KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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)
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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)
QUESTION 1 | KCSE 2023 | INTEGERS | PAPER 1 | FORM 1 LEVELWithout using a calculator, evaluate [-13+5-70÷5] / [9-14× -3÷21]. (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 (4t-13) ms^-2. The initial velocity of the particle was 18 ms-¹.
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)upper-row (1 -2)lower-row. (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)upper-row (0 -1)lower-row. 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 = x² + 2x the straight lines x = 1, x = 3 and the x-axis28/12/2023 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 x-axis.
(3 marks) In a transformation an object of area x cm² is mapped on to an image whose area is 13x cm².28/12/2023 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 (x-1 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 (ax-70)°. 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)
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