KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
These are Mathematics questions and answers categorized according to topics, papers i.e. Paper 1 and 2, Levels i.e. form 1 to form 4, kcse year the examination was done and section A or B
Select topic/category to open topical questions from that particular option provided.
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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).
| 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.
In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°22/3/2024 | angle properties of a circle | FORM 3 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 16 |In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°
Determine the total area of the shaded regions to 2 decimal places. (4 marks) | 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 | ANGLES AND PLANE FIGURES | FORM 1 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 14 |The sum of interior angles of a regular polygon is 1620°. Calculate the number of sides of the polygon. (2 marks)
| FACTORIZATION | FORM 3 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 13 |Use factorization method to solve the equation: 1/8 x^2 + x = 48.
| SIMILARITY and Enlargement | FORM 2 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 12 |The areas of the lids of two similar cylinders are 16 cm² and 25 cm². If the volume of the bigger cylinder is 800 cm³, find the volume of the smaller cylinder. (4 marks)
| geometrical constructions | FORM 1 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 11 |Using a ruler and a pair of compasses only, construct triangle ABC such that AB = 4.5 cm, BC = 8.1 cm and angle CBA = 60°. Measure angle CAB.
(3 marks) | logarithms | FORM 3 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 10 |Use logarithm tables to evaluate √(2.5 × 0.064) / 8.1
A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top.22/3/2024 | LENGTH | FORM 1 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 9 |A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top. The cable is anchored on the ground at a distance of 2.5 m from the foot of the pole. Determine the height of the pole. (3 marks)
| GCD | FORM 1 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 7 |Three metal rods of lengths 234 cm, 270 cm and 324 cm were cut into shorter pieces, all of the same length, to make window grills.
Calculate the length of the longest piece that can be cut from each of the rods and hence the total number of pieces that can be obtained from the rods. (4 marks) | LINEAR INEQUALITIES | FORM 2 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 6 |Find the integral values of x which satisfy the inequality 3x ≤ 2x + 3 < 4x + 5. (3 marks)
| VOLUME AND CAPACITY | FORM 2 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 5 |A cylindrical container of height 45 cm has a capacity of 25 litres. Find the radius of the container to the nearest millimetre. (3 marks)
Use cube tables to calculate, to 4 significant figures, the volume of a cube whose side is 0.4321 m22/3/2024 | VOLUME AND CAPACITY | FORM 2 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 4 |Use cube tables to calculate, to 4 significant figures, the volume of a cube whose side is 0.4321 m. (3 marks)
| TIME | FORM 1 LEVEL | SECTION I | PAPER 1 | ALT B | KCSE 2011 | QUESTION 3 |On a certain day a journalist started travelling at 0850 hours to attend a meeting. He travelled for 6½ hours and then rested for 1 hour 45 minutes. He attended the meeting for 3% hours and travelled for 35 minutes to a hotel.
Determine the time, in 12-hour clock system, the journalist arrived at the hotel. (3 marks) 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) |
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