KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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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)
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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.
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 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) 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)
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) |
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