KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
(a)Complete the table below for the equation y = x2-4x+2
(b) On the grid provided draw the graph y = x2 - 4x + 2 for 0 ≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis.
(c) Use the graph to solve the equation, x2 -4x + 2 = 0 (d) By drawing a suitable line, use the graph in (b) to solve the equation x2 -5x + 3 = 0.
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Form 3 Mathematics
The 5th and 10th terms of an arithmetic progression are 18 and -2 respectively.
(a) Find the common difference and the first term. (b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum. Form 3 Mathematics
In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen.
Form 3 MathematicsForm 4 Mathematics
The position of two points C and D on the earth’s surface are (θ°N, l0°E) and (θ°N, 30°E)
respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. Form 4 Mathematics
The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11.
Determine the quartile deviation of the data. Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
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. |
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