​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

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)

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

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.

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 3

ANSWER

​The height of tree seedlings in a nursery were measured and recorded as in the table below 

​In the diagram below ON = a and OL = b, LX = sLN, OM = 3a and MK = 2b       

​Draw the quadrilateral with vertices at A (-6,-1) B (-6,-4) C (3,-7) and D (3,2). 

​Find the value of y in the equation 

​Jecinta made a profit of 25% by selling a pair of shoes at Ksh. 1500. What percentage profit would she have made if she sold the same shoes at 1600? (3mks)

​Given that Cos A = 5/13 and angle A is acute, find Tan A without using tables or calculators    (2mks)

​The figure below is a cross-section of a model of a swimming pool of length 30cm. 

​The unshaded region in the figure below is reflected in the x-axis. Write down the inequalities which satisfy the new region. (3mks) 

​A line L1 passes through points A (3,3), B(5-1) and it is bisected by L2. Determine the equation of L2 in the form y = mx + c    (3mks) 

​A car starts from rest and builds up a speed of 40m/s in 1 min 40 seconds.  It then travels at this 
speed for 5 minutes.  Brakes are then applied and the car is brought to a halt in 2 minutes.
(a) Draw a velocity-time graph to represent the information above. (3mks)
(b) Use your graph to find
(i) the initial acceleration. (2mks)
(ii) the deceleration when the car is brought to a halt. (2mks)
(iii) the distance traveled in km. (3mks)

ANSWER

​ANSWER

​The figure below is a right pyramid of rectangular base of length 12cm and width 9cm.  
The slanting edge has a length of 19.5cm.

​ANSWER

​The volume of two similar cans is 96cm³ and 1.5 litres.  If the total surface area of the smaller can
is 144cm², determine the surface area of the larger can.                                                       (3mks)

ANSWER

Calculate the surface area of the solid regular hexagonal prism shown below, giving your
answer to 3sf.     (4mks)

​ANSWER