KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 5 | KCSE 2023 | L.C.M | PAPER 1 | FORM 1 LEVELTwo light bulbs are set to light after every 40 seconds and 60 seconds respectively. If they light exactly at the same time initially, calculate:
(a) the time, in minutes, they will take to light together again. (2 marks) (b) the number of times they would light together in the first half an hour. (1 mark)
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QUESTION 4 | KCSE 2023 | VOLUME & CAPACITY | PAPER 1 | FORM 2 LEVELA cylindrical solid of radius 7 cm has a conical top of the same radius. The height of the cylindrical part of the solid is 17 cm. The conical top has a vertical height of 9 cm. Calculate the volume of the solid. (Take π = 22/7) (3 marks)
QUESTION 3 | KCSE 2023 | AREA OF A TRIANGLE | PAPER 1 | FORM 2 LEVELA triangle ABC is such that AB = 11 cm, BC = 8 cm and ABC = 53°. Calculate the area of the triangle correct to 2 decimal places. (2 marks)
QUESTION 2 | KCSE 2023 | INDICES | PAPER 1 | FORM 2 LEVELSimplify the expression [3a²b^-3] / [2^-1 a^-2 b²] (2 marks)
QUESTION 1 | KCSE 2023 | INTEGERS | PAPER 1 | FORM 1 LEVELWithout using a calculator, evaluate [-13+5-70÷5] / [9-14× -3÷21]. (3 marks)
Find the area enclosed by the curve y = x² + 2x the straight lines x = 1, x = 3 and the x-axis28/12/2023 QUESTION 16 | KCSE 2021 | Integration | PAPER 2 | FORM 4 LEVELFind the area enclosed by the curve y = x² + 2x the straight lines x = 1, x = 3 and the x-axis.
(3 marks) In a transformation an object of area x cm² is mapped on to an image whose area is 13x cm².28/12/2023 QUESTION 15 | KCSE 2021 | Matrices & Transformations | PAPER 2 | FORM 4 LEVELIn a transformation an object of area x cm² is mapped on to an image whose area is 13x cm². Given that the matrix of the transformation is [(x 7)upper row and (x-1 3x)lower row] find the possible values of x. (3 marks)
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)
QUESTION 13 | KCSE 2021 | GEOMETRICAL CONSTRUCTION | PAPER 2 | FORM 1 LEVELThe figure below shows triangle XYZ. Using a ruler and a pair of compasses, locate a point M on the triangle such that M is 2 cm from line YX and is equidistant from lines YX and YZ. Measure length YM. (3 marks)
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) QUESTION 11 | KCSE 2021 | LONGITUDES | PAPER 2 | FORM 4 LEVELA point Q is 2000 nm to the West of a point P(40°N, 155°W). Find the longitude of Q to the nearest degree. (3 marks)
QUESTION 10 | KCSE 2021 | TRIGONOMETRY III | PAPER 2 | FORM 4 LEVELThe equation of a trigonometric wave is y = 4 sin (ax-70)°. The wave has a period of 180°.
(a) Determine the value of a. (1 mark) (b) Deduce the phase angle of the wave. (1 mark) 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 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 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) |
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