies on VA such that VX: XA = 2: 3

(4 marks)

10 marks

The number x is chosen at random from the set (0,3,6,9) and the number y is chosen at random

from the set (0,2,4,6,8). Calculate the probability of each of the following separate events.

(i) x > 6 (1 mark)

(ii) x + y = 11 (2 marks)

(iii) x > y (3 marks)

(iv) xy = 0 (2 marks)

(v) 10x + y < 34 (2 marks)

10 marks

P and Q are two points on the same parallel of latitude 66o 251, whose longitudes differ by

120o. Calculate in kilometres. Radius of the earth =6370.

a) The radius of the parallel of latitude where P and Q lie. (2 marks)

b) The distance of P and Q measured along the parallel of latitude. (2 marks)

c) (i) find the length of the straight line joining PQ (2 marks)

(ii) Find the distance between P and Q along the same latitude in nautical miles. (2 marks)

(iii)If an aircraft took 30min to fly from P to Q, Calculate its speed in knots. (2 marks)

10 marks

a) Use the trapezium rule to estimate the area between the curve y = 3x^{2} + 1, lines x=1 and x=3

and x-axis. Use five ordinates. (5 marks)

b) Using integration method find the exact area under a curve y=3x^{2} + 1 (3 marks)

d) Find the percentage error in estimating the area. (2 marks)

10 marks

The table below shows the rate at which income tax is charged for all income earned in a month

in 2015.

Taxable Income p.m (Kenya pound)1 -236 237 -472 473 -708 709 – 944 945 and over |
Rate in % per Kenya pound10% 15% 20% 25% 30% |

A total of Ksh. 14,500 is deducted from Mrs. Momanyi monthly salary .She is entitled to a house

allowance of Ksh. 8,000 a person relief of Ksh. 1064 month and Monthly insurance relief at the rate

of 15% of the premium paid. Every month she pays the following.

(i) Electricity bill shs.780

(ii) Water bill shs. 560

(iii) Co-operative shares shs. 1200

(iv) Loan repayment Ksh. 5000

(v) Monthly insurance premiums of Ksh 1260

(a) Calculate her P.A.Y.E (2Marks)

(b)Calculate her monthly taxable income . (6Marks)

(c) Calculate her basic salary per month (2Marks)

10 marks

Mr. Wanyama wishes to take student from wonderful mixed secondary school for a tour. The total

number of pupils to be taken should not exceed 60. Each girl must contribute sh.10,000 and each boy

sh.15,000 and money to be contributed must not exceed sh.120,000. If this trip is to be successful the number of boys must conditionally be greater than girls.

a) Write down five inequalities to represent this information taking the number of boys and girls to be

x and y respectively. (4 marks)

b) Represent the above information on the graph paper below. (4 marks)

c) What is the optimum number of boys and girls to be taken in order to be minimise cost. (2 mark)

10 marks

In the figure below, line BD is the diameter of the circle, centre O and AE is a tangent.

Angle CBA = 110^{o} and angle BAC =26^{o}

Find the following angles, giving reasons for each answer.

a) ∠ABD (3marks)

b) ∠DAE (1mk)

c) ∠AED (3marks)

d) ∠AOD (3marks)

10 marks