KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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| 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).
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| 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. SURFACE AREA OF SOLIDS | KCSE 1997 | PAPER 1 | FORM 2 LEVEL | SECTION BThe figure below shows a portable kennel.
MATRICES | FORM 3 LEVEL | KCSE 1997 | SECTION B | PAPER 1The figure on the grid shows a triangular shaped object ABC and its image A'B'C'. (a)
(d) Hence find the area of the image A” B” C LINEAR EQUATIONS | FORM 2 LEVEL | KCSE 1997 | PAPER 1 | SECTION BThe coordinates of the points P and Q are (1, -2) and (4, 10) respectively. A point T divides the line PQ in the ratio 2:1.
VECTORS I | FORM 2 LEVEL | PAPER 1 | SECTION B | KCSE 1997In the figure below, OA is equal to A, OB is equal to B, AB is equal to BC, and OB is to BD in a ratio of 3:1. (a) Determine
SCALE DRAWING - BEARING | FORM 1 LEVEL | KCSE 1996 | PAPER 2 | QUESTION 20 | SECTION BFour towns, R, T, K, and G, are arranged in the following manner: T is located 84 km directly north of R, K is positioned 60 km away from R on a bearing of 295°, and G is located 30 km away from K on a bearing of 340°. To create a scale drawing that accurately represents the relative positions of these towns, a scale of 1 cm representing 10 km will be used. Find (a) The distance and the bearing of T from K (b) The distance and the bearing G from T (c) The bearing of R from G COMMERCIAL ARITHMETIC I | PAPER 2 | SECTION B | KCSE 1996 FORM 1 LEVELTwo businessmen jointly purchased a minibus capable of accommodating 25 paying passengers at full capacity. The fare for a one-way trip between towns A and B was set at Kshs 80 per passenger. The minibus operated three round trips between the two towns on a daily basis. The daily cost of fuel amounted to Kshs 1500. Additionally, the driver and conductor received daily allowances of Kshs 200 and Kshs 150 respectively. An additional Kshs 4,000 per day was allocated for maintenance, insurance, and loan payments.
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