KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
 surface area of solids  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 24 The figure below represents a frustum of a cone with dimensions as shown.
Taking π = 3.142, calculate:
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 SCALE DRAWING  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 23 A piece of land is in the shape of a quadrilateral ABCD. Point B is 450 m east of A. Point D is 500 m from A on a bearing of 310°. Point C is 700 m from D on a bearing of 080°.
 SCALE DRAWING  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 22 In the figure below, BC = 12 cm, ∠ACB = 40°, ∠ BAD = 60°, BCD is a straight line and CE is parallel to BA.
Calculate:
 CHORDS AND TANGENTS  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 21 In the figure below, points L, M, N and P are on the circumference of a circle centre O. Line LON is a diameter of the circle. PL = PN and angle NLM = 20°.
Find, giving a season in each case, the size of each of the following angles. (a) ∠ MPN; (2 marks) (b) ∠ PLN; (2 marks) (c) ∠ LPM; (2 marks) (d) ∠ MNP; (2 marks) (e) ∠ PMO; (2 marks)  MATRICES AND TRANFORMATIONS  FORM 4 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 20 The figure below shows triangle ABC with coordinates A (1, 3), B (1, 1) and C (3, 2).
 COMMERCIAL ARITHMETIC  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 19 Three partners, Amani, Furaha and Nehema, contributed a total capital of Ksh 750 000 to start a business. Amani contributed 1/3 of the money, Furaha contributed 2/5 of the money and Nehema contributed the rest.
After some time the business realised a profit of 36% of the capital. The profit was taxed at the rate of 5%. After taxation, each of the partners received Ksh 20 000 of the profit. The remainder of the profit was shared among the three partners in the ratio of their contributions. Calculate:
 LINEAR EQUATIONS  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 18 Three straight lines L₁, L₂, and L3, are such that:
L1, cuts the yaxis at y = 5 and has a gradient of 2; L₂ is perpendicular to L1, at the point where L1, cuts the xaxis; L3, is parallel to L2, and passes throught point (1, 2).
 COMMERCIAL ARITHMETIC  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 17 A salesman was paid a basic salary of Ksh 48 000 per month plus a commission of 3% for sales of goods worth above Ksh 500 000.
 SIMULTANEOUS EQUATIONS  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 15 Solve the simulataneous equations:
p  q = 3 p²  q² = 21 ALT B  GRAPHICAL METHODS   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 24Some water is heated in a beaker and then left to cool for 12 minutes. After the heating is stopped, the relationship between the water temperature C, in degrees centigrade and the time t, after heating is given as C = 100 1/2 T^2.
ALT B  vectors ii   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 23The figure below shows a triangle OAC in which B is the midpoint of OC and D is the midpoint of AC.
Given that OA = 2i + 5j and OB = 4i + j,
ALT B  AREA APPROXIMATION   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 22A quadrant (a quarter of a circle) of radius 10 cm is drawn on the grid below. The quadrant is divided into 5 vertical strips.
ALT B  TRIGONOMETRY I   FORM 2 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 21Triangle ABC is such that AB = 4 cm, BC = 7 cm and angle ABC = 100°. Calculate to 2 decimal places:
ALT B  PROBABILITY   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 20A bag contains 5 yellow (Y) balls and 3 blue (B) balls. All the balls are identical except for the colour. A ball is drawn at random from the bag without replacement and its colour noted. A second ball is draw at random from the same bag and its colour also noted.
ALT B  STATISTICS II   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 19The table below represents the number of streams in 20 schools.
Calculate: (a) the mean number of streams per school; (3 marks) (b) the variance; (5 marks) (c) the standard deviation correct to 2 decimal places. (2 marks) ALT B  SEQUENCE AND SERIES   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 18The terms of an Arithmetic sequence are 2,5,8,11, ...
ALT B  COMMERCIAL ARITHMETIC II   FORM 3 LEVEL  SECTION ii  PAPER 2  KCSE 2010  QUESTION 17A shop sells a certain type of fridge at a cash price of Ksh 80 000. If the fridge is bought on Hire Purchase (H.P), a deposit of Ksh 24 000 is paid. A customer is also charged 15% per annum simple interest on the balance of the cash price after deposit is paid. Khamala bought one such fridge on H.P. He paid the balance plus the interest in 5 equal monthly instalments.
ALT B  VOLUME AND CAPACITY  SECTION 2  QUESTION 22  KCSE 2010  FORM 2 LEVELThe volume of a cuboid is 64m³. The volume of a smaller similar cuboid is 512 cm³.
ALT B  LINEAR MOTION  SECTION 2  QUESTION 23  KCSE 2010  FORM 3 LEVELThe figure below is a velocity  time graph for a car that travelled from t = 0 to t = 60, where t is time in seconds. Use the graph to calculate:
ALT B  SCALE DRAWING  SECTION 2  QUESTION 24  KCSE 2010  FORM 1 LEVELThe angle of elevation of the top of a vertical mast, viewed by an observer 50m away, was found to be 16.7°.
ALT B  SCALE DRAWINGBEARING  SECTION 2  QUESTION 21  KCSE 2010  FORM 1 LEVELTowns A, B and C are located such that B is 400 km to the north of A and town C is 750 km on a bearing of 225° from town B.
ALT B  SURFACE AREA OF SOLIDS  SECTION 2  QUESTION 20  KCSE 2010  FORM 2 LEVELThe diagram below represents a pipe whose crosssection is shaded. The pipe has internal radius of 0.26m and an external radius of 0.3m.
PROBABILITY  PAPER 1  SECTION B  KCSE 1997  FORM 3 LEVELThe water supply in a town depends entirely on two water pumps, A and B. The probability of pump A filling is 0.1, and the probability of pump B failing is 0.2. Calculate the probability that:
LONGITUDES & LATITUDES  KCSE 1997  PAPER 1  SECTION B  FORM 4 LEVELA ship leaves an island (5°N, 45°E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km) GEOMETRIC CONSTRUCTION  KCSE 1997  PAPER 1  SECTION B  FORM 1 LEVELUsing ruler and compasses only, construct triangle ABC such that AB = 4 cm, BC = 5 cm, and ∠ABC = 120°. Measure AC.
On the diagram, construct a circle which passes through the vertex of the triangle ABC. Measure the radius of the circle. Measure the shortest distance from the centre of the circle to line BC. 
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