KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
Form 4 Mathematics
The table below shows marks scored by 42 students in a test.
a) Starting with the mark of 25 and using equal class intervals of 10, make a frequency distribution table.
b) On the grid provided , draw the ogive for the data c) Using the graph in (b) above , estimate: (i) The median mark (ii) The upper quartile mark
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Form 4 Mathematics
The equation of a curve is given by y = 5x − 1/2 x^{2}
(a) On the grid provided, draw the curve of y = 5x − 1/2 x^{2} for 0 ≤ x ≤ 6 (b) By integration, find the area bounded by the curve, the line x =6 and the xaxis. (c) (i) On the same grid as in,(a).draw the line y = 2x. (ii) Determine the area bounded by the curve and the line y = 2 x. Form 4 Mathematics
(a) Complete the table below, giving the values correct to 1 decimal place.
b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)^{0} and y = √3 cos χ for 0^{0} ≤ χ ≤ 240^{0}.
c) Use the graphs drawn in (b) above to determine: i) the value of χ for which 2sin (χ + 20) = √3 cos χ; ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ. Form 4 Mathematics
The figure ABCDEF below represents a roof of a house. AB=DC=12 m, BC = AD = 6m, AE = BF = CF= DE = 5m and EF = 8m
(a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD.
(b) calculate the angle between : (I) the planes ADE and ABCD (II) The line AE and the plane ABCD, correct to 1 decimal place; (III) The planes ABFE and DEFE, correct to 1 decimal place. Form 3 Mathematics
(a) Complete the table below for y = x^{3}+4x^{2}5x5
(b) On the grid provided, draw the graphs of y = x^{3} +4x^{2}5x5 for 5 ≤ x ≤ 2
(c) (i) Use the graph to solve the equation x^{3} +4x^{2} – 5x – 5 = 0 (ii) By drawing a suitable straight line on the graph, solve the equation x^{3} + 4x^{2} – 5x 5 =  4x – 1 Form 3 MathematicsForm 1 Mathematics
The hire purchase (H.P) price of a public address system was Kshs 276000. A deposit of Kshs 60000 was paid followed by 18 equal monthly installments.
The cash price of the public address system was 10% less than the H.P price. (a) Calculate (i) The monthly installments (ii) The cash price (b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash. The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years. Calculate the amount repaid to the bank by the end of the second year (c) Express as a percentage of the Hire Purchase price, the difference between the amount repaid to the bank and the Hire Purchase price Form 4 MathematicsForm 4 Mathematics
The position of two towns are (2^{0} S,30^{0} E) and 2^{0}S, 37.4 ^{0}E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
Form 3 Mathematics
Solve the equation; 6 cos^{2} x +7 sin x – 8 = 0 for 0^{0} ≤ x ≤ 90^{0}
Form 3 MathematicsForm 4 Mathematics
A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
Form 1 Mathematics
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened Form 3 Mathematics
Two machines, M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of the items produces
by machine M are defective while 3% of the items produced by machine N are defective. If an item is selected at random from the factory, find the probability that it is defective Form 2 Mathematics
The position vectors of points F, G, and H are f, g, and h respectively. Point H divides FG in the ratio 4:1. Express h in terms of f and g
Form 3 Mathematics
(a) expand (1 − ?)^{5}
(b) Use the expansion in (a) up to the term in x^{3} to approximate the value of (0.98)^{5} Form 3 Mathematics
The equation of a circle is given by x^{2} +4x +y^{2} 2y – 4 = 0. Determine the centre and radius of the circle
Form 1 MathematicsForm 3 Mathematics
A quadratic curve passes through the points (2, 0) and (1, 0). Find the equation of the curve in the form y = ax^{2} +bx +c, where a, b and c are constants
Form 3 Mathematics
The sum of n terms of the sequence; 3, 9, 15, 21, … is 7500. Determine the value of n
Form 2 Mathematics
The figure below represents a cone of height 12 cm and base radius of 9 cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm.
a) Calculate:
i. The base radius of the conical hole; ii. The volume, in terms of π, of the smaller cone that was removed. b) (i) Determine the slant height of the original cone. (ii) Calculate, in terms of it, the surface area of the remaining solid after the smaller cone is removed. Form 2 Mathematics
(a) On the grid provided, draw the square whose verticals are A (6, 2), B (7, 2), C (7, 1) and D (6, 1).
(b) On the same grid, draw: i. AʹBʹCʹDʹ, the image of ABCD, under an enlargement scale factor 3, centre (9, 4); ii. AʹʹBʹʹCʹʹDʹʹ, the image of AʹBʹCʹDʹ, under a reflection in the line x = 0; iii. AʹʹʹBʹʹʹCʹʹʹDʹʹʹ, the the image of AʹʹBʹʹCʹʹDʹʹ under a rotation of + 90 about (0,0) (c) Describe a single transformation that maps AʹBʹCʹDʹ onto AʹʹʹBʹʹʹCʹʹʹDʹʹʹ Form 3 Mathematics
In the figure below, OABC is a trapezium. AB parallel to OC and OC = 5AB. D is a point on OC such that OD: DC = 3:2
a) Given that OA = p and AB = q, express in terms of p and q:
i. OB; ii. AD; iii. CB; b) Lines OB and AD intersect at point X such that AX = kAD and OX = rOB, where k and r are scalars. Determine the values k and r. 
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