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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 1996PP1QN14

3/6/2023

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Make V the subject of the formula:


T = ½ m (u2 – v2) (3 marks)


MARKING SCHEME
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K.C.S.E Mathematics Q & A - MODEL 2000PP1QN09

1/6/2023

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Form 2 Mathematics | Topical Questions and Answers


ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN10

28/5/2023

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Form 3 Mathematics


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K.C.S.E Mathematics Q & A - MODEL 2002PP1QN003

23/5/2023

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Form 3 Mathematics


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the displacement, s metres of a moving particle after t seconds in given by

22/5/2023

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the displacement, s metres of a moving particle after t seconds in given by

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 24
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​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 23 ON MATRIX

22/5/2023

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​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 23 ON MATRIX

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 23
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THE NUMBER OF STUDENTS IN 40 SCHOOLS IN A CERTAIN SUB-COUNTY WERE RECORDED AS FOLLOWS:

22/5/2023

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​THE NUMBER OF STUDENTS IN 40 SCHOOLS IN A CERTAIN SUB-COUNTY WERE RECORDED AS FOLLOWS:

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 22
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​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 21 ON VECTORS

22/5/2023

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​​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 21 ON VECTORS

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 21
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A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

22/5/2023

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A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 20
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The average speed of a pick-up was 20 km/h faster than the average speed of a lorry. The pick-up took 45 minutes less than the lorry to cover a distance of 180 km.

22/5/2023

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The average speed of a pick-up was 20 km/h faster than the average speed of a lorry. The pick-up took 45 minutes less than the lorry to cover a distance of 180 km.
(a) If the speed of the lorry was x was x km/h:
(i) write expressions in terms of x for the time taken by the lorry and the pick-up respectively to cover the distance of 180 km;
(2 marks)
(ii) determine the speed of the lorry and that of the pick-up.
(5 marks)
(b) The distance between towns A and B is 240 km. On a certain day the pick-up started from town A at 8.30 a.m. and the lorry started from town B at the same time. Determine the time that the lorry and the pick-up met.
(3 marks)

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 19
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A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slanting height of the conical part is 10 cm. (Тake л = 3.142)

22/5/2023

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A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slanting height of the conical part is 10 cm. (Тake л = 3.142).
Calculate the:
(a) height of the solid; (2 marks)
(b) surface area of the solid, correct to 1 decimal place; (4 marks)
(c) volume of the solid, correct to 1 decimal place. (4 marks)

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 18
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Three business partners, Kosgei, Kimani and Atieno contributed Ksh 1 750 000 towards an investment. Kosgei contributed 20% of the money. Kimani and Atieno contributed the remainder in the ratio 3:5 respectively.

22/5/2023

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Three business partners, Kosgei, Kimani and Atieno contributed Ksh 1 750 000 towards an investment. Kosgei contributed 20% of the money. Kimani and Atieno contributed the remainder in the ratio 3:5 respectively.
(a)
(i) Calculate the amount of money Kimani contributed. (2 marks)
(ii) Find the ratio of the contributions by the three partners. (2 marks)

(b) The money earned a compound interest at a rate of 8% per annum. After 3 years, the partners withdrew the interest and donated 10% to a charitable organisation. The partners then shared the remainder in the ratio of their contributions.
Calculate the amount of money, to the nearest shilling, that each partner received. (6 marks)

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 17
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The figure below shows a quadrilateral ABCD and a mirror line M1M2

22/5/2023

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The figure below shows a quadrilateral ABCD and a mirror line M1M2

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 16
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In a 4×400 m relay competition, a team of athletes each completed their round in 45 sec, 43 sec, 44 sec and 45 sec respectively. If the race started at 1:35:31 p.m., find the time when the team completed the race.

22/5/2023

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In a 4×400 m relay competition, a team of athletes each completed their round in 45 sec, 43 sec, 44 sec and 45 sec respectively. If the race started at 1:35:31 p.m., find the time when the team completed the race. (3 marks)

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 15
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A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the

22/5/2023

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A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the height of the electric pole correct to 1 decimal place. (2 marks)

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 14
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A chord of a circle, 7cm long, subtends an angle of 60 degrees at the centre of the circle. Determine the area, correct to 2 decimal places, of the major segment of the circle.

22/5/2023

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A chord of a circle, 7cm long, subtends an angle of 60 degrees at the centre of the circle. Determine the area, correct to 2 decimal places, of the major segment of the circle.

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 13
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A Kenyan Non-Governmental Organization (NGO) received a donation of 200000 US dollars. The money was converted into Kenyan shillings in a bank which buys and sells foreign currency as follows:

22/5/2023

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A Kenyan Non-Governmental Organization (NGO) received a donation of 200000 US dollars. The money was converted into Kenyan shillings in a bank which buys and sells foreign currency as follows:

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 12
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Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which AB=6cm, BC=5cm and angle ADC=150 degrees

22/5/2023

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Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which AB=6cm, BC=5cm and angle ADC=150 degrees

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 11
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In the figure below, AB and CD are arcs of two concentric circles, centre O. Angle AOB=60 degrees and AD=BC=7cm.

22/5/2023

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In the figure below, AB and CD are arcs of two concentric circles, centre O. Angle AOB=60 degrees and AD=BC=7cm.

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 10
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​Given that sin(θ+30°)=cos2θ, find the value of cos(θ+40°)

22/5/2023

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​Given that sin(θ+30°)=cos2θ, find the value of cos(θ+40°). (3 marks)

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 9
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​Using the grid provided below, solve the simultaneous equations. x-4y = -5-x+2y= 1

22/5/2023

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​Using the grid provided below, solve the simultaneous equations.
x-4y = -5
-x+2y= 1
(3 marks)

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 8
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The sum of the interior angles of a regular polygon is 1260°. Find the size of each exterior angle of the polygon. (3 marks)

22/5/2023

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​The sum of the interior angles of a regular polygon is 1260°. Find the size of each exterior angle of the polygon. (3 marks)

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 7
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The line 2y+x=1 is perpendicular to a line L. Line L passes through point (2,-1). Determine the equation of L in the form Y = mx + c, where m and c are constants.

22/5/2023

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The line 2y+x=1 is perpendicular to a line L. Line L passes through point (2,-1). Determine the equation of L in the form Y = mx + c, where m and c are constants.

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 6
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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN13

22/5/2023

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Given that y = b - bx2 make x the subject


​K.N.E.C Marking Scheme
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SIMPLIFY:

21/5/2023

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KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 5

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