KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 24  KCSE 2023  VECTORS I  PAPER 2  FORM 2 LEVELIn the following figure OABC is a trapezium. OA is parallel to CB and OA = 3 CB. M is the midpoint of AB. (a) Given that OA = 3a and OC = c express in terms of a and c.
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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 8xÂ² Â 4xÂ³.1/1/2024 QUESTION 20  KCSE 2023  TRIGONOMETRY III  PAPER 2  FORM 3 LEVEL
QUESTION 19  KCSE 2023  pROBABILITY  PAPER 2  FORM 3 LEVEL
QUESTION 18  KCSE 2023  COMMERCIAL ARITHMETIC II  PAPER 2  FORM 3 LEVELA welfare group invested Ksh 75 000 in shares and another Ksh 75 000 in a piece of land for a period of 5 years. The shares appreciated in value at a rate of 6% per annum (p.a) for a period of 3 years. In the remaining period of 2 years, the shares appreciated in value at a rate of 4.5% every 6 months. During the 5 years, the piece of land appreciated in value at a constant annual rate. At the end of the 5th year, the values of the two investments were equal.
QUESTION 17  KCSE 2023  SEQUENCES & SERIES  PAPER 2  FORM 3 LEVELThe first term of an arithmetic progression (A.P.) is a and the common difference d. The 7th term of the A.P. is 11. The sum of the first 12 consecutive terms of the A.P. is 123.
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 14  KCSE 2023  LINEAR MOTION  PAPER 2  FORM 3 LEVELA stone was thrown upwards from a point 8 metres above the ground. The following graph shows the height, h metres of the stone above the ground at time / seconds in the interval 0 ≤ t ≤ 4. Determine the rate of change of h at t = 2 seconds. (3 marks)
QUESTION 13  KCSE 2023  FORMULA & VARIATIONS  PAPER 2  FORM 3 LEVELA quantity v varies directly as the square of u and inversely as the cube root of w. When u = 5 and w = 8, the value of' v = 375. Find the value of v when u = 8 and w = 125. (3 marks)
QUESTION 12  KCSE 2023  QUADRATIC EQUATIONS  PAPER 2  FORM 4 LEVELThe length and width of a rectangular floor of a room are 10 m and 7 m respectively. A rectangular carpet of area 28 m² is placed on the floor. The carpet leaves a uniform space of x m with each of the walls of the room.
Form a quadratic equation in x and hence solve for x. (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}
QUESTION 10  KCSE 2023  COMMERCIAL ARITHMETIC II  PAPER 2  FORM 3 LEVELThe following table shows monthly income tax rates of a certain year. In that year, a monthly relief of Ksh 2 400 was allowed. The net tax on Lesianto's monthly income was Ksh 1 500.
Calculate Lesianto's monthly income. (3 marks) QUESTION 9  KCSE 2023  GRAPHICAL METHODS  PAPER 2  FORM 3 LEVELThe following figure shows a circle centre O.
Given thatÂ pÂ = 5iÂ Â jÂ + 3k,Â qÂ = 8iÂ +Â jÂ andÂ rÂ = 2pÂ Â q, determine the magnitude ofÂ r1/1/2024 QUESTION 8  KCSE 2023  VECTORS II  PAPER 2  FORM 3 LEVELGiven that p = 5i  j + 3k, q = 8i + j and r = 2p  q, determine the magnitude of r. (3 marks)
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 6  KCSE 2023  TRIGONOMETRY II  PAPER 2  FORM 3 LEVELSolve 6cos²(x) = 5sin(x) for 0≤x≤ 180°. (4 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 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)
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 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

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