KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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
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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
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.
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 Form 4 Mathematics
The equation of a curve is given by y = 5x − 1/2 x2
(a) On the grid provided, draw the curve of y = 5x − 1/2 x2 for 0 ≤ x ≤ 6 (b) By integration, find the area bounded by the curve, the line x =6 and the x-axis. (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
Two towns A and B lie on the same latitude in the northern hemisphere. When its 8am at A, the time at B is 11.00am.
Form 1 MathematicsA businessman obtained a loan of sh.450,000 from a bank to buy a matatu valued at the same amount. The bank charges interest at 24% per annum compounded equation. 2x2 + x – 5 = 0 to 1 decimal place.
Form 3 MathematicsForm 4 MathematicsThe diagram below is a sketch of the curve y =x2 + 5.
Form 2 MathematicsForm 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 00 ≤ χ ≤ 2400.
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 MathematicsForm 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 2 Mathematics
A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.
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. Form 4 Mathematics
The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s = t3 – 5t2 + 3t + 10
a) Find s when t =2. b) Determine: i. The velocity of the particle when t = 5 seconds; ii. The value of t when the particle is momentarily at rest. c) Find the time, when the velocity of the particles is maximum. Form 2 Mathematics
Two towns, A and B are 80km apart. Juma started cycling from town A to town B at 10.00 am at an average speed of 40 km/h. Mutuku started his journey from
town B to town A at 10.30 am and travelled by car at an average speed of 60 km/h. a) Calculate: i. The distance from town A when Juma and Mutuku met; (5 mks) ii. The time of the day when the two met. (2 mks) b) Kamau started cycling from town A to town B at 10.21 am. He met Mutuku at the same time as Juma did. Determine Kamau’s average speed. |
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