Form 4 Mathematics
(b) On the grid provided draw PQRS and its image P'Q'R'S’
(ii) On the same Grid draw P"Q"R‘S”.
(d) (i) Find a single matrix that maps P"Q"R’S" onto P’Q’R’S’. (ii) Describe fully the transformation thai maps P"Q”R"S" onto P’Q’R’s’.
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Form 3 Mathematics
In the figure below, OA = a, OB = b and BX meets OY at C. OX:OA = 1:2 and BY:YA = 1:3.
(a) Express in terms of a and b:
(ii) OY; (iii) BX. (b) Given that OC = hOY and BC = kBX, determine the values of h and k.
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Form 4 Mathematics
The amount of money contributed by a group of students during a fundraising for a needy student was as shown in the table below.
(a) On the grid provided draw an ogive to represent the data.
(b) Use the graph to estimate: (i) The median; (ii) The quartile deviation; (iii) The percentage number of students who contributed at least Ksh 750.50.
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Form 4 Mathematics
A workshop makes cupboards and tables using two artisans A and B every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B. Every table made requires 2 days of work by artisan A and 2 days of work by artisan B.
In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days. The workshop made x cupboards and y tables in that month. (a) Write all the inequalities which must be satisfied by x and y. (b) Represent the inequalities in (a) on the grid provided. (c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table. Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.
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Form 4 Mathematics
A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
(a) Calculate the distance between P and R in: (i) nm; (ii) km. (b) Determine the position of point R. (c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m.
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Form 4 Mathematics
The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m
(a) On the figure, construct
(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM. (ii) the locus of a point Q such that ∠KQL = 90°. (b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM. (ii) Find the area of the region R in m². (Take ℼ= 3.142).
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Form 3 Mathematics
Mbaka bought some plots at Ksh 400,000 each. The value of each plot appreciated at the rate of 10% per annum.
(a) Calculate the value of a plot after 2 years. (b) After some time t, the value of a plot was Ksh 558,400. Find t, to the nearest month. (c) Mbaka sold all the plots he had bought after 4 years for Ksh2,928,200. Find the percentage profit Mbaka made, correct to 2 decimal places.
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Form 3 Mathematics
The length of a shadow' of a mast was measured at intervals of 1 hour and recorded as shown in the table below.
(a) On the grid provided, draw the graph of length against time.
(b) Determine the rate of change of the shadow’ length at = 2
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Form 4 Mathematics
The vertices of a triangle PQR are P(-3, 2), Q(0,-1) and R(2, -1). A transformation matrix maps triangle PQR onto triangle P’Q' R' whose vertices are P'(-7, 2), Q'(2, -1) and R’(4, -1).
Find M-1, the transformation that maps P'Q'R' onto PQR.
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Form 3 Mathematics
The table below' shows income tax rates in a certain year.
In that year, mawira earned a salary of 41000 per month. calculate mawira's income tax per month given that a monthly tax relief of ksh 1162 was allowed
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Form 4 Mathematics
The figure ABCDEFGH represents a box.
The top lid of the box is opened such that the height OT is 35cm. Calculate the:
(a ) angle the top lid makes with the plane FGHE; (b) length BE, correct to 2 decimal places.
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Form 4 Mathematics
Determine the amplitude and the period of the function y = 3 sin(2x + 40°).
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Form 4 Mathematics
In a mathematics test, the scores obtained by 30 students were recorded as shown in the table below.
The score K with a frequency of 6 is not given. 
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Form 3 Mathematics
OAB is a Sector of a circle of radius r cm. Angle AOB = 60°.
Find, in its simplest form, an expression in terms of r and π for the perimeter of the sector. 
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Form 4 Mathematics
Find the coordinates of the turning point of the curve y= x²-14x +10
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Form 3 Mathematics
A bag contains 6 red counters and 4 blue counters. Two counters are picked from the bag at random, without replacement.
(a) Represent the events using a tree diagram. (b) Find the probability that the two counters picked are of the same colour.
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Form 2 Mathematics
An arc of a circle subtends an angle of 150° at the circumference of the circle. Calculate the angle subtended by the same arc at the centre of the circle.
ANSWER
Form 3 Mathematics
A quantity P varies inversely as the square of another quantity L.When P = 0.625, L = 4. Determine P when L= 0.2.
ANSWER
Form 1 Mathematics
Two types of flour, X and Y, cost Ksh60 and Ksh 72 per kilogram respectively.
The two types are mixed such that the cost of a kilogram of the mixture is Ksh 70. Calculate the ratio X:Y of the mixture.
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Form 3 Mathematics
Simplify
Give the answer in the form a + b √c where a, b and c are integers.
ANSWER
Form 4 Mathematics
The equation of a curve is y=x3+x2-x-1
(i) Determine the stationary point of the curve (Îi) the nature of the stationary points in (a) (i) above. (b) Determine: (i) the equation of the tangent to the curve at x = 1; (ii) the equation of the normal to the curve at x = 1.
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Form 4 Mathematics
The shaded region on the graph below shows a piece of land ABCD earmarked for building a sub-county hospital.
(a) Write down the ordinates of curves AB and DC for x = 0, 200, 400, 600, 800, 1000 and 1200.
(b) Use trapezium rule, with 6 strips to estimate the area of the piece of land ABCD, in hectares. (c) Use mid-ordinate rule with 3 strips to estimate the area of the piece of land, in hectares.
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