KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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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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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) QUESTION 5 | KCSE 2023 | L.C.M | PAPER 1 | FORM 1 LEVELTwo light bulbs are set to light after every 40 seconds and 60 seconds respectively. If they light exactly at the same time initially, calculate:
(a) the time, in minutes, they will take to light together again. (2 marks) (b) the number of times they would light together in the first half an hour. (1 mark) QUESTION 4 | KCSE 2023 | VOLUME & CAPACITY | PAPER 1 | FORM 2 LEVELA cylindrical solid of radius 7 cm has a conical top of the same radius. The height of the cylindrical part of the solid is 17 cm. The conical top has a vertical height of 9 cm. Calculate the volume of the solid. (Take π = 22/7) (3 marks)
QUESTION 3 | KCSE 2023 | AREA OF A TRIANGLE | PAPER 1 | FORM 2 LEVELA triangle ABC is such that AB = 11 cm, BC = 8 cm and ABC = 53°. Calculate the area of the triangle correct to 2 decimal places. (2 marks)
QUESTION 2 | KCSE 2023 | INDICES | PAPER 1 | FORM 2 LEVELSimplify the expression [3a²b^-3] / [2^-1 a^-2 b²] (2 marks)
QUESTION 1 | KCSE 2023 | INTEGERS | PAPER 1 | FORM 1 LEVELWithout using a calculator, evaluate [-13+5-70÷5] / [9-14× -3÷21]. (3 marks)
QUESTION 24 | KCSE 2021 | DIFFERENTIATION | PAPER 1 | FORM 4 LEVELThe equation of a curve is given as y = 1/3 X^3 - 1/2X^2 - 2X - 1/3.
QUESTION 23 | KCSE 2021 | STATISTICS I | PAPER 1 | FORM 2 LEVELThe masses of 40 adults who attended a health clinic were recorded as follows. (a) Complete the frequency distribution table below for the above information. Use classes of size 5 starting with the class 40 - 44. (4 marks) (b) State the modal class. (1 mark)
(c) Estimate: (i) the mean mass. (2 marks) (ii) the median mass. (3 marks) QUESTION 22 | KCSE 2021 | VECTORS I | PAPER 1 | FORM 2 LEVELThe position vectors of A and B are (-4, 6) and (-8, 2) respectively.
Point M is the midpoint of AB and point N is the midpoint of OA.
QUESTION 21 | KCSE 2021 | Quadratic Equations | PAPER 1 | FORM 3 LEVEL(a) Solve for x (x - 4)^2 = (x - 8)(2x + 7). (4 marks) (b) John cycled 6 km from his home to school at an average speed of (2x - 3) km/h.
Peter walked 2.4 km from his home to the school at an average speed of x km/h. Peter took 16 minutes less than John. Determine the time, in minutes, that John took to reach the school. (6 marks) QUESTION 20 | KCSE 2021 | Trigonometry i | PAPER 1 | FORM 2 LEVELThe figure below is a quadrilateral ABCD in which AB = 8 cm, BC = 6 cm, CD = AD, Angle ABC = 70° and Angle ADC = 50°.
QUESTION 19 | KCSE 2021 | MATRICES | PAPER 1 | FORM 3 LEVELElimu School bought 25 textbooks and 35 exercise books for Ksh 13 500 from bookshop A. From the same bookshop Soma School bought 21 textbooks and 38 exercise books and spent Ksh 1 300 less than Elimu School.
Take x to represent the price of a textbook and y to represent the price of an exercise book.
QUESTION 18 | KCSE 2021 | AREA & VOLUME OF A QUADRILATERAL | PAPER 1 | FORM 2 LEVEL
QUESTION 17 | KCSE 2021 | MASS | PAPER 1 | FORM 1 LEVELA factory packs fruit jam in cylindrical tins of radius 5 cm and height 15 cm. The tins are then packed into rectangular cartons each measuring 60 cm long, 30 cm wide and 30 cm high.
QUESTION 16 | KCSE 2021 | Differentiation | PAPER 1 | FORM 4 LEVELA curve is given by y = 2x³ - 3x² - 12x + 12. (1 mark)
(a) Find the gradient function of the curve. (b) Determine the equation of the normal to the curve at the point (1, -1), in the form y=mx+c, where m and c are constants. (3 marks) QUESTION 15 | KCSE 2021 | Indices and Logarithms | PAPER 1 | FORM 2 LEVELSolve the equation 8^[x+1] - 2^[3x-1] = 120. (4 marks)
QUESTION 14 | KCSE 2021 | Similarity and Enlargement | PAPER 1 | FORM 2 LEVELThe height of a cone is 12 cm. A frustrum whose volume is one eighth the volume of the cone is cut off. Determine the height of the frustrum. (3 marks)
QUESTION 13 | KCSE 2021 | Time | PAPER 1 | FORM 1 LEVELAli left Mombasa for Nairobi on Tuesday at 2.30 a.m. He arrived in Mtito Andei after 3 hours 12 minutes. He stayed in Mtito Andei for 36 hours and then left for Nairobi. He took 5 hours Ham 25 minutes to arrive in Nairobi.
Determine the day and time in the 12 hour system Ali arrived in Nairobi. (3 marks) QUESTION 12 | KCSE 2021 | Geometrical Constructions | PAPER 1 | FORM 1 LEVELLine AB drawn below is a side of a trapezium ABCD. (a) Using a ruler and pair of compasses only, complete trapezium ABCD in which AB is parallel to DC, BAD = 67.5°, AD = 5 cm, BC = 5.5 cm and ∠ABC is acute. (3 marks)
(b) Measure the length of DC. (1 mark) QUESTION 11 | KCSE 2021 | Trigonometry II | PAPER 1 | FORM 3 LEVELSolve for Θ (2 marks)
sin (2Θ - 15) = cos 3Θ. The cost of one litre of Petrol is Ksh 110. John's vehicle covers 12 km on one litre of petrol.25/12/2023 QUESTION 10 | KCSE 2021 | Rates, Ratio, Percentage and Proportion | PAPER 1 | FORM 1 LEVELThe cost of one litre of Petrol is Ksh 110. John's vehicle covers 12 km on one litre of petrol. He used Ksh 2 805 on petrol to travel from town A to town B. Jane's vehicle consumes 12.5 litres of Petrol for every 100 km travelled.
Calculate the amount of money that Jane would use to travel from town A to B on the same road. (3 marks) |
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