KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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PROBABILITY  PAPER 1  SECTION B  KCSE 1997  FORM 3 LEVELThe water supply in a town depends entirely on two water pumps, A and B. The probability of pump A filling is 0.1, and the probability of pump B failing is 0.2. Calculate the probability that:
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MATRICES  FORM 3 LEVEL  KCSE 1997  SECTION B  PAPER 1The figure on the grid shows a triangular shaped object ABC and its image A'B'C'. (a)
(d) Hence find the area of the image A” B” C COMMERCIAL ARITHMETIC II  QUESTION 21  KCSE 1996  FORM 3 LEVEL  SECTION BKubai saved Kshs 2,000 during the first year of employment. In each subsequent year, he saved 15% more than the preceding year until he retired.
statistics ii  kcse 1996  question 19  paper 2  section bIn an agricultural research centre, the length of a sample of 50 maize cobs was measured and recorded. The recorded measurements are presented in the frequency distribution table below. Calculate
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 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 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)
QUESTION 6  KCSE 2023  TRIGONOMETRY II  PAPER 2  FORM 3 LEVELSolve 6cos²(x) = 5sin(x) for 0≤x≤ 180°. (4 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)
The following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S29/12/2023 QUESTION 22  KCSE 2023  TRIGONOMETRY II  PAPER 1  FORM 3 LEVELThe following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S. Lines PQ = PR = 2.7 cm, PS = 6 cm, SR = 7 cm and ∠PQR = 65°.
QUESTION 20  KCSE 2023  Commercial arithmetic II  PAPER 1  FORM 3 LEVELNeema went to the market to buy bananas worth Ksh 2 100 for a school. The seller offered a discount of Ksh 3 per banana which enabled Neema to buy 35 more bananas.
QUESTION 16  KCSE 2023  GRAPHICAL METHODS  PAPER 1  FORM 3 LEVELOn the following cartesian plane provided, solve the simultaneous equations.
y = 4/3 x + 2; 3y = x  3 QUESTION 13  KCSE 2023  MATRICES  PAPER 1  FORM 3 LEVELGiven Matrix P = [4 2]upperrow[7 1]lowerrow, Q = [1 5]upperrow[6 3]lowerrow and R = 20P^1 + Q, Determine matrix R. (3 Marks)
QUESTION 10  KCSE 2023  COMMERCIAL ARITHMETIC II  PAPER 1  FORM 3 LEVELA salesman sells story books and textbooks. The cost price of a story book is sh 600 while that of a textbook is sh 900. The salesman is paid a commission of 10% on the cost of any book sold. One day, the salesman sold twice as many story books as textbooks. He earned a commission of sh 8 400.
Determine the total number of story books sold. (3 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 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:

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