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 x-axis 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 8x² - 4x³.1/1/2024 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 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
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