KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 2  KCSE 2023  Approximation & Errors  PAPER 2  FORM 3 LEVELThe masses of two students in a class were measured as 30.5 kg and 36.8 kg. Determine the least possible difference in the masses of the two students. (3 marks)
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QUESTION 1  KCSE 2023  INDICES & LOGARITHMS  PAPER 2  FORM 2 LEVELSolve the equation 1 + log(2x – 9) = log(3x + 5)  log 2. (3 marks)
QUESTION 24  KCSE 2023  Geometrical constructions  PAPER 1  FORM 1 LEVELIn this question, use a ruler and a pair of compasses only. Line PR is a diagonal of a quadrilateral PQRS, PR = 6 cm
QUESTION 23  KCSE 2023  differentiation  PAPER 1  FORM 4 LEVELThe displacement, x metres, of a particle moving a long straight line after t seconds is given by x = t³/3  3t² + 9.
The following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S29/12/2023 QUESTION 22  KCSE 2023  TRIGONOMETRY II  PAPER 1  FORM 3 LEVELThe following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S. Lines PQ = PR = 2.7 cm, PS = 6 cm, SR = 7 cm and ∠PQR = 65°.
The end of term test scores of 100 students were recorded as shown in the following table.29/12/2023 QUESTION 21  KCSE 2023  STATISTICS I  PAPER 1  FORM 2 LEVELThe end of term test scores of 100 students were recorded as shown in the following table.
QUESTION 20  KCSE 2023  Commercial arithmetic II  PAPER 1  FORM 3 LEVELNeema went to the market to buy bananas worth Ksh 2 100 for a school. The seller offered a discount of Ksh 3 per banana which enabled Neema to buy 35 more bananas.
QUESTION 19  KCSE 2023  Surface Area and Volume of Solids  PAPER 1  FORM 2 LEVELThe following figure shows a right pyramid VABCD. The base ABCD of the pyramid is a square of side 8 cm. The length of the slanting edges VA = VB = VC = VD = 10 cm. Calculate:
(a) the vertical height of the pyramid correct to 2 decimal places. (4 marks) (b) surface area of the pyramid. (4 marks) (c) the volume of the pyramid. (2 marks) QUESTION 18  KCSE 2023  MATRICES & TRANSFORMATIONS  PAPER 1  FORM 4 LEVELOn the following grid, triangle PQR is drawn.
QUESTION 17  KCSE 2023  LINEAR MOTION  PAPER 1  FORM 2 LEVELTwo towns, A and B are 400 km apart. A motor cyclist travelling at an average speed of 60 km/h left town A for town B at 1.20 p.m. A matatu travelling at an average speed of 80 km/li also left town A for town B at 2.00 p.m.
QUESTION 16  KCSE 2023  GRAPHICAL METHODS  PAPER 1  FORM 3 LEVELOn the following cartesian plane provided, solve the simultaneous equations.
y = 4/3 x + 2; 3y = x  3 QUESTION 15  KCSE 2023  DIFFERENTIATION  PAPER 1  FORM 4 LEVELThe equation of a curve curve is given by y = 3x²  2x. Determine the equation of a normal to the at x = 2. (4 marks)
QUESTION 14  KCSE 2023  Statistics I  PAPER 1  FORM 2 LEVELIn a sub county the number of children per family was recorded from 30 families. The data recorded is as follows: (a) Represent the data in a frequency distribution table. (1 mark)
(b) Calculate the mean number of children per family. (2 marks) QUESTION 13  KCSE 2023  MATRICES  PAPER 1  FORM 3 LEVELGiven Matrix P = [4 2]upperrow[7 1]lowerrow, Q = [1 5]upperrow[6 3]lowerrow and R = 20P^1 + Q, Determine matrix R. (3 Marks)
QUESTION 12  KCSE 2023  VECTORS I  PAPER 1  FORM 2 LEVELVectors a, b and e are represented on the following grid. On the following grid, represent:
(a) the resultant vector a + b (2 marks) (b) the resultant vector (a + b) + c (2 marks) QUESTION 11  KCSE 2023  AREA APPROXIMATION  PAPER 1  FORM 4 LEVELThe equation of a curve is given by y = x². Using the trapezium rule with 4 strips, estimate the area enclosed by the curve y = x², the lines x = 1, x = 5 and the xaxis. (4 marks)
QUESTION 10  KCSE 2023  COMMERCIAL ARITHMETIC II  PAPER 1  FORM 3 LEVELA salesman sells story books and textbooks. The cost price of a story book is sh 600 while that of a textbook is sh 900. The salesman is paid a commission of 10% on the cost of any book sold. One day, the salesman sold twice as many story books as textbooks. He earned a commission of sh 8 400.
Determine the total number of story books sold. (3 marks) QUESTION 9  KCSE 2023  THREE DIMENSIONAL GEOMETRY  PAPER 1  FORM 4 LEVELIn the following figure, triangle ABC is a uniform cross section of a solid ABCDEF. Given that BE is one of the edges of the solid, complete the sketch showing hidden edges with broken lines. (3 marks)
QUESTION 8  KCSE 2023  SCALE DRAWING  PAPER 1  FORM 2 LEVELFrom a point on top of a cliff 40 m high, two boats A and B are observed due East. The angle of depression of boat A is 32° and that of boat B is 52°. Determine the distance between the two boats, correct to 2 decimal places. (4 marks)
QUESTION 7  KCSE 2023  Quadratic Expressions  PAPER 1  FORM 3 LEVELSimplify and hence factorise the expression (5x  4y) (4x + 5y)  9xy. (3 marks)
QUESTION 6  KCSE 2023  TRIGONOMETRY II  PAPER 1  FORM 3 LEVELSolve the equation cos 2θ = sin θ for 0^c ≤ θ ≤ π^c/4. Leave the answer in terms of n^c.
(3 marks) QUESTION 5  KCSE 2023  L.C.M  PAPER 1  FORM 1 LEVELTwo light bulbs are set to light after every 40 seconds and 60 seconds respectively. If they light exactly at the same time initially, calculate:
(a) the time, in minutes, they will take to light together again. (2 marks) (b) the number of times they would light together in the first half an hour. (1 mark) QUESTION 4  KCSE 2023  VOLUME & CAPACITY  PAPER 1  FORM 2 LEVELA cylindrical solid of radius 7 cm has a conical top of the same radius. The height of the cylindrical part of the solid is 17 cm. The conical top has a vertical height of 9 cm. Calculate the volume of the solid. (Take π = 22/7) (3 marks)
QUESTION 3  KCSE 2023  AREA OF A TRIANGLE  PAPER 1  FORM 2 LEVELA triangle ABC is such that AB = 11 cm, BC = 8 cm and ABC = 53°. Calculate the area of the triangle correct to 2 decimal places. (2 marks)
QUESTION 2  KCSE 2023  INDICES  PAPER 1  FORM 2 LEVELSimplify the expression [3a²b^3] / [2^1 a^2 b²] (2 marks)

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