SECTION I (50 marks)

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

- Round off each of the following numbers in the expression to 3 significant figures, hence evaluate the expression. (2 marks)
- Given the matrices
**A**= (^{2}_{3}^{4}_{0}) and**B**= (^{2}_{1}^{3}_{1}), find**AB**– 5**B**. (3 marks) - Three types of coffee A, B and C are mixed such that A:B = 4:3 and B:C = 1:2.

Determine the mass of type C in the mixture of 52kg. (3 marks) - In the Geometric Progression (G.P), the 4th term is 24, and the sixth term is 96.

Determine:- The common ratio of the G.P; (2 marks)
- The first term of the G.P. (2 marks)

- Two fair dice are rolled together and the sum of the numbers showing on the top faces noted.
- Represent all the possible outcomes in the probability space. (2 marks)
- Determine the probability that the sum is greater than 6 but less than 10. (1 mark)

- Two points A and B are such that
**OA**= (^{2}_{5}) and AB = (^{4}_{4}), M is a point on**AB**such that**AM**:**MB**= 3:1.

Determine:- OB: (2 marks)
- the coordinates of M. (2 marks)

- In the figure below, TPR is the tangent to circle at P. Angle APB = 75
^{0}and angle BPR twice angle APT

Determine the size of angle BAP. (2 marks) - Given that 2 cosâ¡ (
*x*-30)^{0 }= -0.9,determine the value of*x*for 0° ≤ x ≤ 180^{0}correct to two decimal places. (3 marks) - The vertices of a triangle RST are R(1, 3), S(1, 7) and T(-1, 4). Triangle RST is mapped onto triangle R'S'T' by transformation matrices
**P**= (^{0}_{1}^{1}_{0}) followed by Q= (^{-1}_{0}^{0}_{-1})

Find the coordinates of R'S'T'. (3 marks) - Using the method of completing the square, solve the equation 2x
^{2 }+ 8x=15, correct to one decimal place. (3 marks) -
- Using a ruler and a pair of compasses only, construct an inscribed circle in triangle ABC given below. (2 marks)

- Measure the radius of the circle. (1 mark)

- Using a ruler and a pair of compasses only, construct an inscribed circle in triangle ABC given below. (2 marks)
- In a camp, there was enough food for 2000 people on equal rations for 90 days. After 20 days 500 more people joined the camp. Calculate the number of days that the remaining food would be used to feed the people. (4 marks)
- Figure PQRS below represents a garden which,

PQ = 80 m, PS = 75 m, SQ = 40 m, ∠SQR=68° and <SPQ = ∠SRQ.

Calculate to 2 significant figures the length of SR. (3 marks) - The table below shows part of income tax rates in a certain year.

In a certain month of that year, Abdala’s income was Kshs 21 820. He was entitled to a monthly personal relief of Ksh 1162. Calculate the income tax paid by Abdala that month. (4 marks) - Ali and Kinjo bought the same type of pencils and rubbers from the same shop. Ali bought 2 pencils and 3 rubbers for Ksh 66, Kinjo bought 7 pencils and 2 rubbers for Ksh 129. Find the cost of a pencil. (3 marks)
- The table below shows marks scored by students in a mathematics test.

On the grid provided below, draw an ogive to represent the data. (3 marks)

**SECTION II** (50 marks)*Answer only five questions from this section in the spaces provided.*