KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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 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).
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ALT B  AREA APPROXIMATION   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 22A quadrant (a quarter of a circle) of radius 10 cm is drawn on the grid below. The quadrant is divided into 5 vertical strips.
ALT B  STATISTICS II   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 19The table below represents the number of streams in 20 schools.
Calculate: (a) the mean number of streams per school; (3 marks) (b) the variance; (5 marks) (c) the standard deviation correct to 2 decimal places. (2 marks) ALT B  LONGITUDES AND LATITUDES   FORM 4 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 14The positions of two points A and B on the surface of the earth are A(32.8°N, 26°E) and B(21.2°S, 26°E).
Calculate in kilometres the shortest distance between A and B. (Take the radius of the earth to be 6370 km and π = 22/7) (3 marks) ALT B  MATRICES & TRANSFORMATIONS  SECTION 1  QUESTION 17  KCSE 2010  FORM 4 LEVELThe points A(6,1), B(3,2), C(4,5) and D (9,5) are vertices of an object ABCD as shown in the figure below.
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) QUESTION 23  KCSE 2023  INTEGRATION  PAPER 2  FORM 4 LEVELThe following figure is a sketch of a curve whose equation is y = 3x²  9x. The curve cuts the xaxis at O(0, 0) and at R(3, 0). The curve cuts the line y and Q. The coordinates of Q is (4, 12). Line RN is perpendicular to PQ at N.
QUESTION 22  KCSE 2023  LOCI  PAPER 2  FORM 4 LEVELIn this question, use a ruler and a pair of compasses only. The following figure is drawn to scale. It shows sides AB and AD of a trapezium ABCD in which AB and DC are parallel. Angle DAB = 40° and vertex C is not shown.
QUESTION 21  KCSE 2023  LINEAR PROGRAMMING  PAPER 2  FORM 4 LEVELAn express train operates between two towns. The train pulls x coaches on first class and y coaches on economy class. Each first class coach can hold 72 passengers while each economy class coach can hold 120 passengers.
The table below shows values of x and some values of y for the curve y = 14+ 10x 8x²  4x³.1/1/2024 QUESTION 20  KCSE 2023  TRIGONOMETRY III  PAPER 2  FORM 3 LEVEL
QUESTION 16  KCSE 2023  3d geometry  PAPER 2  FORM 3 LEVELP, Q and R are points on a level ground. Q is 4.5 m south of P. R is to the east of P and 5.3 m from Q. A vertical post at P is supported by a cable of length 3.5 m. The cable joins the top T of the post to point R.
Calculate the angle between the cable and the level ground correct to 2 decimal places. (3 marks) QUESTION 15  KCSE 2023  differentiation  PAPER 2  FORM 4 LEVELThe gradient function of a curve is given by dy/dx = 3  4x. If the curve passes through the point (1, 10), find the equation of the curve. (3 marks)
QUESTION 11  KCSE 2023  MATRICES & TRANSFORMATION  PAPER 2  FORM 4 LEVEL
A transformation matrix T = [1 0] [k 0] maps P(2, 3) onto P'(2, 10). Point Q(4, 4) is transformed under the same matrix T. Find the coordinates of Q', the image of Q. (3 marks)
T = \begin{pmatrix} 1 & 0 \\ K & 0 \\ \end{pmatrix}
The following table shows the frequency distribution of marks scored by 40 students in a test1/1/2024 QUESTION 7  KCSE 2023  STATISTICS II  PAPER 2  FORM 4 LEVELThe following table shows the frequency distribution of marks scored by 40 students in a test. Calculate the upper quartile mark. (3 marks)
QUESTION 5  KCSE 2023  LONGITUDES & LATITUDES  PAPER 2  FORM 4 LEVELA plane took 3 hours to fly from P(66.42°N, 30°E) to Q(66.42°N, 52.5°E). Determine the speed of the plane in knots correct to one decimal place. (3 marks)
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.
QUESTION 18  KCSE 2023  MATRICES & TRANSFORMATIONS  PAPER 1  FORM 4 LEVELOn the following grid, triangle PQR is drawn.
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 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 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 24  KCSE 2021  lINEAR mOTION  PAPER 2  FORM 4 LEVELA particle was moving along a straight line. The acceleration of the particle after t seconds was given by (4t13) ms^2. The initial velocity of the particle was 18 ms¹.
QUESTION 23  KCSE 2021  TRIGONOMETRY III  PAPER 2  FORM 4 LEVEL(a) Complete the table below giving the values correct to 1 decimal place. (b) On the grid provided and using the same axis, draw the graphs of y = 2sin(3/4 x)  2cos(3/4 x) and y = 1 + 2cos x for 0° ≤x≤ 360°. (4 marks)
QUESTION 22  KCSE 2021  STATISTICS II  PAPER 2  FORM 4 LEVELWorkers in a factory commute from their homes to the factory. The table below shows the distances in kilometres, covered by the workers. The mean distance covered was 14.5 km.
QUESTION 21  KCSE 2021  MATRICES & TRANSFORMATIONS  PAPER 2  FORM 4 LEVELThe vertices of the triangle shown on the grid are A' (3,3), B' (1,1) and C' (3,1). Triangle A'B'C' is the image of triangle ABC under a transformation whose matrix is (0 1)upperrow (1 2)lowerrow. (a) Find the coordinates of triangle A, B and C. (4 marks)
(b) Triangle A"B"C" is the image of triangle A'B'C' under a transformation matrix (2 marks) (2 0)upperrow (0 1)lowerrow. Determine the coordinates of A", B" and C". (c) On the same grid provided, draw triangles ABC and A"B"C". (2 marks) (d) Determine a single matrix, that maps ABC onto A" B"C". (2 marks) Find the area enclosed by the curve y = x² + 2x the straight lines x = 1, x = 3 and the xaxis28/12/2023 QUESTION 16  KCSE 2021  Integration  PAPER 2  FORM 4 LEVELFind the area enclosed by the curve y = x² + 2x the straight lines x = 1, x = 3 and the xaxis.
(3 marks) 
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