KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 4 | KCSE 2023 | CIRCLES, CHORDS AND TANGENTS | PAPER 2 | FORM 3 LEVELIn this question, use a ruler and a pair of compasses. The following figure shows a circle, centre O. A tangent to the circle at P is drawn. Construct another tangent to the circle to intersect the drawn tangent at an angle of 60°. (3 marks)
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QUESTION 3 | KCSE 2023 | Formula & Variations | PAPER 2 | FORM 3 LEVELQUESTION 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)
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 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)
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 LEVEL |
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