KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
| 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 co-ordinates 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 y-axis at y = 5 and has a gradient of 2; L₂ is perpendicular to L1, at the point where L1, cuts the x-axis; 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 mid-point of OC and D is the mid-point 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 DRAWING-BEARING | 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 cross-section 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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