##### Mathematics Paper 2 Question Paper

### KCSE CLUSTER TESTS 24

#### Mathematics Paper 2

### 1. SECTION I (50 Marks)

Use logarithm tables to evaluate

3 marks

A perpendicular line is drawn from a point (1,2) to the line 3y + 2x+1 = 0 . Find the

equation of the perpendicular line in the form y=mx+c (3mks)

3 marks

Simplify

3 marks

Illustrate on a number line the solution of the following inequality (2mks)

2 marks

A quantity y is partly constants and partly varies as x. When x=3 and y=1 and when

x=4 , y=10. Find y in terms of x, hence find y when x=6. (4mks)

4 marks

The size of an interior angle of a rectangular polygon is 3x while its corresponding

exterior angle is (x-20)0. Find the number of sides of the polygon. (3mks)

3 marks

a) Expand and simplify

b) Use the expansion up to the fourth term to find the value of (0.98)^{6} to four decimal

places. (2mks)

3 marks

The image of the point (0,2), under an enlargement with scale factor 3 is (4,6). Find

the centre of enlargement. (3mks)

3 marks

In the figure above AB=5cm and CD=7cm. DC is the tangent to the circle. Find the

length of BC. (3mks)

3 marks

Make r the subject of the formula

3 marks

A shopkeeper mixes sugar costing ksh.120 per kg with another type which costs

ksh.140 per kg. Find the ratio in which the two types should be mixed so that if a

kilogram of the mixture is sold at ksh.150, a profit of 20% is realized. (3mks)

3 marks

Mr. Maina deposits ksh 60,000 in a bank which pays 12% interest per annum

compounded quarterly. Find the amount in the account after 3years. (3mks)

3 marks

Find the centre and radius of a circle which is given by

(3mks)

3 marks

The position vectors for points M and N are

Find

the length MN. (3mks)

3 marks

What is the percentage error in using 0.33 in estimating

(3mks)

3 marks

Write down the inequalities represented by the region R. (4mks)

4 marks

### 2. SECTION II (50 Marks)

Income rates for income earned were charged as follows.

Mrs. Lunani a civil servant earns a basic salary of Ksh.30,000. Her house allowance in ksh 12000 per month. Other allowances are transport ksh. 1300, and medical allowance of ksh 2500. She is entitled to a family relief of ksh 1240 per month. Calculate;

a) i) Her taxable income per month. (2mks)

ii) Net tax. (5mks)

b) In addition, the following deduction were made:

NHIF Ksh 230

Service charge Ksh 100

Loan repayment Ksh 5000

Co-operatives shares Ksh 2000

Calculate her net salary (3mks)

10 marks

The table below shows marks scored by 100 form four candidates in a mathematics

test.

a) Draw a cumulative frequency graph to illustrate the data. (4mks)

b) From your graph, estimate

i) The median (1mk)

ii) Semi- interquartile range (3mks)

iii) The pass mark if 65% of students are to pass. (2mks)

10 marks

An arithmetic progression has the first term a and common difference d.

a) Write down the third, ninth and twenty fifth terms of progression in terms of a and d. (3mks)

b) The arithmetic progression above is increasing and that the third, ninth and twenty fifth terms form the first three consecutive terms of a geometric progression. The sum of the seventh and twice the sixth terms of the arithmetic progression of 78.

Calculate:

i) The first term and common difference of the arithmetic progression. (5mks)

ii) The sum of the first nine term of the arithmetic progression. (2mks)

10 marks

In the figure below E, is the mid-point of BC; AD:DC=3:2 and F is the meeting point of BD and AE.

10 marks

A parallelogram has vertices A(0,0), B(-3,1), C(1,3) and D(4,2)

10 marks

A bag contains 5 green and 3 white marbles. Three marbles are drawn at random without replacement.

a) Determine the probability that:

i) More green marbles than white marbles are drawn. (4mks)

ii) At least one green marbles is drawn. (4mks)

iii) The marbles drawn are of the same colour. (2mks)

10 marks

The figure below shows circles that intersect at points A and B. Point E is the centre of the smaller circle and lies on the circumference of the larger one.

FAC and FBD are straight lines.

Calculate:

a) The obtuse angle AEB (2mks)

Giving reasons find the value of:

b) Angle ACB (3mks)

c) Angle BAD (3mks)

d) Angle EBF (2mks)

10 marks

a) Find the inverse of a matrix

b) Nasimiyu bought 2 chemistry books and 3 mathematical books at a total of ksh 2100, Wakachala bought 4 chemistry books and 7 mathematics books for a total of ksh 4700.

i) Form a matrix equation to represent the above information. (1mk)

ii) Use matrix method to find the price of a chemistry book and that of a mathematics book. (3mks)

c) Wesimikha High School bought 40 chemistry books and 50 mathematics books. A discount of 5% was allowed on each chemistry book whereas a discount of 8% was allowed on each mathematics book.

Calculate the percentage discount on the cost of all the books bought. (4mks)

10 marks