KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

​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)

​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)

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)

​(i) Expand

​to the term in x cubed.

​(ii) Use your expansion to estimate the value of

​Correct to one decimal place.         (2mks)

​Chords AB and CD of a circle meet at X.

​If AB = 8cm, BX = 5cm and DX = 6.  Calculate the length of chord CD. (3mks)

WORKED ANSWER:

2X² + 2y² - 6X + 10y + 9 = 0 is the equation of a circle.  Find the radius and the centre of the circle. (4mks)

​Given that P = QXⁿ make n the subject of the formula and simplify your answer.                     (3mks)

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

Worked Answer:

​The initial salary of Mr. Lutta is sh. 42, 000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands.  (3mks)

​​Worked Answer:

Find the value of a and b where a and b are ​rational numbers.   (3mks)

​Worked Answer:

Solve the equation below.  (3 marks)

Worked Answer:

Use logarithms correct to 4 decimal places to evaluate. (3mks)

Worked Answer:

(a) Given that y = 7 + 3x-x², complete the table below.(2mks)

Worked Solution

(b) On the grid provided and using a suitable scale draw the graph of y = 7 + 3x-x². (2mks)

(c) On the same grid draw the straight line and use your graph to solve the equation x² - 4x– 3 = 0.    (3mks)

(d) Determine the coordinates of the turning point of the curve. (2mks)

Worked Solution:

​A man invests Ksh.24, 000 in an account which pays 16% interest p.a. the interest is compounded quarterly. Find the amount in the account after 1½ years.                                              (3mks)

Worked Solution