KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
The table below shows values of x and some values of for the curve y = x3 -2x2 -9x + 8 for -3 ≤ x ≤ 5. Complete the table.
(b) On the grid provided, draw the graph of y = x3- 2x2- 9x + 8 for -3 ≤ x ≤ 5 for Use the scale; 1 cm represents 1 unit on the x-axis 2 cm represents 10 units on the y-axis
(c) (i) Use the graph to solve the equation x2 - 2x3 -9x + 8 = 0. (ii) By drawing a suitable straight line on the graph, solve the equation x2 - 2x2- 11x + 6 = 0.
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Form 4 Mathematics
The vertices ofa rectangle ABCD are: A(0,2), B(0,4), C(4,4) and D(4,2). The vertices of its image under a transformation T are; A’(0,2) , B’(0,4) , C’(8,4) and D’(8,2).
On the grid provided, draw the rectangle ABCD and its image A’B’C’D’ under T. (ii) Describe fully the T. (iii) Determine the matrix of transformation. (b). On the same grid as in (a), draw the image of rectangle ABCD under a shear with line x =-2 invariant and A(0, 2) is mapped onto A”(0,0). Form 3 Mathematics
The income tax rates of a certain year were as shown in the table below:
In that year, Shaka’s monthly earnings were as follows: Basic salary Ksh 28600
House allowance Ksh 15 000 Medical allowance Ksh 3 200 Transport allowance Ksh 540 Shaka was entitled to a monthly tax relief of Ksh 1056. (a) Calculate the tax charged on Shaka’s monthly earnings. (b) Apart from income tax, the following monthly deductions were made; a Health Insurance fund of Ksh 500, Education Insurance of Ksh 1 200 and 2% of his basic salary for widow and children pension scheme. Calculate Shaka’s monthly net income from his employment. Form 3 Mathematics
Given that OA = 3i+ 4j+ 7k, OB= 4i + 3j + 9k and OC = i + 6j + 3k. show that points A, B and C are collinear.
Form 4 MathematicsForm 3 Mathematics
A committee of 3 people was chosen at random from a group of 5 men and 6 women. Find the probability that the committee consisted of more men than women.
Form 4 Mathematics
A basket ball team scored the points in 6 matches: 10, 12, 14, 16, 28 and 30. Using an assumed mean of l5. Determine the standard deviation correct to 2 decimal places.
Form 4 Mathematics
Determine the amplitude, period and the phase angle of the curve: y = 5/2 sin (4θ + 60°)
Form 3 Mathematics
The equation of a circle is x2+ y2 - 4x + 6y + 4 = 0. On the grid provided, draw the circle.
Form 4 Mathematics
An aircraft took off from a point P (65° S, 76° W) and flew due North to a point Q. The distance between P and Q is 5400 nm.
Determine the position of Q. Form 4 MathematicsForm 1 Mathematics
Using a ruler and a pair of compasses only, construct:
(a) a triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = 45° (b) the circle that touches all the sides of the triangle. Form 3 Mathematics
Two teachers are chosen randomly from a staff consisting 3 women and 2 men to attend a HIV/AIDs seminar. Calculate the probability that the two teachers chosen are:
(a) Of the same sex
(b) Of opposite sex Form 2 Mathematics
Given that sin (90 – x)0 = 0.8, where x is an acute angle, find without using mathematical tables the value of tan x0.
Form 3 MathematicsA point R divides a line PQ internally in the ration 3:4. Another point S, divides the line PR externally in the ration 5:2. Given that PQ = 8cm, calculate the length of RS, correct to 2 decimal places. Form 1 MathematicsThe size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon. Form 2 MathematicsThe area of a rhombus is 60cm2. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus Form 1 MathematicsForm 3 MathematicsForm 2 Mathematics
Without using mathematical tables or a calculator, evaluate
5/6 log10 64 + log10 50 - 41og10 2. Form 1 Mathematics
A miller was contracted to make porridge flour to support a feeding program. He mixed millet, sorghum, maize and Omena in the ration 1:2:5:1. The cost per kilogram of millet was Ksh 90, sorghum Ksh 120, maize Ksh 30 and omena Ksh 150.
Calculate: (a) the cost of one kilogram of the mixture; (b) the selling price of 1 kg of the mixture if the miller made a 30% profit. |
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