KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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)
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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) QUESTION 7 | KCSE 2021 | Quadratic Expressions | PAPER 1 | FORM 3 LEVELSimplify (4 + 2y)² - (2y - 4)². (2 marks)
QUESTION 6 | KCSE 2021 | LINEAR motion | PAPER 1 | FORM 3 LEVELIn a race Kipsang maintained an average speed of 5 m/s. When he was 310 m to the finishing line, Mutunga was 50 m behind him. However, Mutunga finished the race 10 m ahead of Kipsang.
Determine Mutunga's average speed. (3 marks) QUESTION 5 | KCSE 2021 | Angles & Plane Figures | PAPER 1 | FORM 1 LEVELThe size of two interior angles of an irregular polygon each measures 90°. All the other remaining interior angles each measure 150°.
Determine the number of sides of the polygon. (3 marks) QUESTION 4 | KCSE 2021 | LINEAR Inequalities | PAPER 1 | FORM 2 LEVELSolve [5/3] - 2x < 1- [2/3]x <= 2 - x. Hence list the integral values that satisfy the 3 -2x<1-x2-x. 3 inequalities. (3 marks)
QUESTION 3 | KCSE 2021 | Rotation | PAPER 1 | FORM 2 LEVELComplete the figure below to show a rotational symmetry of order 3 about O. (3 marks)
QUESTION 2 | KCSE 2021 | L.c.m | PAPER 1 | FORM 1 LEVELTwo bells ring at intervals of 35 and 42 minutes respectively. The bells ring together at 8.48 a.m. Determine the time when the bells will ring together again. (3 marks)
QUESTION 1 | KCSE 2021 | Fractions | PAPER 1 | FORM 1 LEVEL |
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