KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The equation of acurve is given by y = x3 – 4x2 – 3x
(a) Find the value of y when x = -1 (b) Determine the stationary points of the curve (c) Find the equation of the normal to the curve at x = 1
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Form 1 Mathematics
The figure below represents a piece of land in the shape of a quadrilateral in which AB =240M, BC = 70m CD = 200m ˂BCD = 1500 ˂ABC = 900
Calculate
(a) The size of ˂BAC correct to 2decimal places (b) The length AD correct to one decimal place (c) The area of the piece of land, in hectares, correct to 2 decimal places Form 1 Mathematics
Using a pair of compasses and a ruler only, construct
(a) (i) Triangle ABC in which AB =5cm, ˂BAC = 300 and ˂ABC = 1050 (ii) A circle that passes through the vertices of the triangle ABC. Measure the radius (iii) The height of triangle ABC WITH AB as the base. Measure the height (b) Determine the area of the circle that lies outside the triangle correct to 2decimal places Form 4 Mathematics
(a) Complete the table below for the function y = x2 – 3x + 6 in range -2 ≤ x ≤ 8
(b) Use the trapezium rule with strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x - axis
(c) Use the mid-ordinate rule with 5 strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis (d) By integration, determine the actual area bounded by the curve y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis Form 2 Mathematics
The figure below shows a right pyramid VABCDE. The base ABCDE is regular pentagon. AO = 15cm and VO = 36 cm.
Calculate:
(a) The area of the base correct to 2 decimal places (b) The length AV (c) The surface area of the correct to 2decimal places (d) The volume of the pyramid correct to 4 significant figures Form 2 Mathematics
The figure below represents a speed time graph for a cheetah which covered 825m in 40 seconds.
(a) State the speed of the cheetah when recording of its motion started
(b) Calculate the maximum speed attained by the cheetah (c) Calculate the acceleration of the cheetah in: (i) The first 10 seconds (ii) The last 20 seconds (d) Calculate the average speed of the cheetah in first 20 seconds Form 2 Mathematics
The lengths, in cm, of pencils used by pupils in a standard one class on a certain day were recorded as follows.
(a) Using a class width of 3, and starting with the shortest length of the pencils, make a frequency distribution table for the data.
(b) Calculate: (i) The mean length of the pencils (ii) The percentage of pencils that were longer than 8cm but shorter than 15cm. (c) On the grid provided, draw a frequency polygon for the data Form 2 Mathematics
A line L passes through (-2, 3) and (-1, 6) and is perpendicular to a line P at (-1, 6).
(a) Find the equation of L (b) Find the equation of P in the form ax + by = c,where a, b and c are constants. (c) Given that another line Q is parallel to L and passes through point (1, 2) find the x and y intercepts of Q (d) Find the point of the intersection of lines P and Q Form 2 Mathematics
Points A(-2, 2) and B(-3, 7) are mapped onto Aʹ(4, -10) and Bʹ(0, 10) by an enlargement. Find the scale factor of the enlargement
Form 1 Mathematics
Twenty five machines working at a rate of 9 hours per day can complete job in 16 days. A contractor intends to finish the job in 10days using similar machines
working at a rate of 12 hours per day. Find the number of machines the contractor requires to complete the job. Form 3 Mathematics
A minor arc of a circle subtends an angle of 105 at the centre of the circle. If the radius of the circle is 8.4cm, find the length of the major arc ( take ? = 22/7)
Form 2 Mathematics
The figure below shows a rectangular container of dimensions 40cm by 25cm by 90cm. a cylindrical pipe of radius 7.5cm is fitted in the container as shown.
Water is poured into the container in the space outside the pipe such that the water level is 80% the height of the container. Calculate the amount of the
water, in litres, in the container in 3 significant figures. Form 2 Mathematics
Solve 4 ≤ 3x – 2 ˂ 9 + x hence list the integral value that satisfies the inequality.
Form 1 Mathematics
A cow is 4 years 8 months older than a heifer. The product of their ages is 8 years. Determine the age of the cow and that of the heifer.
Form 1 Mathematics
The sum of interior angles of a regular polygon is 18000. Find the size of each exterior angle
Form 1 Mathematics
A plane leaves an airstrip L and flies on a bearing of 0400 to airstrip M, 500km away. The plane then leaves on a bearing of 3160 to airstrip N. The bearing ofN from L is 3500. By scale drawing, determine the distance between airstrips M and N.
Form 2 Mathematics
The area of a sector of a circle, radius 2.1cm, is 2.31cm^2. The arc of the sector subtends an angle θ, at the centre of the circle. Find the value of θ in radians to
2 correct decimal places Form 1 MathematicsForm 2 Mathematics
The mass of solid cone of radius 14cm and height 18cm is 4.62kg. find its density in g/cm3
Form 2 Mathematics
Given the simultaneous equations
5x + y = 19 -x + 3y = 9
Form 1 Mathematics
A dealer has three grades of coffee X,Y and Z. Grade X costs sh 140 per kg, grade y costs sh 160 per kg grade Z costs sh.256 per kg.
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