KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 14 | KCSE 2021 | VECTORS II | PAPER 2 | FORM 3 LEVELThe position vectors of points P, Q and R are OP = 6i - 2j + 3k, OQ = 12i - 5j + 6k and OR = 8i - 3j + 4k. Show that P, Q and R are collinear points. (3 marks)
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QUESTION 12 | KCSE 2021 | Probability | PAPER 2 | FORM 3 LEVELA box contains 3 brown balls and 9 green balls. The balls are identical except for the colours. Two balls are picked at random without replacement.
(a) Draw a tree diagram to show all the possible outcomes. (1 mark) (b) Determine the probability that the balls picked are of different colours. (2 marks) The table below shows the values of t and the corresponding values of h for a given relation28/12/2023 QUESTION 9 | KCSE 2021 | GRAPHICAL METHODS | PAPER 2 | FORM 3 LEVELThe table below shows the values of t and the corresponding values of h for a given relation. (a) On the grid provided, draw a graph to represent the information on the table given. (2 marks) (b) Use the graph to determine, correct to 1 decimal place, the rate of change of h at t = 3. (2 marks)
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)
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 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 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 11 | KCSE 2021 | Trigonometry II | PAPER 1 | FORM 3 LEVELSolve for Θ (2 marks)
sin (2Θ - 15) = cos 3Θ. 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 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 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.
QUESTION 14 | KCSE 2022 | VECTORS II | PAPER 2 | FORM 3 LEVELPoint P(8, 4, -1) divides line AB internally in the ratio 4: 1. The position vector of point A with respect to the origin O is [-4 8 3]
Determine the coordinates of point B. (3 marks) 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. QUESTION 13 | KCSE 2022 | COMMERCIAL ARITHMETICS II | PAPER 2 | FORM 3 LEVEL The table below shows income tax rates in a certain year.
A tax relief of Ksh 1 408 per month was allowed. Calculate the monthly income tax paid by an employee whose monthly taxable income was Ksh 26545.75. (3 marks) QUESTION 9 | KCSE 2022 | GRAPHICAL METHODS | PAPER 2 | FORM 3 LEVELThe population growth of a colony of bacteria was recorded at intervals of 5 seconds(s) as shown in the table below (a) On the grid provided, draw a graph of the population of bacteria against time. (2 marks) (b) Use the graph to determine, correct to 2 decimal places, the average rate of change of the population of bacteria between t = 5 seconds and t = 20 seconds. (2 marks)
QUESTION 10 | KCSE 2022 | GRAPHICAL METHODS | PAPER 2 | FORM 3 LEVEL A circle centre C(5, 5) passes through points A(1, 3) and B(a, 9). Find the equation of the circle and hence the possible values of a. (3 marks)
QUESTION 8 | KCSE 2022 | ANGLE PROPERTIES OF A CIRCLE | PAPER 2 | FORM 3 LEVEL In the figure below, O is the centre of the circle. Points A, B, C and D lie on the circumference of the circle. Line AB is parallel to the straight line EDO and line FAE is a tangent to the circle at A. FAB = a°, DOA = b°, DCB = 70°
Determine the values of a and b. (4 marks) K.C.S.E MATHEMATICS Q & A - MODEL 1997PP2QN12Find the Values of A and B Where B Are Rational Numbers |
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