KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 24 | KCSE 2021 | lINEAR mOTION | PAPER 2 | FORM 4 LEVELA particle was moving along a straight line. The acceleration of the particle after t seconds was given by (4t-13) ms^-2. The initial velocity of the particle was 18 ms-¹.
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QUESTION 23 | KCSE 2021 | TRIGONOMETRY III | PAPER 2 | FORM 4 LEVEL(a) Complete the table below giving the values correct to 1 decimal place. (b) On the grid provided and using the same axis, draw the graphs of y = 2sin(3/4 x) - 2cos(3/4 x) and y = 1 + 2cos x for 0° ≤x≤ 360°. (4 marks)
QUESTION 22 | KCSE 2021 | STATISTICS II | PAPER 2 | FORM 4 LEVELWorkers in a factory commute from their homes to the factory. The table below shows the distances in kilometres, covered by the workers. The mean distance covered was 14.5 km.
QUESTION 21 | KCSE 2021 | MATRICES & TRANSFORMATIONS | PAPER 2 | FORM 4 LEVELThe vertices of the triangle shown on the grid are A' (3,-3), B' (1,-1) and C' (3,-1). Triangle A'B'C' is the image of triangle ABC under a transformation whose matrix is (0 1)upper-row (1 -2)lower-row. (a) Find the coordinates of triangle A, B and C. (4 marks)
(b) Triangle A"B"C" is the image of triangle A'B'C' under a transformation matrix (2 marks) (-2 0)upper-row (0 -1)lower-row. Determine the coordinates of A", B" and C". (c) On the same grid provided, draw triangles ABC and A"B"C". (2 marks) (d) Determine a single matrix, that maps ABC onto A" B"C". (2 marks) QUESTION 20 | KCSE 2021 | COMMERCIAL ARITHMETIC II | PAPER 2 | FORM 3 LEVELThe table below shows income tax rates in a certain year. In the year, the monthly earnings of Kanini were as follows: Basic salary House allowance Ksh 64 500 Ksh 12 000 Kanini contributes 7.5% of her basic salary to a pension scheme. This contribution is exempted from taxation. She is entitled to a personal tax relief of Ksh 1 408 per month. Calculate:
In the figure below, points A, B, C, and E lie on the circumference of the circle centre O28/12/2023 QUESTION 19 | KCSE 2021 | ANGLE PROPERTIES OF A CIRCLE | PAPER 2 | FORM 3 LEVELIn the figure below, points A, B, C, and E lie on the circumference of the circle centre O. Line FAG is a tangent to the circle at A. Chord DE of the circle is produced to intersect with the tangent at F. Angle FAE = 30°, Angle EDC = 110° and Angle OCB =55°
QUESTION 18 | KCSE 2021 | AREA | PAPER 2 | FORM 3 LEVELA rectangular plot measures 50 m by 24 m. A lawn, rectangular in shape, is situated inside the plot with a path surrounding it as shown in the figure below. The width of the path in x m between the lengths of the lawn and those of the plot and 2x m between the widths of the lawn and those of the plot.
QUESTION 17 | KCSE 2021 | COMPOUND PROPORTIONS AND RATES OF WORK | PAPER 2 | FORM 3 LEVELPump P can fill an empty water tank in 7 1/2 hours while pump Q can fill the same tank in 11 1/4 hours. On a certain day, when the tank was empty, both pumps were opened for 2 1/2 hours.
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 24 | KCSE 2022 | LOCI | PAPER 2 | FORM 4 LEVEL In this question use a ruler and a pair of compasses. The line AB drawn below is a side of triangle ABC in LABC which = 90° and BAC = 60°.
In an inter school mathematics contest, schools can register teams in junior and senior categories.23/12/2023 QUESTION 23 | KCSE 2022 | LINEAR PROGRAMMING | PAPER 2 | FORM 4 LEVELIn an inter school mathematics contest, schools can register teams in junior and senior categories. Information on number of students and the participation fee per team in each category is given in the table below. The organising committee projected to register x junior teams and y senior teams.
QUESTION 22 | KCSE 2022 | STATISTICS II | PAPER 2 | FORM 4 LEVELFifty teachers in a sub county attended a workshop. The table below shows the distribution of the distances (d) in kilometres travelled by the teachers from their respective school to the training venue.
QUESTION 21 | KCSE 2022 | COMMERCIAL ARITHMETIC II | PAPER 2 | FORM 3 LEVEL(a) Juma bought a house 4 years ago for Ksh 2500000. The value of the house rose steadily over 4 years to its current value of Ksh 3 700000. Calculate, correct to 2 decimal places, the annual rate of appreciation in the value of the house. (3 marks) (b) At the time Juma bought the house in 21(a), Tony also bought a car valued at Ksh 5 100000. The value of the car depreciated steadily at a rate of 2% every 4 months. Determine correct to the nearest shilling, the current value of the car. (3 marks) (c) The house bought in 21(a) continued to appreciate in value at the same rate while the car bought in 21(b) continued to depreciate in value at the same rate. Determine the number of years from the time of purchase, it would take for the value of the house and that of the car to be equal. Give the answer correct to 1 decimal place. (4 marks)
QUESTION 20 | KCSE 2022 | VECTORS I | PAPER 2 | FORM 2 LEVELIn the diagram below, the vertices of triangle ABC are A(0, 3), B(4.5, 6) and C(10.5, 0).
Points P(3, 5) and Q(9, 1.5) lie on lines AB and BC respectively.
QUESTION 19 | KCSE 2022 | MATRICES AND TRANSFORMATION | PAPER 2 | FORM 4 LEVELmaps triangle A'B'C' into triangle A"B"C". The coordinates of point C" is (10, 8) and the area of triangle A"B"C" is 15 square units.
QUESTION 18 | KCSE 2022 | Probability | PAPER 2 | FORM 3 LEVELTwo bags P and Q contain identical marbles except for the colours. Bag P contains 3 green and 4 red marbles. Bag Q contains 2 green and 3 red marbles. (1 mark)
QUESTION 17 | KCSE 2022 | COMPOUND PROPORTIONS AND RATES OF WORK | PAPER 2 | FORM 3 LEVELA wholesaler stocks two types of rice: Refu and Tamu. The wholesale prices of 1 kg of Refu and 1 kg of Tamu are Ksh 80 and Ksh 140 respectively. The wholesaler also stocks blend A rice which is a mixture of Refu and Tamu rice mixed in the ratio 3: 2.
K.C.S.E MATHEMATICS Q & A-MODEL 1997PP1QN20(A) Draw The Graph Of Y = 6 + X - X2, Taking Integral Value Of X In -4 ≤ X ≤ 5. (The Grid Is Provided. Using The Same Axes Draw The Graph Of Y = 2 – 2x
(B) From Your Graphs, Find The Values Of X Which Satisfy The Simultaneous Equations Y = 6 + X - X2; Y = 2 – 2x (C) Write Down And Simplify A Quadratic Equation Which Is Satisfied By The Values Of X Where The Two Graphs Intersect. |
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