KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Make V the subject of the formula:

MARKING SCHEME

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

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

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

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

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.

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)

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)

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)

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

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)

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)

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.

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:

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

Answer

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

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

Answer

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

Answer

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

Answer

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.

Answer

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 5

ANSWER