KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 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)
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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 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.
QUESTION 16 | KCSE 2022 | LINEAR MOTION | PAPER 2 | FORM 2 LEVELThe velocity v m/s of a particle moving in a straight line is (-2t+4) m/s. Determine the distance moved by the particle during the first second of its motion. (3 marks)
QUESTION 15 | KCSE 2022 | LONGITUDES | PAPER 2 | FORM 4 LEVELAn aircraft took off from an airport A(0°, 40°W) at 1100 h local time. The aircraft landed at airport B(0°, 65°W) at 1200 h local time.
Determine the speed of the aircraft in knots. (4 marks) 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 1997PP2QN05The figure below represents a circle a diameter 28 cm with a sector subtending an angle of 75^0 at the center. Find the area of the shaded segment to 4 significant figures
K.C.S.E MATHEMATICS Q & A - MODEL 1997PP2QN06A pyramid of height 10 cm stands on a square base ABCD of side 6 cm
K.C.S.E MATHEMATICS Q & A - MODEL 1997PP2QN02Mary Has 21 Coins Whose Total Value Is Kshs 72. There Are Twice As Many Five Shillings Coins As There Are Ten Shillings Coins. The Rest Are One Shillings Coin. Find The Number Of Ten Shillings Coins That Mary Has.
K.C.S.E MATHEMATICS Q & A - MODEL 1997PP2QN04On the figure below construct (i) The perpendicular bisector of BC (ii) The locus of a point P which moves such a way that ∠APB = ∠AVB and P is on the same side of AB on the same side of AB as C K.C.S.E MATHEMATICS Q & A - MODEL 1997PP2QN01Evaluate Without Using Mathematical Tables;
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 12 | KCSE 2022 | STATISTICS II | PAPER 2 | FORM 4 LEVELThe data below represents the number of animals owned by 7 neighbours:
9, 5, 14, 6, 8, 13 and 15. Calculate, correct to the nearest whole number, the standard deviation of the number of animals. (3 marks) QUESTION 11 | KCSE 2022 | TRIGONOMETRY III | PAPER 2 | FORM 4 LEVEL The figure below represents the curve of the function y = 1 − A sin wx for the range −35◦ ≤ x ≤ 50◦. Determine the values of A and R.
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) |
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