KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 2 MathematicsForm 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 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 MathematicsThe length of a hallow cylindrical pipe is 6 metres. Its external diameter is 11cm and has a thickness of 1cm. Calculate the volume in cm3 of the material used to make the pipe. Take П as 3.142 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 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. Form 2 Mathematics
Given the inequalities x – 5 ≤ 3 x – 8 < 2 x – 3.
a) Solve the inequalities; b) Represent the solution on a number line. Form 2 MathematicsForm 2 Mathematics
A cylindrical pipe 2 ½ metres long has an internal diameter of 21 millimetres and an external diameter of 35 millimetres. The density of the material that makes the pipe is 1.25 g/cm3.
Calculate the mass of mass of the pipe in kilograms. (Take π = 22/7). Form 2 Mathematics
A triangle ABC is such that AB = 5 cm, BC = 6 cm and AC = 7 cm.
a) Calculate the size of angle ACB, correct to 2 decimal places. b) A perpendicular drawn from A meets BC at N. calculate the length AN correct to one decimal place. Form 2 Mathematics
A straight line passes through points (-2, 1) and (6, 3).
Find: a) equation of the line in the form y = mx + c; b) the gradient of a line perpendicular to the line in (a) Form 2 Mathematics
Chelimo’s clock loses 15 seconds every hour. She sets the correct time on the clock at 0700h on a Monday. Determine the time shown on the clock when the correct
time was 1900h on Wednesday the same week. Form 2 Mathematics
Two straight paths are perpendicular to each other at point p.One path meets a straight road at point A while the other meets the same road at B. Given that PA is 50 metres while PB is 60 metres. Calculate the obtuse angle made by path PB and the road.
Form 2 Mathematics
The length of a solid prism is 10cm. Its cross section is an equilateral triangle of side 6cm.
Find the total surface area of the prism. Form 2 Mathematics
The masses in kilograms of 20 bags of maize were;
90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102 and 105. Using an assumed mean of 96kg, calculate the mean mass, per bag, of the maize. Form 2 Mathematics
Given that P = 2i- 3j + k, Q = 3i – 4j- 3k and R = 3P + 2 Q, find the magnitude of R to 2 significant figures.
Form 2 MathematicsForm 2 Mathematics
In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS - 80°.
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures: (i) the perpendicular distance between PQ and RS; (ii) the length of TS. (c) Using the cosine rule, find the length of RS correct to 2 significant figures. (d) Calculate, correct to one decimal place, the area of triangle RST. Form 2 Mathematics
The vertices of quadrilateral OPQR are O (0,0), P(2,0), Q(4,2) and R(0,3).
The vertices of its image under a rotation are O'(l, -1), P'(l, -3), Q'(3, -5) and R'(4, -1). (a) (i) On the grid provided, draw OPQR and its image O'P'Q'R'. (ii) By construction, determine the centre and angle of rotation. (b) On the same grid as (a) (i) above, draw O"P"Q"R", the image of O'P'Q'R' under a reflection in the line y = x. (i) directly congruent; (ii) oppositely congruent. |
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