KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
 surface area of solids  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 24 The figure below represents a frustum of a cone with dimensions as shown.
Taking π = 3.142, calculate:
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 SCALE DRAWING  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 23 A piece of land is in the shape of a quadrilateral ABCD. Point B is 450 m east of A. Point D is 500 m from A on a bearing of 310°. Point C is 700 m from D on a bearing of 080°.
 SCALE DRAWING  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 22 In the figure below, BC = 12 cm, ∠ACB = 40°, ∠ BAD = 60°, BCD is a straight line and CE is parallel to BA.
Calculate:
 CHORDS AND TANGENTS  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 21 In the figure below, points L, M, N and P are on the circumference of a circle centre O. Line LON is a diameter of the circle. PL = PN and angle NLM = 20°.
Find, giving a season in each case, the size of each of the following angles. (a) ∠ MPN; (2 marks) (b) ∠ PLN; (2 marks) (c) ∠ LPM; (2 marks) (d) ∠ MNP; (2 marks) (e) ∠ PMO; (2 marks)  MATRICES AND TRANFORMATIONS  FORM 4 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 20 The figure below shows triangle ABC with coordinates A (1, 3), B (1, 1) and C (3, 2).
 COMMERCIAL ARITHMETIC  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 19 Three partners, Amani, Furaha and Nehema, contributed a total capital of Ksh 750 000 to start a business. Amani contributed 1/3 of the money, Furaha contributed 2/5 of the money and Nehema contributed the rest.
After some time the business realised a profit of 36% of the capital. The profit was taxed at the rate of 5%. After taxation, each of the partners received Ksh 20 000 of the profit. The remainder of the profit was shared among the three partners in the ratio of their contributions. Calculate:
 LINEAR EQUATIONS  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 18 Three straight lines L₁, L₂, and L3, are such that:
L1, cuts the yaxis at y = 5 and has a gradient of 2; L₂ is perpendicular to L1, at the point where L1, cuts the xaxis; L3, is parallel to L2, and passes throught point (1, 2).
 COMMERCIAL ARITHMETIC  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 17 A salesman was paid a basic salary of Ksh 48 000 per month plus a commission of 3% for sales of goods worth above Ksh 500 000.
In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°22/3/2024  angle properties of a circle  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 16 In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°
Determine the total area of the shaded regions to 2 decimal places. (4 marks)  SIMULTANEOUS EQUATIONS  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 15 Solve the simulataneous equations:
p  q = 3 p²  q² = 21  ANGLES AND PLANE FIGURES  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 14 The sum of interior angles of a regular polygon is 1620°. Calculate the number of sides of the polygon. (2 marks)
 FACTORIZATION  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 13 Use factorization method to solve the equation: 1/8 x^2 + x = 48.
 SIMILARITY and Enlargement  FORM 2 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 12 The areas of the lids of two similar cylinders are 16 cm² and 25 cm². If the volume of the bigger cylinder is 800 cm³, find the volume of the smaller cylinder. (4 marks)
 geometrical constructions  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 11 Using a ruler and a pair of compasses only, construct triangle ABC such that AB = 4.5 cm, BC = 8.1 cm and angle CBA = 60°. Measure angle CAB.
(3 marks)  logarithms  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 10 Use logarithm tables to evaluate √(2.5 × 0.064) / 8.1
A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top.22/3/2024  LENGTH  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 9 A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top. The cable is anchored on the ground at a distance of 2.5 m from the foot of the pole. Determine the height of the pole. (3 marks)
 GCD  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 7 Three metal rods of lengths 234 cm, 270 cm and 324 cm were cut into shorter pieces, all of the same length, to make window grills.
Calculate the length of the longest piece that can be cut from each of the rods and hence the total number of pieces that can be obtained from the rods. (4 marks)  LINEAR INEQUALITIES  FORM 2 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 6 Find the integral values of x which satisfy the inequality 3x ≤ 2x + 3 < 4x + 5. (3 marks)
 VOLUME AND CAPACITY  FORM 2 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 5 A cylindrical container of height 45 cm has a capacity of 25 litres. Find the radius of the container to the nearest millimetre. (3 marks)
Use cube tables to calculate, to 4 significant figures, the volume of a cube whose side is 0.4321 m22/3/2024  VOLUME AND CAPACITY  FORM 2 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 4 Use cube tables to calculate, to 4 significant figures, the volume of a cube whose side is 0.4321 m. (3 marks)
 TIME  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 3 On a certain day a journalist started travelling at 0850 hours to attend a meeting. He travelled for 6½ hours and then rested for 1 hour 45 minutes. He attended the meeting for 3% hours and travelled for 35 minutes to a hotel.
Determine the time, in 12hour clock system, the journalist arrived at the hotel. (3 marks) ALT B  GRAPHICAL METHODS   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 24Some water is heated in a beaker and then left to cool for 12 minutes. After the heating is stopped, the relationship between the water temperature C, in degrees centigrade and the time t, after heating is given as C = 100 1/2 T^2.

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