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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 2010PP2QN24

26/8/2020

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Form 3 Mathematics


In the figure below, P, Q, R and S are points on the circle centre O. PRT and USTV are straight lines.
Line USTV is a tangent to the circle at S, ZRST = 50° and LRTV = 150°.
Picture
(a) Calculate the size of:
(i) angle ORS; 
(ii) angle USP; 
(iii) angle PQR. 
(b) Given that RT = 7 cm and ST 9 cm, calculate to 3 significant figures:
(i) the length of line PR; 
(ii) the radius of the circle.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN23

26/8/2020

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Form 2 Mathematics


In a uniformly accelerated motion the distance, s metres, travelled in time t seconds varies partly as the time and partly as the square of the time. When the time is 2 seconds, the distance travelled is 80 metres and when the time is 3 seconds, the distance travelled is 135 metres.
(a) Express s in terms of t. 
(b) Find:
(i) the distance travelled in 5 seconds; 
(ii) the time taken to travel a distance of 560 metres.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN22

26/8/2020

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Form 3 Mathematics


The first term of an Arithmetic Progression (A.P.) with six terms is p and its common difference is c. Another AP. with five terms has also its first term asp and a common difference of d. The last terms of the two Arithmetic Progressions are equal.
(a) Express d in terms of c. 
(b) Given that the 4th term of the second A.P. exceeds the 4th term of the first one by 1, find the values of e and d. 
(c) Calculate the value of p if the sum of the terms of the first A.P. is 10 more than the sum of the terms of the second A.P.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN21

26/8/2020

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Form 3 Mathematics


 A hail can accommodate 600 chairs arranged in rows. Each row has the same number of chairs. The chairs are rearranged such that the number of rows are increased by 5 but the number of chairs per row is decreased by 6.
(a) Find the original number of rows of chairs in the hall. 
(b) After the re-arrangement 450 people were seated in the hail leaving the same number of empty chairs in each row. Calculate the number of empty chairs per row.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN20

26/8/2020

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Form 4 Mathematics


 A carpenter takes 4 hours to make a stool and 6 hours to make a chair. It takes the carpenter and at least 144 hours to make x stools and y chairs. The labour cost of making a stool is Ksh 100 and that of a chair is Ksh 200. The total labour cost should not exceed Ksh 4 800. The carpenter must make at least 16 stools and more than 10 chairs.
(a) Write down inequalities to represent the above information. 
(b) Draw the inequalities in (a) above on the grid provided.
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​(c) The carpenter makes a profit of Ksh 40 on a stool and Ksh loo on a chair.
Use the graph to determine the maximum profi.t the carpenter can make.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN19

26/8/2020

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Form 4 Mathematics


The positions of three ports A, B and C are (34°N, 16°W), (34°N. 24°E) and (26°S, 16°W) respectively.
(a) Find the distance in nautical miles between:
(i) Ports A and B to the nearest nautical miles; 
(ii) Ports A and C. 
(b) A ship left Port A on Monday at 1330 h and sailed to Port B at 40 knots.
Calculate:
(i) the local time at Port B when the ship left Port A; 
(ii) the day and the time the ship arrived at port B. 
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN18

26/8/2020

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Form 3 Mathematics


In the figure below OJKL is a parallelogram in which OJ = 3p and OL 2r.
Picture
(a) If A ¡s a point on LK such that LA = 1/2 AK and a point B divides the line JK externally in the ratio 3:1, express OB and AJ in terms of p and r. 
(b) Line OB intersects AJ at X such that OX = mOB and AX= nAJ.
(i) Express OX in terms of p, r and m. 
(ii) Express OX in terms of p, r and n. 
(iii) Determine the values of m and n and hence the ratio in which point X divides line AJ.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN17

26/8/2020

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Form 4 Mathematics


(a) Complete the table below, giving the values correct to 2 decimal places.
Picture
(b) On the grid provided and using the same axes draw the graphs of y = cos x° and y= sin x°— cos x°  for 0° ≤  x ≤  180°.Use the scale; 1 cm for 20°on the x-axis  and 4cm fort unit on the y-axis. 
(c) Using the graph in part (b):
(i) solve the equation sin x° — cos x° 1.2; 
(ii) solve the equation cos x°=  1/2 sinx; 
(iii) determine the value of cos x° in part (c) (ii) above.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN16

26/8/2020

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Form 3 Mathematics


The circle shown below cuts the x-axis at (—2,0) and (4,0). It also cuts y-axis at (0,2) and (0,-4).
Picture
Determine the:
(a) (i) coordinates of the centre;
(ii) radius of the circle.
(b) equation of the circle in the form x2 +y2 + ax + by c where a, b and c are constants.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN15

26/8/2020

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Form 3 Mathematics


Find the value of x given that
log (15—5x)— 1 =log(3x—2)
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN13

26/8/2020

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Form 1 Mathematics


 (a) Using line AB given below, construct the locus of a point P such that angle APB 90. 
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(b) On the same diagram locate two possible positions of point C such that point C is on the locus of P and is equidistant from A and B. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN12

26/8/2020

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Form 3 Mathematics


(a) Expand and simp1ify (2 —x)5. (b) Use the first 4 terms of the expansion in part
(a) above to find the approximate value of (1.8)5 to 2 decimal places.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN11

26/8/2020

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Form 4 Mathematics


A particle starts from O and moves in a straight line so that its velocity V ms-1 after time t seconds is given by V = 3t-t2. The distance of the particle from O at time t seconds is s metres.
(a) Express s in terms of t and c where c is a constant.
(b) Calculate the time taken before the particle returns to 0.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN10

25/8/2020

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Form 3 Mathematics


Picture
(a) Determine in terms of k, the x coordinate of point B'.
(b) If OAB’ is a right angled triangle in which angle OB’A is acute, find two possible values of k.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN09

25/8/2020

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Form 3 Mathematics


A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours, b
Two balls are drawn at random, one after the other from the first bag and placed in the second bag.
Calculate the probability that the 2 balls are both white.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN08

25/8/2020

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Form 4 Mathematics


The heights, in centimeters, of 100 tree seedlings are shown in the table below.
Picture
Find the quartile deviation of the heights.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN07

25/8/2020

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Form 1 Mathematics


When Ksh 40 000 was invested in a certain bank for 5 years it earned a simple interest of Ksh 3 800.
Find the amount that must have been invested in the same bank at the same rate for 7 - years to earn a simple interest of Ksh 3 420.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN06

25/8/2020

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Form 1 Mathematics


 Five people can build 3 huts in 21 days. Find the number of people, working at the same rate that will build 6 similar huts in 15 days. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN05

25/8/2020

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Form 1 Mathematics


The length of a flower garden is 2 m less than twice its width. The area of the garden is 60 m2.
 Calculate its length.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN04

25/8/2020

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Form 1 Mathematics


A tea dealer mixes two brands of tea, x and y, to obtain 35 kg of the mixture worth Ksh 62 per kg. 1f brand x is valued at Ksh 68 per kg and brandy at Ksh 53 per kg, calculate the ratio, in its simplest form, in which the brands x and y are mixed. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN03

25/8/2020

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Form 3 Mathematics


In the figure below, O is the centre of the circle which passes through the points T, C and D. Line TC is parallel to OD and line ATB  is a tangent to the circle at T. Angle DOC = 36°.
Picture
Calculate the size of angle CTB. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN02

25/8/2020

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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 2010PP2QN01

25/8/2020

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Form 3 Mathematics


The length and width of a rectangle measured to the nearest millimeter are 7.5 cm and 5.2 cm respectively.
Find, to four significant figures, the percentage error in the area of the rectangle.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN24

25/8/2020

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Form 2 Mathematics


A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm2.
(a) Express in terms of x:
(i) the internal height h, of the box;
(ii) the internal volume V, of the box.
(b) Find:
(i) the value of x for which the volume V is maximum;
(ii) the maximum internal volume of the box.
answers
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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN23

25/8/2020

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Form 2 Mathematics


The frequency distribution table below represents the number of kilograms of meat sold in a butchery.
Picture
(a) State the modal frequency
(b)Calculate the mean mass.
(c)Calculate the median mass.
answer
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