KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 Mathematics
The length of a room is 3 m shorter than three times its width. The height of the room is a quarter of its length. The area of the floor is 60 m^{2}.
(a) Calculate the dimensions of the room. (b) The floor of the room was tiled leaving a border of width y m, all round. If the area of the border was 1.69m^{2}, find: (i) the width of the border; (ii) the dimensions of the floor area covered by tiles.
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Form 3 Mathematics
(a) The 5th term of an AP is 82 and the 12th term is 103.
Find: (i) the first term and the common difference; (ii) the sum of the first 21 terms. (b) A staircase was built such that each subsequent stair has a uniform difference in height. The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145 cm. Calculate the height of the 1st stair and the uniform difference in height of the stairs. Form 4 Mathematics
A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B.
He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B, (a) Write the inequalities in terms of x and y which satisfy the above information. (b) On the grid provided represent the inequalities in part (a) above (c) The trader makes a profit of Ksh 12 on a packet of type A rice and Ksh 8 on a packet of type B rice. Determine the maximum profit the trader can make. Form 3 Mathematics
Three quantities X, Y and Z are such that X varies directly as the square root ofY and inversely as the fourth root of Z. When X = 64, Y = 16 and Z = 625.
(a) Determine the equation connecting X, Y and Z. (b) Find the value of Z when Y = 36 and X = 160. (c) Find the percentage change in X when Y is increased by 44%. Form 4 Mathematics
The figure below represents a cuboid ABCDEFGH in which AB = 16 cm, BC = 12 cm and CF = 6 cm.
(a) Name the projection of the line BE on the plane ABCD.
Calculate correct to 1 decimal place: (i) the size of the angle between AD and BF; (ii) the angle between line BE and the plane ABCD; (iii) the angle between planes HBCE and BCFG. (c) Point N is the midpoint of EF. Calculate the length BN, correct to 1 decimal place. Form 3 Mathematics
The table below shows values of x and some values of for the curve y = x^{3} 2x^{2} 9x + 8 for 3 ≤ x ≤ 5. Complete the table.
(b) On the grid provided, draw the graph of y = x^{3} 2x^{2} 9x + 8 for 3 ≤ x ≤ 5 for Use the scale; 1 cm represents 1 unit on the xaxis 2 cm represents 10 units on the yaxis
(c) (i) Use the graph to solve the equation x^{2}  2x^{3} 9x + 8 = 0. (ii) By drawing a suitable straight line on the graph, solve the equation x^{2}  2x^{2} 11x + 6 = 0. 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 x^{2}+ y^{2}  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 MathematicsForm 2 Mathematics
Without using mathematical tables or a calculator, evaluate
5/6 log_{10} 64 + log_{10} 50  41og_{10} 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. Form 3 Mathematics
The roots of a quadratic equation are x = 3/5 and x = 1. Form the quadratic equation in the form ax^{2} + bx + c = 0 where a, b and c are integers.
Form 4 Mathematics
The equation of a curve is given as y = 2x^{3} 9/2 x^{2} 15x + 3.
(a) Find: (i) the value of y when x = 2; (ii) the equation of the tangent to the curve at x = 2. (b) Determine the turning points of the curve. Form 3 Mathematics
An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs, (a) Write an expressions in terms of x for: (i) original price per chair; (ii) price per chair after discount. (b) Determine: (i) the number of chairs the institution originally intended to buy; (ii) price per chair after discount; (iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%. Form 4 Mathematics
(b) Mambo bought 3 exercise books and 5 pens for a total of Ksh 165. 1f Mambo had bought 2 exercise books and 4 pens, he would have spent Ksh 45 less. Taking x to represent the price of an exercise book and y to represent the price of a pen:
(i) Form two equations to represent the above information. (ii) Use matrix method to find the price of an exercise book and that of a pen. (iii) A teacher of a class of 36 students bought 2 exercise books and 1 pen for each student. Calculate the total amount of money the teacher paid for the books and pens. 
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