KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

​(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)

​(a)  ERS  =

(b) Find the matrix representing the single transformation mapping the image found in (a) above
 back to the object figure ABCD. (2mks)

​(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

​Auma, Hassan and Kamau competed in a game of darts.  Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(a) Draw a probability tree diagram to show all the possible outcomes.  (2mks)

​(b) Calculate the probability that
(i) No one hit the target.        (2mks)

​(ii) Only one of them hit the target.       (2mks)

​(iii) At least one of them hit the target.       (2mks)

​(iv) At least one of them missed the target.     (2mks)

​Mr. Kimutai a teacher from Tuiyotich Secondary School earns K₤ 12000 per annum and lives in a house provided by the employer at a minimum rent of Ksh.2000 per month.  He gets a family relief of K₤ 1320p.a. and is entitled to a relief of 10% of his insurance of K₤ 800p.a.

​(a) Calculate his annual tax bill based on the table below. (6mks)

​(b) Kimutai other deductions include.
- W.C.P.S = sh 600.00pm
- NHIF = sh 500.00pm
Calculate Kimutai’s net salary monthly. (4mks)

​A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

​Find; 
(a) The value of t when P is instantaneously at rest.     (2mks)

(b) An expression for the distance, S metres, moved by P after t seconds given that when t = 0, s = 0 (2mks)

​(c) The total distance traveled by P in the first 3 seconds after passing point Q.     (3mks)

(d) The distance of P from Q when the acceleration is zero. (3mks)

​The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ.  Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q  the vectors.
(i) PQ

​(ii) PM.                    (2mks)

​(iii) ON.                     (2mks)

​(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways.      (2mks)

(ii) Find the value of h and K.   (2mks)

(iii) Find the ratio PX : XM.               (1mk)

(a) Complete the table for y = Sin x + 2cos x. (2mks)

​(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

​(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(d) Find the range of values of x for which y≤-0.5. (3mks)

The diagram below shows a square based pyramid V vertically above the middle of the base.  PQ = 10cm and VR = 13cm.  M is the midpoint of VR.

​Find
(a) (i) the length of vector PR.                 (2mks)

​(ii) The height of the pyramid.                 (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS.   (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

(ii) If it is 1200hrs at P, what is the local time at Q.      (3mks)

​Solve for θ in the equation sin (3 θ + 120)degrees

Worked Answer:

In the figure below, EAF and EDG are tangents to the circle. AB is parallel to DC, angle FAB = 46° and angle AED = 110°.

​Find the values of angles P and q. (3mks)

Worked Answer:

(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below. ​

​(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field.         (4mks)

​(ii) Find the area of the field. (3mks)

(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance.    (3mks)

(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)

(b) Determine the 
(i) Distance between B and C           (1mk)

(ii) Bearing of D from B                      (2mks)

(c) Find the distance and bearing of D from C.  (2mks)

​(a) The diagram represents a solid frustum with base radius of 35cm and top radius of 21cm.The frustum is 22.5cm high and is made of a metal whose density is 4g/cm³.  
Taking  = 22/7, calculate

​(i) The volume of the metal that makes the frustum. (6mks)

​(ii) The mass of the frustum.                      (2mks)

​(b) The frustum is melted in down and recast into a solid cube in the process 20% of the metal is lost.  Calculate to 2d.p the length of each side of the cube.                                                                    (2mks)

PAPER 1, SECTION B, STATISTICS II, FORM 4 LEVEL, 10 MARKS

​A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

​Using 19.7 as a working mean calculate:

​(a) Mean (4mks)

​(b) Standard deviation (5mks)

​(c) State the modal class (1mk)

Paper 1, Section B

​A bus left Nairobi at 7.00 am and traveled towards Eldoret at an average speed of 80Km/hr. At 7.45 a.m a car left Eldoret towards Nairobi at an average speed of 120Km/hr. The distance between Nairobi and Eldoret is 300 km. Calculate:

(a) The time the bus arrived at Eldoret.   (2mks)

(b) The time of the day the two met.   (4mks)

(c) The distance of the bus from Eldoret when the car arrived in Nairobi.   (2mks)

(d) The distance from Nairobi when the two met. (2mks)