KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
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Form 3 Mathematics
The first, fifth and seventh terms of an Arithmetic Progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (G.P).
The first term of each progression is 64, the common difference of the AP is d and the common ratio of the G.P is r. (a) (i) Write two equations involving d and r. (ii) Find the values of d and r. (b) Find the sum of the first 10 terms of: (i) The Arithmetic Progression (A.P); (ii) The Geometric Progression (G.P). Form 1 Mathematics
The cash price of a laptop was Ksh 60 000. On hire purchase terms, a deposit of Ksh 7 500 was paid followed by 11 monthly installments of Ksh 6 000 each.
(a) Calculate: (i) the cost of a laptop on hire purchase terms; (ii) the percentage increase of hire purchase price compared to the cash price. (b) An institution was offered a 5% discount when purchasing 25 such laptops on cash terms. Calculate the amount of money paid by the institution. (c) Two other institutions, X and Y, bought 25 such laptops each. Institutions X bought the laptops on hire purchase terms. Institution Y bought the laptops on cash terms with no discount by securing a loan from a bank. The bank charged 12% p.a. compound interest for two years. Calculate how much more money institution Y paid than institution X. Form 4 MathematicsForm 3 Mathematics
The equation of a circle centre (a, b) is x2 – y2 – 6x - 10y + 30 = 0. Find the values of a and b.
Form 4 Mathematics
A point M (60°N, 18°E) is on the surface of the earth. Another point N is situated at a distance of 630 nautical miles east of M.
Find: (a) the longitude difference between M and N; (b) The position of N. Form 2 Mathematics
Vector OP= 6i - j and OQ = -2i - 5j. A point N divides PQ internally in the ratio 3:1.
Find PN in terms of i and j. Form 4 MathematicsForm 1 MathematicsForm 3 Mathematics
The radius of a spherical ball is measured as 7 cm, correct to the nearest centimeter. Determine, to 2 decimal places, the percentage error in calculating
the surface area of the ball. Form 3 Mathematics
The sides of a triangle were measured and recorded as 8 cm, 10 cm and 15 cm. Calculate the percentage error in perimeter, correct to 2 decimal places.
Form 3 Mathematics
a) Expand (a – b)6
b) Use the first three term of the expansion in a (a) to find the approximate value of (1.98)6 Form 1 MathematicsForm 2 Mathematics
The vertices of a triangle are A(1,2), B(3,5) and C(4,1). The coordinates of C' the image of C under a translation vector T, are (6-2).
(a) Determine the translation vector T. (b) Find the coordinates of A' and B' under translation vector T. Form 3 Mathematics
The ages in years of five boys are 7, 8, 9, 10 and 11 while those of five girls are 4, 5, 6, 7 and 8. A boy and a girl are picked at random and the sum of their ages is recorded.
(a) Draw a probability space to show all the possible outcomes. (b) Find the probability that the sum of their ages is at least 17 years. Form 2 MathematicsForm 2 Mathematics
(a) Solve the inequalities 2x — 5 > - 11 and 3 + 2x ≤ 13, giving the answer as a combined inequality.
(b) List the integral values of x that satisfy the combined inequality in (a) above. Form 1 Mathematics
Three grades A, B, and C of rice were mixed in the ratio 3:4:5. The cost per kg of each of the grades A, B and C were Ksh 120, Ksh 90 and Ksh 60 respectively.
Calculate: (a) The cost of one kg of the mixture; (b) The selling price of 5 kg of the mixture given that the mixture was sold at 8% profit, Form 2 Mathematics
The frequency table below shows the daily wages paid to casual workers by a certain company.
(a) Draw a histogram to represent the above information.
(b) (i) State the class in which the median wage lies. (ii) Draw a vertical line, in the histogram, showing where the median wage lies. (c) Using the histogram, determine the number of workers who earn sh 450 or less per day. |
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