KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
A trader bought 2 cows and 9 goats for a total of Ksh 98, 200. If she had bought 3 cows and 4 goats she would have spent Ksh 2,200 less.
a) Form two equations to represent the above information. b) Use matrix method to determine the cost of a cow and that of a goat. c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat. i. Calculate the total amount of money she received. ii. Determine, correct to 4 significant figures, the percentage profit the trader made from the sale of the animals
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Form 3 Mathematics
(a) solve the equation;
(b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2.
i. Calculate the perimeter of the floor. ii. A rectangular carpet is placed on the floor of the hall leaving an area of 64m2. If the length of the carpet is twice its width, determine the width of the carpet. Form 4 Mathematics
The acceleration of a body moving along a straight line is (4 - t) m/s2 and its velocity is v m/s after t seconds.
(a) (i) If the initial velocity of the body is 3 m/s, express the velocity v in terms of t. (ii) Find the velocity of the body after 2 seconds. (b) Calculate: (i) the time taken to attain maximum velocity; (ii) the distance covered by the body to attain the maximum velocity. Form 3 Mathematics
A box contains 3 brown, 9 pink and 15 white clothes pegs. The pegs are identical except for the colour.
(a) Find the probability of picking: (i) a brown peg; (ii) a pink or a white peg. (b) Two pegs are picked at random, one at a time, without replacement. Find the probability that: (i) a white peg and a brown peg are picked; (ii) both pegs are of the same colour. Form 4 Mathematics
A tourist took 1 h 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E). (Take the radius of the earth to be 6370km and π =22/7
(a) Find the average speed of the aircraft. (b) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E). The average speed of the second aircraft was 90% that of the first aircraft. Determine the time, to the nearest minute, the aircraft took to travel from U to V (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 3 Mathematics
In June of a certain year, an employee's basic salary was Ksh 17000. The employee was also paid a house allowance of Ksh 6000, a commuter allowance
of Ksh 2500 and a medical allowance of Ksh 1 800. In July of that year, the employee's basic salary was raised by 2%. (a) Calculate the employees: (i) basic salary for July; (ii) total taxable income in July of that year. (b) In that year, the Income Tax Rates were as shown in the table below:
Given that the Monthly Personal Relief was Ksh 1056, calculate the net tax paid by the employee.
Form 3 Mathematics
In triangle OPQ below, OP = p, OQ = q. Point M lies on OP such that OM : MP = 2 : 3 and point N lies on OQ such that ON : NQ = 5:1. Line PN
intersects line MQ at X.
(a) Express in terms of p and q:
(i) PM (ii) QM. (c) Given that PX = kPN and QX = rQM, where k and r are scalars: (i) write two different expressions for OX in terms of p, q, k and r; (ii) find the values of k and r; (iii) determine the ratio in which X divides line MQ. Form 4 MathematicsForm 1 Mathematics
Amaya was paid an initial salary of Ksh 180 000 per annum with a fixed annual increment. Bundi was paid an initial salary of Ksh 150000 per annum with a
10% increment compounded annually. (a) Given that Amaya's annual salary in the 11th year was Ksh 288 000, determine: (i) his annual increment; (ii) the total amount of money Amaya earned during the 11 years. (b) Determine Bundi's monthly earnings, correct to the nearest shilling, during the eleventh year. (c) Determine, correct to the nearest shilling: (i) the total amount of money Bundi earned during the 11 years. Form 2 Mathematics
In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS - 80°.
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures: (i) the perpendicular distance between PQ and RS; (ii) the length of TS. (c) Using the cosine rule, find the length of RS correct to 2 significant figures. (d) Calculate, correct to one decimal place, the area of triangle RST. Form 1 Mathematics
Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs. (b) Use the scale drawing to determine: (i) the distance between T and S in metres: (ii) the bearing of T from S. (c) Find the area of the field, in hectares, correct to one decimal place. Form 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
(a) Find: (i) the x - intercept of the curve; (ii) the y - intercept of the curve. (b) (i) Determine the stationery points of the curve. (ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum. (c) Sketch the curve. Form 2 Mathematics
The vertices of quadrilateral OPQR are O (0,0), P(2,0), Q(4,2) and R(0,3).
The vertices of its image under a rotation are O'(l, -1), P'(l, -3), Q'(3, -5) and R'(4, -1). (a) (i) On the grid provided, draw OPQR and its image O'P'Q'R'. (ii) By construction, determine the centre and angle of rotation. (b) On the same grid as (a) (i) above, draw O"P"Q"R", the image of O'P'Q'R' under a reflection in the line y = x. (i) directly congruent; (ii) oppositely congruent. Form 3 MathematicsForm 1 Mathematics
Two alloys, A and B, are each made up of copper, zinc and tin. In alloy A, the ratio of copper to zinc is 3:2 and the ratio of zinc to tin is 3:5.
(a) Determine the ratio, copper: zinc: tin, in alloy A. (b) The mass of alloy A is 250 kg. Alloy B has the same mass as alloy A but the amount of copper is 30% less than that of alloy A. Calculate: (i) the mass of tin in alloy A; (ii) the total mass of zinc and tin in alloy B. (c) Given that the ratio of zinc to tin in alloy B is 3:8, determine the amount of tin in alloy B than in alloy A. Form 2 MathematicsForm 4 Mathematics
The displacement s metre of a particle moving along straight line after t seconds is given by. S = 3t + 3/2 t2 – 2t3
Form 4 MathematicsForm 4 Mathematics
A building contractor has two lorries, P and Q, used to transport at least 42 tonnes of sand to a building site. Lorry P carries 4 tonnes of sand per trip while lorry Q
carries 6 tonnes of sand per trip. Lorry P uses 2 litres of fuel per trip while lorry Q uses 4 litres of fuel per trip. The two lorries are to use less than 32 litres of fuel. The number of trips made by lorry P should be less than 3 times the number of trips made by lorry Q. Lorry P should make more than 4 trips. (a) Taking x to represent the number of trips made by lorry P and y to represent the number of trips made by lorry Q, write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities and shade the unwanted regions. (c) Use the graph drawn in (b) above to determine the number of trips made by lorry P and by lorry Q to deliver the greatest amount of sand. Form 3 Mathematics
The cost C, of producing n items varies partly as n and partly as the inverse of n. To produce two items it costs Ksh 135 and to produce three items it costs Ksh 140. Find:
(a) the constants of proportionality and hence write the equation connecting C and n; (b) the cost of producing 10 items; (c) the number of items produced at a cost of Ksh 756. Form 4 MathematicsForm 3 Mathematics
The table below shows values of x and some values of y for the curve y = x3 + 2x2 - 3x – 4 f o r - 3 ≤ x ≤ 2.
(a) Complete the table by filling in the missing values of y, correct to 1 decimal place.
(b) On the grid provided, draw the graph of y = x3+ 2x2 - 3x - 4. Use the scale: 1 cm represents 0.5 units on x -axis. 1 cm represents 1 unit on y-axis. (c) Use the graph to: (i) solve the equation x3 + 2x2 - 3x - 4 = 0; (ii) estimate the coordinates of the turning points of the curve. Form 4 Mathematics
The table below shows the values of x and corresponding values of y for a given curve.
a) Use the trapezium rule with seven ordinates and the values in the table only to estimate the area enclosed by the curve, x – axis and the line x = П/2 to four decimal places. (Take П = 3.142) b) The exact value of the area enclosed by the curve is known to be 0.8940.Find the percentage error made when the trapezium rule is used. Give the answer correct to two decimal places. Form 1 Mathematics
Four points B,C,Q and D lie on the same plane. Point B is 42km due South – West of point Q. Point C is 50km on a bearing of S 600 E from Q.
Point D is equidistant B, Q and C.
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