KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
QUESTION 8 | KCSE 2021 | COMMERCIAL ARITHMETICS II | PAPER 2 | FORM 3 LEVELThe cash price of a gas cooker is Ksh 20 000. A customer bought the cooker on hire purchase terms by paying a deposit of Ksh 10 000 followed by 18 equal monthly instalments of Ksh 900 each. Annual interest, compounded quarterly, was charged on the balance for the period of 18 months. Determine, correct to 1 decimal place, the rate of interest per annum. (4 marks)
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QUESTION 7 | KCSE 2021 | Three Dimensional Geometry | PAPER 2 | FORM 4 LEVELThe figure below represents a prism ABCDEFGH of length 6 cm. The cross section BCFG of the prism is a trapezium in which GF = 11 cm, BC = 8 cm, BG = 5 cm and GFC = BCF = 90°. Calculate correct to 1 decimal place the angle between the line FA and the plane GFEH. (3 marks)
QUESTION 6 | KCSE 2021 | Formula & Variations | PAPER 2 | FORM 3 LEVELFour quantities P, Q, R and S are such that P varies directly as the square root of Q and inversely as the square of the difference of R and S. Quantity Q is increased by 44% while quantities R and S are each decreased by 10%.
Find the corresponding percentage change in P correct to 1 decimal place. (4 marks) QUESTION 5 | KCSE 2021 | Circles, Chords & Tangents | PAPER 2 | FORM 3 LEVELThe figure below shows a circle and a point P outside the circle Using a ruler and pair of compasses, construct a tangent to the circle from P. (4 marks)
QUESTION 4 | KCSE 2021 | Formula & Variations | PAPER 2 | FORM 3 LEVELQUESTION 3 | KCSE 2021 | Quadratic Equations | PAPER 2 | FORM 3 LEVELThe expression ax² - 30x + 9 is a perfect square, where a is a constant. Find the value of a.
(2 marks) QUESTION 2 | KCSE 2021 | Sequence & series | PAPER 2 | FORM 3 LEVELThe first term of a Geometric Progression (G.P) is 2. The common ratio of the G.P is also 2. The product of the last two terms of the G.P is 512. Determine the number of terms in the G.P. (3 marks)
QUESTION 1 | KCSE 2021 | Compound proportions and rates of work | PAPER 2 | FORM 4 LEVELAn empty tank of capacity 18480 litres is to be filled with water using a cylindrical pipe of diameter 0.028 m. The rate of flow of water from the pipe is 2 m/s. Find the time in hours it would take to fill up the tank. (Take π = 22/7). (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) QUESTION 9 | KCSE 2021 | Matrices & Transformations | PAPER 1 | FORM 4 LEVELA translation T maps A(-6, 2) onto A'(3, 5).
(a) Determine the translation vector T. (1 mark) (b) A point P'(-4, 2) is the image of P under T. Determine the coordinates of P. (2 marks) QUESTION 8 | KCSE 2021 | Commercial Arithmetics II | PAPER 1 | FORM 3 LEVELA table is sold at Ksh 4 500 and a chair at Ksh 2 000. A salesman earns a commission of 8% on every table and 5% on every chair sold. On a certain week, he sold 3 more chairs than tables and his total earnings were Ksh 3 980.
Determine the number of chairs he sold that week. (3 marks) |
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