KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
ALT B  SCALE DRAWING  SECTION 2  QUESTION 24  KCSE 2010  FORM 1 LEVELThe angle of elevation of the top of a vertical mast, viewed by an observer 50m away, was found to be 16.7°.
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Three alarms are programmed to sound at intervals of 25 minutes, 30 minutes and 35 minutes.2/3/2024 ALT B  LCM  SECTION 1  QUESTION 14  KCSE 2010  FORM 1 LEVELThree alarms are programmed to sound at intervals of 25 minutes, 30 minutes and 35 minutes. Given that the three alarms sound together at a particular time, determine the time, in hours, it will take for them to sound together again. (4 marks)
ALT B  FRACTIONS  SECTION 1  QUESTION 7  KCSE 2010  FORM 1 LEVELWithout using a calculator, evaluate: (3 marks)
PROBABILITY  PAPER 1  SECTION B  KCSE 1997  FORM 3 LEVELThe water supply in a town depends entirely on two water pumps, A and B. The probability of pump A filling is 0.1, and the probability of pump B failing is 0.2. Calculate the probability that:
LONGITUDES & LATITUDES  KCSE 1997  PAPER 1  SECTION B  FORM 4 LEVELA ship leaves an island (5°N, 45°E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km) GEOMETRIC CONSTRUCTION  KCSE 1997  PAPER 1  SECTION B  FORM 1 LEVELUsing ruler and compasses only, construct triangle ABC such that AB = 4 cm, BC = 5 cm, and ∠ABC = 120°. Measure AC.
On the diagram, construct a circle which passes through the vertex of the triangle ABC. Measure the radius of the circle. Measure the shortest distance from the centre of the circle to line BC. SURFACE AREA OF SOLIDS  KCSE 1997  PAPER 1  FORM 2 LEVEL  SECTION BThe figure below shows a portable kennel.
MATRICES  FORM 3 LEVEL  KCSE 1997  SECTION B  PAPER 1The figure on the grid shows a triangular shaped object ABC and its image A'B'C'. (a)
(d) Hence find the area of the image A” B” C LINEAR EQUATIONS  FORM 2 LEVEL  KCSE 1997  PAPER 1  SECTION BThe coordinates of the points P and Q are (1, 2) and (4, 10) respectively. A point T divides the line PQ in the ratio 2:1.
VECTORS I  FORM 2 LEVEL  PAPER 1  SECTION B  KCSE 1997In the figure below, OA is equal to A, OB is equal to B, AB is equal to BC, and OB is to BD in a ratio of 3:1. (a) Determine
kcse 1996  paper 1  section a  question 3  commercial arithmetic  form 1 levelThe cost of 5 skirts and 3 blouses is Kshs 1750. Mueni bought three of the skirts and one of the blouses for Kshs 850. Find the cost of each item (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)

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