KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The diagram below shows a sketch of the line y = 3x and the curve y = 4 – x^{2} intersecting at points P and Q.
a) Find the coordinates of P and Q
(b) Given that QN is perpendicular to the x axis at N, calculate (i) The area bounded by the curve y = 4 – x^{2}, the x axis and the line QN (ii) The area of the shaded region that lies below the x axis (iii)The area of the region enclosed by the curve y = 4x^{2}, the line y – 3x and the y axis
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Form 4 Mathematics
Mwanjoki flying company operates a flying service. It has two types of aeroplanes. The smaller one uses 180 litres of fuel per hour while the bigger one uses 300 litres per hour.
The fuel available per week is 18,000 litres. The company is allowed 80 flying hours per week while the smaller aeroplane must be flown for y hours per week. (a) Write down all the inequalities representing the above information (b) On the grid provided on page 21, draw all the inequalities in a) above by shading the unwanted regions (c) The profits on the smaller aeroplane is Kshs 4000 per hour while that on the bigger one is Kshs 6000 per hour Use the graph drawn in (b) above to determine the maximum profit that the company made per week. Form 3 Mathematics
The product of the first three terms of geometric progression is 64. If the first term is a, and the common ration is r.
(a) Express r in terms of a (b) Given that the sum of the three terms is 14 (i) Find the value of a and r and hence write down two possible sequence each up to the 4^{th} term. (ii) Find the product of the 50^{th} terms of two sequences Form 1 Mathematics
A solution whose volume is 80 litres is made 40% of water and 60% of alcohol. When litres of water are added, the percentage of alcohol drops to 40%
(a) Find the value of x (b) Thirty litres of water is added to the new solution. Calculate the percentage (c) If 5 litres of the solution in (b) is added to 2 litres of the original solution, calculate in the simplest form, the ratio of water to that of alcohol in the resulting solution Form 3 Mathematics
(a) Two integers x and y are selected at random from the integers 1 to 8. If the
same integer may be selected twice, find the probability that (i) x – y = 2 (ii) x – y is more (iii) x>y (b) A die is biased so that when tossed, the probability of a number r showing up, is given by p ® = Kr where K is a constant and r = 1, 2,3,4,5 and 6 (the number on the faces of the die (i) Find the value of K (ii) if the die is tossed twice, calculate the probability that the total score is 11 Form 4 Mathematics
Triangle ABC is shown on the coordinates plane below
(a) Given that A (6, 5) is mapped onto A (6,4) by a shear with y axis invariant
(i) draw triangle A"B"B", the image of triangle ABC under the shear (ii) Determine the matrix representing this shear (b) Triangle A B C is mapped on to A" B" C" by a transformation defined by the matrix (1 1) (i) Draw triangle A" B" C" (ii) Describe fully a single transformation that maps ABC onto A"B" C" Form 2 Mathematics
A garden measures 10m long and 8 m wide. A path of uniform width is made all round the garden. The total area of the garden and the paths is 168 m^{2}.
(a) Find the width of the path (b) The path is to covered with square concrete slabs. Each corner of the path is covered with a slab whose side is equal to the width of the path.
The rest of the path is covered with slabs of side 50 cm. The cost of making each corner slab is Kshs 600 while the cost of making each smaller slab is Kshs 50.
Calculate (i) The number of smaller slabs used Form 1 Mathematics
A certain sum of money is deposited in a bank that pays simple interest at a certain rate.
After 5 years the total amount of money in an account is Kshs 358 400. The interest earned each year is 12 800 Calculate (i) the amount of money which was deposited (ii) the annual rate of interest that the bank paid (b) A computer whose marked price is Kshs 40,000 is sold at Kshs 56,000 on hire purchase terms. (i) Kioko bought the computer on hire purchase term. He paid a deposit of 25% of the hire purchase price and cleared the balance by equal monthly installments of Kshs 2625 Calculate the number of installments (ii) Had Kioko bought the computer on cash terms he would have been allowed a discount of 12 ½ % on marked price. Calculate the difference between the cash price and the hire purchase price and express as a percentage of the cash price. Form 4 Mathematics
Two places P and Q are at ( 36^{0}N, 125^{0}W) and 36^{0}N, 125^{0}W) and 36^{0} N, 125^{0}W) and 36^{0} N, 55^{0}E) respectively. Calculate the distance in nautical miles between P and Q measured along the great circle through the North pole.
Form 4 Mathematics
A particle moving in a straight line passes through a fixed point O with a velocity of 9m/s. The acceleration of the particle, t seconds after passing through O is given by a = ( 10 – 2t) m/s^{2}.Find the velocity of the particle when t – 3 seconds
Form 3 MathematicsForm 1 Mathematics
The figure below is drawn to scale. It represents a field in the shape of an equilateral triangle of side 80m
The owner wants to plant some flowers in the field. The flowers must be at most, 60m from A and nearer to B than to C. If no flower is to be more than 40m from BC, show by shading, the exact region where the flowers may be planted
Form 3 Mathematics
The points which coordinates (5,5) and (3,1) are the ends of a diameter of a circle centre A
Determine:
(a) the coordinates of A
(b) The equation of the circle, expressing it in form x^{2} + y^{2} + ax + by + c = 0 where a, b, and c are constants Form 3 MathematicsForm 4 MathematicsForm 3 Mathematics
The data below represents the ages in months at which 6 babies started walking:
9,11, 12, 13, 11, and 10. Without using a calculator, find the exact value of the variance Form 3 Mathematics
By correcting each number to one significant figure, approximate the value of 788 x 0.006. Hence calculate the percentage error arising from this approximation.
Form 2 MathematicsForm 2 MathematicsForm 4 Mathematics
A particle moves along straight line such that its displacement S metres from a given point is S = t^{3} – 5t^{2} + 4 where t is time in seconds
Find
(a) the displacement of particle at t = 5 (b) the velocity of the particle when t = 5 (c) the values of t when the particle is momentarily at rest (d) The acceleration of the particle when t = 2 Form 2 Mathematics
The figure below is a model representing a storage container. The model whose total height is 15cm is made up of a conical top, a hemispherical bottom and the middle part is cylindrical. The radius of the base of the cone and that of the hemisphere are each 3cm. The height of the cylindrical part is 8cm.
(a) Calculate the external surface area of the model
(b) The actual storage container has a total height of 6 metres. The outside of the actual storage container is to be painted. Calculate the amount of paint required if an area of 20m^{2} requires 0.75 litres of the paint Form 3 Mathematics
In the diagram below, the coordinates of points A and B are ( 1,6) and (15,6) respectively)
Point N is on OB such that 3 ON = 2OB. Line OA is produced to L such that OL = 3 OA
(a) Find vector LN
(b) Given that a point M is on LN such that LM: MN = 3: 4, find the coordinates of M (c) If line OM is produced to T such that OM: MT = 6:1 (i) Find the position vector of T (ii) Show that points L, T and B are collinear 
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