KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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.
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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) QUESTION 20  KCSE 2021  COMMERCIAL ARITHMETIC II  PAPER 2  FORM 3 LEVELThe table below shows income tax rates in a certain year. In the year, the monthly earnings of Kanini were as follows: Basic salary House allowance Ksh 64 500 Ksh 12 000 Kanini contributes 7.5% of her basic salary to a pension scheme. This contribution is exempted from taxation. She is entitled to a personal tax relief of Ksh 1 408 per month. Calculate:
In the figure below, points A, B, C, and E lie on the circumference of the circle centre O28/12/2023 QUESTION 19  KCSE 2021  ANGLE PROPERTIES OF A CIRCLE  PAPER 2  FORM 3 LEVELIn the figure below, points A, B, C, and E lie on the circumference of the circle centre O. Line FAG is a tangent to the circle at A. Chord DE of the circle is produced to intersect with the tangent at F. Angle FAE = 30°, Angle EDC = 110° and Angle OCB =55°
QUESTION 18  KCSE 2021  AREA  PAPER 2  FORM 3 LEVELA rectangular plot measures 50 m by 24 m. A lawn, rectangular in shape, is situated inside the plot with a path surrounding it as shown in the figure below. The width of the path in x m between the lengths of the lawn and those of the plot and 2x m between the widths of the lawn and those of the plot.
QUESTION 17  KCSE 2021  COMPOUND PROPORTIONS AND RATES OF WORK  PAPER 2  FORM 3 LEVELPump P can fill an empty water tank in 7 1/2 hours while pump Q can fill the same tank in 11 1/4 hours. On a certain day, when the tank was empty, both pumps were opened for 2 1/2 hours.
Find the area enclosed by the curve y = xยฒ + 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) In a transformation an object of area x cmยฒ is mapped on to an image whose area is 13x cmยฒ.28/12/2023 QUESTION 15  KCSE 2021  Matrices & Transformations  PAPER 2  FORM 4 LEVELIn a transformation an object of area x cm² is mapped on to an image whose area is 13x cm². Given that the matrix of the transformation is [(x 7)upper row and (x1 3x)lower row] find the possible values of x. (3 marks)
QUESTION 14  KCSE 2021  VECTORS II  PAPER 2  FORM 3 LEVELThe position vectors of points P, Q and R are OP = 6i  2j + 3k, OQ = 12i  5j + 6k and OR = 8i  3j + 4k. Show that P, Q and R are collinear points. (3 marks)
QUESTION 13  KCSE 2021  GEOMETRICAL CONSTRUCTION  PAPER 2  FORM 1 LEVELThe figure below shows triangle XYZ. Using a ruler and a pair of compasses, locate a point M on the triangle such that M is 2 cm from line YX and is equidistant from lines YX and YZ. Measure length YM. (3 marks)
QUESTION 12  KCSE 2021  Probability  PAPER 2  FORM 3 LEVELA box contains 3 brown balls and 9 green balls. The balls are identical except for the colours. Two balls are picked at random without replacement.
(a) Draw a tree diagram to show all the possible outcomes. (1 mark) (b) Determine the probability that the balls picked are of different colours. (2 marks) QUESTION 11  KCSE 2021  LONGITUDES  PAPER 2  FORM 4 LEVELA point Q is 2000 nm to the West of a point P(40°N, 155°W). Find the longitude of Q to the nearest degree. (3 marks)
QUESTION 10  KCSE 2021  TRIGONOMETRY III  PAPER 2  FORM 4 LEVELThe equation of a trigonometric wave is y = 4 sin (ax70)°. The wave has a period of 180°.
(a) Determine the value of a. (1 mark) (b) Deduce the phase angle of the wave. (1 mark) The table below shows the values of t and the corresponding values of h for a given relation28/12/2023 QUESTION 9  KCSE 2021  GRAPHICAL METHODS  PAPER 2  FORM 3 LEVELThe table below shows the values of t and the corresponding values of h for a given relation. (a) On the grid provided, draw a graph to represent the information on the table given. (2 marks) (b) Use the graph to determine, correct to 1 decimal place, the rate of change of h at t = 3. (2 marks)
QUESTION 8  KCSE 2021  COMMERCIAL ARITHMETICS II  PAPER 2  FORM 3 LEVELThe cash price of a gas cooker is Ksh 20 000. A customer bought the cooker on hire purchase terms by paying a deposit of Ksh 10 000 followed by 18 equal monthly instalments of Ksh 900 each. Annual interest, compounded quarterly, was charged on the balance for the period of 18 months. Determine, correct to 1 decimal place, the rate of interest per annum. (4 marks)
QUESTION 7  KCSE 2021  Three Dimensional Geometry  PAPER 2  FORM 4 LEVELThe figure below represents a prism ABCDEFGH of length 6 cm. The cross section BCFG of the prism is a trapezium in which GF = 11 cm, BC = 8 cm, BG = 5 cm and GFC = BCF = 90°. Calculate correct to 1 decimal place the angle between the line FA and the plane GFEH. (3 marks)
QUESTION 6  KCSE 2021  Formula & Variations  PAPER 2  FORM 3 LEVELFour quantities P, Q, R and S are such that P varies directly as the square root of Q and inversely as the square of the difference of R and S. Quantity Q is increased by 44% while quantities R and S are each decreased by 10%.
Find the corresponding percentage change in P correct to 1 decimal place. (4 marks) QUESTION 5  KCSE 2021  Circles, Chords & Tangents  PAPER 2  FORM 3 LEVELThe figure below shows a circle and a point P outside the circle Using a ruler and pair of compasses, construct a tangent to the circle from P. (4 marks)
QUESTION 4  KCSE 2021  Formula & Variations  PAPER 2  FORM 3 LEVELQUESTION 3  KCSE 2021  Quadratic Equations  PAPER 2  FORM 3 LEVELThe expression ax²  30x + 9 is a perfect square, where a is a constant. Find the value of a.
(2 marks) QUESTION 2  KCSE 2021  Sequence & series  PAPER 2  FORM 3 LEVELThe first term of a Geometric Progression (G.P) is 2. The common ratio of the G.P is also 2. The product of the last two terms of the G.P is 512. Determine the number of terms in the G.P. (3 marks)
QUESTION 1  KCSE 2021  Compound proportions and rates of work  PAPER 2  FORM 4 LEVELAn empty tank of capacity 18480 litres is to be filled with water using a cylindrical pipe of diameter 0.028 m. The rate of flow of water from the pipe is 2 m/s. Find the time in hours it would take to fill up the tank. (Take π = 22/7). (3 marks)
QUESTION 24  KCSE 2021  DIFFERENTIATION  PAPER 1  FORM 4 LEVELThe equation of a curve is given as y = 1/3 X^3  1/2X^2  2X  1/3.

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