KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
 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)
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 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:
 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  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.
 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
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  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  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  COMMERCIAL ARITHMETIC II   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 15A building was valued at Ksh 720 000 on 1st January 2007. The value of the building appreciated at 2% per annum in the first year. The value of the building then depreciated at the rate of 5% for the next 2 years. Calculate the value of the building at the end of year 2009. (3 marks)
ALT B  graphical methods   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 13The table below gives values of two variables x and y obtained from an experiment.
(a) On the grid provided below, plot the values of y against x and draw the line of best fit. (2 marks) ALT B  CIRCLES, CHORDS AND TANGENTS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 12In the figure below, PRQS is a circle of radius 17cm. Line PQ is a diameter of the circle and is perpendicular to chord RS at T.
ALT B  SEQUENCE AND SERIES   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 11The second term of a geometric sequence is 24 and the fifth term is 192. Find the first term of the sequence. (3 marks)
ALT B  COMPOUND PROPORTIONS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 7An inlet pipe fills an empty water tank in 8 hours while an outlet pipe empties the full tank in 5 hours. When the tank is full, the inlet and outlet pipes are opened at the same time. Calculate:
ALT B  quadratic equations   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 3Solve by factorisation, the quadratic equation:
2x²3x50 = 0 (3 marks) ALT B  FORMULA AND VARIATIONS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 4ALT B  Circles, Tangents and Chords   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 5The figure below shows a circle centre O and external point X.
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  QUADRATIC EQUATIONS  SECTION 1  QUESTION 19  KCSE 2010  FORM 3 LEVELThe length and width of a rectangular plot of land are given as (7x + 5) m and (x + 10) m respectively.
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:

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