- The length of two similar iron bars were given as 12.5 m and 9.23 m. Calculate the maximum possible difference in length between the two bars. (3 marks)
- The first term of an arithmetic sequence is -7 and the common difference is 3.
- List the first six terms of the sequence; (1 mark)
- Determine the sum of the first 50 terms of the sequence. (2 marks)

- In the figure below, BOD is the diameter of the circle centre O. Angle ABD =30
^{0}and angle AXD = 70^{0}.

Determine the size of ;- Reflex angle BOC; (2 marks)
- Angle ACO. (1 mark)

- Three quantities L, M and N are such that L, varies directly as M and inversely as the square of N. Given that L = 2 when M = 12 and N = 6, determine the equation connecting the three quantities. (3 marks)
- The table below shows the frequency distribution of marks of students scored in a test.

Determine the median mark correct to 2 s.f. (4 marks)**Marks****Frequency**1-10 2 11-20 4 21-30 11 31-40 5 41-50 3 - Determine the amplitude and period of the function,
*y*= 2 cos (3*x*- 45)^{0}. (2 marks) - In a transformation, an object with n area of 5 cm
^{2}is mapped onto an image whose area is 30 cm^{2}. Given the matrix of transformation is , find the value of*x*. (3 marks) - Expand (3 - x )
^{7}up to the term containing x^{4}. Hence find the aproximate value of (2.8)^{7}. (3 marks) - Solve for the equation;

2 log 15 - log*x*= log 5 + log (*x*- 4). (4 marks) - The figure below represents a cuboid PQRSTUVW.

PQ = 60 cm, QR = 11 cm, RW = 10 cm.

Calculate the angle between line PW and plane PQRS, correct to 2 decimal places. (3 marks) - Solve the simultaneous equations; (4 marks)

3*x*-*y*= 9*x*^{2}-*xy*= 4 - Muga bought a plot of land for Ksh 280 000. After 4 years, the value of plot was Ksh 495 000. Determine the rate of appreciation, per annum, correct to one decimal place. (3 marks)
- The shortest distance between two points A (40
^{0}N, 20^{0}W) and B(0^{0}S, 20^{0}W) on the surface of the earth IS 8008 km. Given that the radius of the earth is 6370 km, determine the position of B.

(Take π =^{22}/_{7})(3 marks) - Vectors
**r**and**s**are such that**r**= 7**i**+ 2**j**-**k**and**s**= -**i**+**j**-**k**. Find |**r**+**s|**. (3 marks) - The gradient of a curve is given by . The curve passes through the point (1, 0). Find the equation of the curve. (3 marks)
- The graph below shows the rate of cooling of a liquid with respect to time.

Determine the average rate of cooling of the liquid between the second and the eleventh minutes. (3 marks)

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