Form 3 Mathematics
Simplify
Give the answer in the form a + b √c where a, b and c are integers.
ANSWER
 KCSE Mathematics Topical Questions and Answers in PDFForm 1 Topical Questions and Answers for KCSE
Marking Schemes
Form 3 Mathematics(a) complete the table below, giving your values correct to 2 decimal places ( 2 marks) 
(b) On the grid provided, using the same scale and axes, draw the graphs of y = sin x0 and y = 1 – cos x0 ≤ x ≤ 1800 Take the scale: 2 cm for 300 on the x- axis 2 cm for I unit on the y- axis (c) Use the graph in (b) above to (i) Solve equation 2 sin xo + cos x0 = 1 ( 1 mark) (ii) Determine the range of values x for which 2 sin xo > 1 – cos x0 ( 1 mark)
Answer
Form 3 Mathematics
Given that sin 2x = cos (3x — 10°), find tan x, correct to 4 significant figures.
answer
Form 3 MathematicsAbdi and Amoit were employed at the beginning of the same year. Their annual salaries in shillings progressed as follows: Abdi: 60,000, 64 800, 69, 600 (a) Calculate Abdi’s annual salary increment and hence write down an expression for his annual salary in his nth year of employment( 2 marks) (b) Calculate Amoit’s annual percentage rate of salary increment and hence write down an expression for her salary in her nth year of employment. ( 2 marks) (c) Calculate the differences in the annual salaries for Abdi and Amoit in their 7th year of employment ( 4 marks)
Answer
Form 3 MathematicsExpand and simplify (3x – y)4. Hence use the first three terms of the expansion to approximate the value of (6-0.2)4 ( 4 marks)
Answer
Form 3 Mathematics
The table below shows monthly income tax rates for a certain year.
In that year a monthly personal tax relief of Ksh 1 280 was allowed. In a certain month of that year, Sila earned a monthly basic salary of Ksh 52 000, a house allowance of Ksh 7 800 and a commuter allowance of Ksh 5 000.
(a) Calculate: (i) Sila’s taxable income; (ii) the net tax payable by Sila in that month; (b) In July that year, Sila’s basic salary was raised by 4%. Determine Sila’s net salary in July.
answers
Form 3 Mathematics
(a)Complete the table below for the equation y = x2-4x+2
(b) On the grid provided draw the graph y = x2 - 4x + 2 for 0 ≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis.
(c) Use the graph to solve the equation, x2 -4x + 2 = 0 (d) By drawing a suitable line, use the graph in (b) to solve the equation x2 -5x + 3 = 0.
ANSWERS
Form 3 Mathematics
The 5th and 10th terms of an arithmetic progression are 18 and -2 respectively.
(a) Find the common difference and the first term. (b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum.
answer
Form 3 Mathematics
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.
answer
Form 3 Mathematics
In the figure below OP = p, OR = r, PQ:QR = 1:2 and PS = 3PR.
Express QS in terms of p and r.
answer
Form 3 Mathematics
The table below represents a relationship between two variables x and y.
(a) On the grid provided draw the line of best fit.
(b) Use the graph to find the value off when x = 0.
answers
Form 3 Mathematics
Use completing the square method to solve 3x2 + 8x — 6 = 0, correct to 3 significant figures.
answer
Form 3 Mathematics
In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60° at the centre of the circle.
Calculate the area of the shaded region, correct to 1 decimal place.
answer
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