KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
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Form 2 Mathematics
Juma left his home at 8.30a.m. He drove a distance of l40km and arrived at his aunt’s home at 10.15 a.m.
Determine the average speed, in km/h, for Juma’s journey. Form 2 MathematicsForm 4 Mathematics
The equation of a curve is given as y=1/3x3-4x+5
Determine: (a) The value of y when x = 3; (b) The gradient of the curve at x = 3; (c) The turning points of the curve and their nature. Form 1 Mathematics
Three business partners Abila, Bwire and Chirchir contributed Ksh 120 000, Ksh 180 000 and Ksh 240 000 respectively, to boost their business.
They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business (official operations). The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225 000 was realised. (a) Calculate the amount: (i) put back into the business; (ii) used for official operations (b) Calculate the amount of profit each partner got. (c) If the amount put back into the business was added to individuals’s shares proportionately to their initial contribution, find the amount of Chirchir’s new shares. Form 4 Mathematics
(a) On the grid provided, draw the graph of y = 4 -1/4x2 for -4 ≤ x ≤ 4
(b) Using trapezium rule, with 8 strips, estimate the area bounded by the curve and the x-axis. (c) Find the area estimated in part (b) above by integration. (d) Calculate the percentage error in estimating the area using trapezium rule. Form 2 Mathematics
The figure below shows two triangles, ABC and BCD with a common base BC = 3.4 cm. AC = 7.2 cm, CD = 7.5 cm and ABC = 90°.
The area of triangle ABC = Area of triangle ∠BCD.
Calculate, correct to one decimal place:
(a) the area of triangle ABC; (b) the size of ∠BCD; (c) the length of BD; (d) the size of ∠BDC. Form 4 Mathematics
The diagram below shows triangle ABC with vertices A(-1, -3), B(1, -1) and C(0,0), and line M.
(a) Draw triangle A'B'C' the image of triangle ABC under a reflection in the line M.
(i) Draw triangle A"B"C"
(ii) Describe fully the transformation represented by matrix T. (iii) Find the area of triangle A’B'C' hence find area of triangle A"B"C". Form 4 Mathematics
The distance covered by a moving particle through point O is given by the equation, s = t3 - 15t2 + 63t — 10.
Find: (a) distance covered when t = 2 (b) the distance covered during the 3rd second; (c) the time when the particle is momentarily at rest; (d) the acceleration when t = 5. Form 2 Mathematics
Two vertices of a triangle ABC are A (3,6) and B (7,12).
(a) Find the equation of line AB. (b) Find the equation of the perpendicular bisector of line AB. (c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the coordinates of C. Form 2 MathematicsThe diagram below represents a rectangular swimming pool 25m long and 10m wide. The sides of the pool are vertical. The floor of the pool slants uniformly such that the depth at the shallow end is 1m at the deep end is 2.8 m. (a) Calculate the volume of water required to completely fill the pool. (b) Water is allowed into the empty pool at a constant rate through an inlet pipe. It takes 9 hours for the water to just cover the entire floor of the pool. Calculate: (i) The volume of the water that just covers the floor of the pool ( 2 marks) (ii) The time needed to completely fill the remaining of the pool ( 3 marks) Form 3 MathematicsThe points P, Q, R and S have position vectors 2p, 3p, r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6 (a) Find, in the simplest form, the vectors OT and QT in terms P and r ( 4 marks) (i) Show that the points Q, T, and R lie on a straight line ( 3 marks) Form 2 Mathematics
A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.
(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (b) Find the capacity of the tank, in litres, correct to the nearest litre. (c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. Form 1 Mathematics
A photograph print measuring 24cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space i‹ 270cm2, find the value of x.
Form 1 Mathematics
A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa
Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. Form 2 MathematicsForm 3 Mathematics
Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°
Form 2 MathematicsForm 2 Mathematics
Two towns R and S are 245 km apart. A bus travelling at an average speed of 60 km/h left tow: R for town S at 8.00 a.m. A truck left town S for town R at 9.00 a.m and met with the bus c
11.00a.m. Determine the average speed of the truck. Form 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. |
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