- 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 =300 and angle AXD = 700.
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 (3x - 45)0. (2 marks)
- In a transformation, an object with n area of 5 cm2 is mapped onto an image whose area is 30 cm2. Given the matrix of transformation is , find the value of x. (3 marks)
- Expand (3 - x )7 up to the term containing x4. 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)
3x - y = 9
x2 - 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 (400N, 200W) and B(00S, 200W) 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 = 7i + 2j - 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.