KCSE PAST PAPERS 2018: MATHEMATICS Alt.A Paper 2 (121/2) QUESTIONS AND ANSWERS (SECTION I)

KCSE PAST PAPERS 2018: MATHEMATICS ALT.A PAPER 2 (121/2) QUESTIONS AND ANSWERS (SECTION I)

1.

Given that \[\large 2logx^{2}+log\sqrt{x}=klogx\], find the value of k. (2 marks)

2.

A variable P varies directly as t³ and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t = 3. (4 marks)

3.

Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second year, Asia had Ksh 170130 in the financial institution. Determine the amount of money Asia invested. (3 marks)

4.

The figure below represents a wedge ABCDEF. EF = 10 cm, angle FBE = 45⁰ and the angle between the planes ABFE and ABCD is 20⁰.

Calculate length BC, correct to 1 decimal place. (3 marks)

5.

\[\large simplify; \frac{\sqrt{54}+3\sqrt{3}}{\sqrt{3}}\]

6.

In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60⁰ at the centre of the circle.

Calculate the area of the shaded region, correct to 1 decimal place. (4 marks)

7. 

Use completing the square method to solve 3x² + 8x — 6 = 0, correct to 3 significant figures. (3 marks)

8.

Three workers, working 8 hours per day can complete a task in 5 days. Each worker is paid Ksh 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day to complete the same task. (3 marks)

9.

The table below represents a relationship between two variables x and y.

a) On the grid provided draw the line of best fit.     (3 marks)
b) Use the graph to find the value of y when x = 0. (1 mark)

10.

State the amplitude and phase angle of the curve \[y=2sin\left ( \frac{3}{2}x-30^{0} \right ).\]

11.

The mass, in kilograms, of 9 sheep in a pen were:
13,8, 16, 17, 19, 20, 15, 14 and 11.
Determine the quartile deviation of the data. (3 marks)

12.

The position of two points C and D on the earth’s surface are \[(0^{0}N,10^{0}E)and(0^{0}N,30^{0}E)\] respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. (3 marks)

13.

In the figure below OP = p, OR = r, PQ:QR = 1:2 and PS = 3PR.

Express QS in terms of p and r. (4 marks)

14.

In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen. (3 marks)

15.

Under a transformation \[\large T=\begin{pmatrix} 4 & -3\\ 2 & 3 \end{pmatrix}\], triangle OAB is mapped onto triangle \[\large O{A}'{B}' \enspace with\enspace vertices \enspace O(0,0), {A}'(18,0), and\enspace {B}'(18,6)\]. Find the area of triangle OAB. (3 marks)

16.

Find the value of k if \[\large \int_{0}^{2}(kx^{3}-3x^{2})dx=16.\]. (4 marks)

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