THE TABLE BELOW SHOWS THE NUMBER OF STUDENTS IN EACH CLASS IN A SCHOOL. THE PERCENTAGE (%) OF THE STUDENTS IN EACH CLASS WHO WEAR GLASSES IN ALSO SHOWN.

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 24

In the figure below A, B, C and D are points on the circumference of the circle, centre O. A tangent to the circle at A intersects chord CD produced at E. Line AB is parallel to line EC. Angle AED = 45 degrees and angle ABD = 40 degrees.

​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 23

The systolic blood pressure of 60 patients attending a clinic was recorded as follows:

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 22

​A road contractor has to transport 240 tonnes of hardcore. He will use two types of lorries, type A and type B. He has 3 type A lorries and 2 type B lorries. The capacity of each type A lorry is 8 tonnes while that of type B is 15 tonnes. All type A lorries must each make the same number of trips. Similarly all type B lorries must each make the same number of trips. The number of trips made by each type B lorry should be less than twice those made by each type A lorry. Each type A lorry must not make more than 6 trips.

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 21

An aircraft took off from point A (x degrees North, 15 degrees east) at 0720h, local time. It flew due west to another point B (x degrees North, 75 degrees West) a distance of 5005 km from A.

​​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 20

Kering purchased (2x-1) identical pens for Ksh 180. Naraya purchased (3x+1) identical pencils for Ksh 200.

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 19

THE TABLE BELOW SHOES THE INCOME TAX RATES FOR A CERTAIN YEAR

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 18

​A FARMER HAS TWO TRACTORS P AND Q. TRACTOR P, WORKING ALONE, CAN PLOUGH A PIECE OF LAND IN 5 HOURS WHILE TRACTOR Q WOULD TAKE ON AND TWO-THIRDS HOURS LESS THAN TRACTOR P.

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 17

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)

Data collected form an experiment involving two variables X and Y was recorded as shown in the table below.

​K.N.E.C Marking Scheme

Two variables P and L are such that P varies partly as L and partly as the square root of L. Determine the relationship between P and L when L = 16, P = 500 and when L = 25, P = 800. 

​5 marks

marking scheme

The table below shows income tax rates
Monthly income Tax Rate 
(Kshs) (%)
Up to 9680 10
9681 – 18800 15 
18801-27920 20
27921-37040 25
37041 and above 30 
Omari’s monthly taxable income is Ksh. 24200
​
a) Calculate the tax charged on Omari’s monthly earnings. (4mks) 
b) Omari is entitled to the following tax relief of 15% of the premium paid. 
Calculate the tax Omari pays each month if he pays a monthly insurance premium of Ksh. 2400 (2mks) 
c) During a certain month, Omari received additional earnings which were taxed at 20% each shilling. Given that he paid 36.3% more tax that month, calculate the percentage increase in his earning. (4mks) 

​a) Using a ruler and pair of compasses only construct triangle ABC in which AB = 6.5cm, BC= 5.0cm and angle ABC = 600. Measure AC (3mks)  
b) On same side of AB as C (3mks)
    i) Determine the locus of a point P such that angle APB = 600 (3mks)
    ii)  Construct the locus of R such that AR = 3cm. (1mk) 
    iii) Identify the region T such that AR  3 and APB  600 by shading the unwanted part. (3mks)

The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm. 

A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that 

a) The first red bead is the third bead picked. (2mks) 
b) The beads selected were, white and blue: (2mks)
    i) In that order 
    ii) In any order (2mks) 
c) No red bead is picked (2mks) 
d) Beads picked are of the same colour. (2mks)

​A particle moves along a straight line such that its displacement S metres from a given point is S = t^3-5t^2 + 3t + 4. where t is time in seconds.

The distance between A and B is 280km. A car and lorry travelled from A to B. The average speed
of the lorry is 20km/h less than that of the car. The lorry takes 1hr 10min more than the car to travel
from A to B. 

a) If the speed of the lorry is xkm/h, find x (6mks) 
​
b) If the lorry left town A at 8.15a.m and the car left town A and later overtook the lorry at 12.15pm. Calculate the time the car left town A. (4mks) 

A group of people planned to contribute equally towards a water project which needed
Ksh. 2, 000,000 to complete. However 40 members of the group withdrew from the project. As a result each of the remaining members were to contribute Ksh. 2,500 more. 

a) Find the original number of members in the group. (5mks) 

b) Forty five percent of the value of the project was funded by constituency development fund (CDF). Calculate the amount of contribution that would be made by each of the remaining members. (3mks) 

​c) Members contribution were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contribution was 6:9. Calculate the total amount of money contributed by the members. (2mks)