KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
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Form 3 MathematicsForm 3 Mathematics
Use completing the square method to solve 3x2 + 8x — 6 = 0, correct to 3 significant figures.
Form 3 MathematicsForm 4 MathematicsForm 1 Mathematics
Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second
year, Asia had Ksh 170 130 in the financial institution. Determine the amount of money Asia invested. Form 3 Mathematics
A variable P varies directly as t3 and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3.
Form 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 4 MathematicsA stone is thrown vertically upwards from a point O After t seconds, the stone is S metres from O Given that S= 29.4t – 4.9t2, Find the maximum height reached by the stone ( 3 marks) Form 1 MathematicsSuccessive moving averages of order 5 for the numbers 9,8.2, 6.7,5.4, 4.7 and k are A and B. Given that A – B = 0.6 find the value of k. Form 3 MathematicsGiven that Cos 2x0 = 0.8070, find x when 00 < x < 3600 ( 4 marks) Form 2 Mathematics
The volumes of two similar solid cylinders are 4752 cm3 and 1408 cm3. If the area of the curved surface of the smaller cylinder is 352 cm2, find the area of the curved surface of the larger cylinder. ( 4 marks)
Form 3 MathematicsFind, without using Mathematical Tables the values of x which satisfy the equation Log2 (x2 – 9) = 3 log2 (2 + 1) (4 marks) Form 1 MathematicsPipe a can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours, when the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty. If one hour later, pipe C is also opened, find the total time taken to fill the tank (4 marks) Form 3 MathematicsThe first three consecutive terms of a geometrical progression are 3, x and 5 1/3. Find the value of x. ( 2 marks) |
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