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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

K.C.S.E Mathematics Q & A - MODEL 2015PP2QN24

11/9/2020

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Form 4 Mathematics


Picture
a) Determine the coordinates of the image 
b) On the grid provided draw the object and the image 
c i)Describe fully the transformation which maps KLMN onto K'L'M'N' 
ii)Determine the area of the image. 
d)Find a matrix which maps K'L'M'N' onto KLMN

answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN23

11/9/2020

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Form 4 Mathematics


The marks scored by 40 students in a mathematics test were as shown in the table below.
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a) Find the lower class boundary of the modal class 
b) Using an assumed mean of 64, calculate the mean mark 
c i) On the grid provided, draw the cumulative frequency curve for the data 
ii)Use the graph to estimate the semi-interquartile range

answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN22

11/9/2020

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Form 4 Mathematics


A particle was moving along a straight line. The acceleration of the particle after t seconds was given by (9 -3t) ms-2. The initial velocity of the particle was 7 ms-1.
 Find:
 a) the velocity (v) of the particle at any given time (t);
 b) The maximum velocity of the particle;
c)the distance covered by the particle by the time it attained maximum velocity
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN21

11/9/2020

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Form 3 Mathematics


A quantity P varies partly as the square of m and partly as n. When P = 3.8, m = 2 and n = When P = -0.2, m = 3 and n = 2.
(a) Find:
(i) the equation that connects P, m and n; 
(ii) the value of P when m = 10 and n = 4. 
(b) Express m in terms of P and n. 
(c) If P and n are each increased by 10%, find the percentage increase in m correct to 2 decimal places.

answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN20

11/9/2020

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Form 4 Mathematics


The figure below represents a cuboid EFGHJKLM in which EF = 40cm, FG=9cm and GM=30 cm. N is the midpoint of LM.
Picture
Calculate correct to 4 significant figures
a)The length of GL: 
b)The length of FJ 
c)The angle between EM and the plane EFGH; 
d)The angle between eh planes EFGH and ENH; 
e)the angle between the lines EH and GL
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN19

11/9/2020

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Form 4 Mathematics


The equation of a curve is given by y= 1 + 3sin x.
(a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place
Picture
(b) (i) On the grid provided, draw the graph of y - 1 + 3 sin x for 0° ≤ x ≤ 360°.
ii) State the amplitude of the curve y = 1 + 3 sin x.
c) On the same grid draw the graph of y = tan x for 90° ≤ x ≤ 270°. 
d) Use the graphs to solve the equation ; 1+3 sin x = tan x for 90° ≤ x ≤ 270°.
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN18

10/9/2020

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Form 3 Mathematics


Mute cycled to raise funds for a charitable organisation. On the first day, he cycled 40 km. For the first 10 days, he cycled 3 km less on each subsequent day.
Thereafter, he cycled 2km less on each subsequent day.
a) Calculate
i)the distance cycled on the 10th day
ii)The distance cycled on the 16th day 
b) If Mute raised kshs 200 per km, calculate the amount of money collected

answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN17

10/9/2020

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Form 3 Mathematics


In a retail shop, the marked price of a cooker was Ksh 36 000. Wanandi bought the cooker on hire purchase terms. She paid Ksh 6400 as deposit followed by 20 equal monthly installments of Ksh 1750.
(a) Calculate:
(i) The total amount of money she paid for the cooker. 
(ii) The extra amount of money she paid above the marked price. 
(b) The total amount of money paid on hire purchase terms was calculated at a
Compound interest rate on the marked price for 20 months. Determine the rate, per annum, of the compound interest correct to 1 decimal place. 
c) Kaloki borrowed kshs 36000 form a financial institution to purchase a similar cooker. The financial institution charged a compound interest rate equal to the rate in (b) above for 24 months. Calculate the interest kaloki paid correct to the nearest shilling.
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN16

10/9/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN15

10/9/2020

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Form 3 Mathematics


Solve the equation sin ( ½ x – 300) = cos x for 00 < x < 900.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN14

10/9/2020

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Form 4 Mathematics


The positions of two points P and Q, on the surface of the earth are P(45 °N, 36°E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN13

10/9/2020

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Form 4 Mathematics


Evaluate
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answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN11

10/9/2020

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Form 4 Mathematics


In a nomination for a committee, two people were to be selected at random from a group of 3 men and 5 women. Find the probability that a man and a woman were selected
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN10

10/9/2020

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Form 4 Mathematics


Below is a lien AB and a point X. Determine the locus of a point P equidistant from points A and B and 4 cm from X.
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answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN09

10/9/2020

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Form 3 Mathematics


The diameter of a circle, centre O has its end points at M(— 1, 6) and N(5, —2).
Find the, equation of the circle in the form x2+y2 + ax + by = c where a, b and c are constants
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN08

10/9/2020

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Form 3 Mathematics


Use the expansion of (x — y)5 to evaluate (9.8)5 correct to 4 decimal places.
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN07

10/9/2020

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Form 2 Mathematics


Find the value of x given that log (x - 1) + 2 = log (3x + 2) + log 25.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN06

10/9/2020

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Form 1 Mathematics


The length and width of a rectangular signboard are (3x +12) cm and (x — 4) cm respectively.
If the diagonal of the signboard is 200cm, determine its area.

answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN05

10/9/2020

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Form 1 Mathematics


Eleven people can complete 3/5 of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate can
take to complete the remaining job.

answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN04

10/9/2020

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Form 3 Mathematics


In the figure below, O is the centre of the circle. A, B, C and D are points on the circumference of the circle. Line AB is parallel to line DC and angle ADC = 55°.
Picture
Determine the size of angle ACB
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN03

10/9/2020

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Form 3 Mathematics


An arc 11 cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at
the centre of the same circle.

answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN02

10/9/2020

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Form 3 Mathematics


Simplify
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answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN01

10/9/2020

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Form 3 Mathematics


The length and width of a rectangular piece of paper were measured as 60 cm and 12 cm respectively. Determine the relative error in the calculation of its area.
ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN24

10/9/2020

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Form 4 Mathematics


The gradient of the curvey y = 2x3 – 9x2 + px – 1 at x = 4 is 36.
 a)Find :
 i) the value of p;
 ii)The equation of the tangent to the curve at x = 0.5.
b) Find the coordinates of the training points of the curve
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN23

10/9/2020

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Form 2 Mathematics


The figure below represents a conical flask. The flask consists of a cylindrical part and a frustum of a cone. The diameter of the base is 10cm while that of the neck is 2 cm. the vertical height of the flask is 12cm.
Picture
Calculate, correct to 1 decimal place
a) The slant height of the frustum part 
b) The slant height of the smaller cone that was cut off to make the frustum part 
c) The external surface area of the flask. (Take π =3.142)

answer
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