KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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)
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QUESTION 9 | KCSE 2023 | GRAPHICAL METHODS | PAPER 2 | FORM 3 LEVELThe following figure shows a circle centre O.
Given that p = 5i - j + 3k, q = 8i + j and r = 2p - q, determine the magnitude of 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
QUESTION 23 | KCSE 2023 | differentiation | PAPER 1 | FORM 4 LEVELThe displacement, x metres, of a particle moving a long straight line after t seconds is given by x = t³/3 - 3t² + 9.
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°.
The end of term test scores of 100 students were recorded as shown in the following table.29/12/2023 QUESTION 21 | KCSE 2023 | STATISTICS I | PAPER 1 | FORM 2 LEVELThe end of term test scores of 100 students were recorded as shown in the following table.
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 19 | KCSE 2023 | Surface Area and Volume of Solids | PAPER 1 | FORM 2 LEVELThe following figure shows a right pyramid VABCD. The base ABCD of the pyramid is a square of side 8 cm. The length of the slanting edges VA = VB = VC = VD = 10 cm. Calculate:
(a) the vertical height of the pyramid correct to 2 decimal places. (4 marks) (b) surface area of the pyramid. (4 marks) (c) the volume of the pyramid. (2 marks) QUESTION 18 | KCSE 2023 | MATRICES & TRANSFORMATIONS | PAPER 1 | FORM 4 LEVELOn the following grid, triangle PQR is drawn.
QUESTION 17 | KCSE 2023 | LINEAR MOTION | PAPER 1 | FORM 2 LEVELTwo towns, A and B are 400 km apart. A motor cyclist travelling at an average speed of 60 km/h left town A for town B at 1.20 p.m. A matatu travelling at an average speed of 80 km/li also left town A for town B at 2.00 p.m.
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 15 | KCSE 2023 | DIFFERENTIATION | PAPER 1 | FORM 4 LEVELThe equation of a curve curve is given by y = 3x² - 2x. Determine the equation of a normal to the at x = 2. (4 marks)
QUESTION 14 | KCSE 2023 | Statistics I | PAPER 1 | FORM 2 LEVELIn a sub county the number of children per family was recorded from 30 families. The data recorded is as follows: (a) Represent the data in a frequency distribution table. (1 mark)
(b) Calculate the mean number of children per family. (2 marks) QUESTION 13 | KCSE 2023 | MATRICES | PAPER 1 | FORM 3 LEVELGiven Matrix P = [4 2]upper-row[-7 -1]lower-row, Q = [-1 5]upper-row[6 -3]lower-row and R = 20P^-1 + Q, Determine matrix R. (3 Marks)
QUESTION 12 | KCSE 2023 | VECTORS I | PAPER 1 | FORM 2 LEVELVectors a, b and e are represented on the following grid. On the following grid, represent:
(a) the resultant vector a + b (2 marks) (b) the resultant vector (a + b) + c (2 marks) QUESTION 11 | KCSE 2023 | AREA APPROXIMATION | PAPER 1 | FORM 4 LEVELThe equation of a curve is given by y = x². Using the trapezium rule with 4 strips, estimate the area enclosed by the curve y = x², the lines x = 1, x = 5 and the x-axis. (4 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) |
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