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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

K.C.S.E Mathematics Q & A - MODEL 2019PP2QN24

24/9/2020

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Form 4 Mathematics


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(b) On the grid provided draw PQRS and its image P'Q'R'S’
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(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’.

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN23

24/9/2020

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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.
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(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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN22

24/9/2020

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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.
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(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.

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN21

24/9/2020

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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN20

24/9/2020

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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.

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN19

24/9/2020

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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
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(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).

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN18

24/9/2020

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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.

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN16

24/9/2020

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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.
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(a) On the grid provided, draw the graph of length against time.
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(b) Determine the rate of change of the shadow’ length at = 2 
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN15

24/9/2020

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Form 3 Mathematics


Solve for x in log(7x—3) + 2 log 5 = 2 + log(x + 3).
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN14

24/9/2020

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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.
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN13

24/9/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN12

24/9/2020

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Form 3 Mathematics


The table below' shows income tax rates in a certain year.
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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 
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN11

24/9/2020

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Form 4 Mathematics


The figure ABCDEFGH represents a box.
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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN10

24/9/2020

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Form 4 Mathematics


Determine the amplitude and the period of the function y = 3 sin(2x + 40°).
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN09

24/9/2020

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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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answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN08

24/9/2020

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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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answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN07

24/9/2020

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Form 4 Mathematics


Find the coordinates of the turning point of the curve y= x²-14x +10 
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN06

24/9/2020

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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN05

24/9/2020

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Form 2 Mathematics


Solve the equations:
x + 3y = 13
x² + 3y² = 43
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN04

24/9/2020

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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
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN03

23/9/2020

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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
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN02

23/9/2020

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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.
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN01

23/9/2020

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Form 3 Mathematics


Simplify
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Give the answer in the form a + b √c where a, b and c are integers.
ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN24

23/9/2020

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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN23

23/9/2020

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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.
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(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.
answers
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