KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation;
S =t3 -6t2 + 9t + 5. a) Calculate the gradient to the curve at t=0.5 seconds b) Determine the values of s at the maximum and minimum turning points of the curve. c) On the space provided, sketch the curve of s= t3-6t2+9t + 5.
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Form 3 Mathematics
A group of people planned to contribute equally towards a water project which needed Ksh 200 000 to complete, However, 40 members of the group without from the project.
As a result, each of the remaining members were to contribute Ksh 2500. a) Find the original number of members in the group. b) Forty five percent of the value of the project was funded by Constituency Development Fund (CDF). Calculate the amount of contribution that would be made by each of the remaining members of the group. c) Member‟s contributions were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contributed was 6:19; calculate the total amount of money contributed by the members. Form 2 Mathematics
The diagram below represents a conical vessel which stands vertically. The which stands vertically,. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take π=22/7).
a) Calculate the volume of the water in the vessels in cm3
b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate: (i) The radius of the new water surface in the vessel; (ii) The volume of the metal sphere in cm3 (iii) The radius of the sphere. Form 2 Mathematics
The diagram below shows a triangle ABC with A (3, 4), B (1, 3) and C (2, 1).
a) Draw triangle A'B'C' the image of ABC under a rotation of +900+ about (0, 0).
b) Drawn triangle A"B" the image of A"B'C" under a reflection in the line y=x. c) Draw triangle A"B" C. the image under a rotation of -900 about (0, 0) d) Describe a single transformation that maps triangle ABC"" onto angle A"""B"""C""" e) Write down the equations of the lines of symmetry of the quadrilateral BB"A""A Form 2 Mathematics
The diagram below represents two vertical watch-towers AB and CD on a level ground. P and Q are two points on a straight road BD. The height of the tower AB is 20m road a BD is 200m.
a) A car moves from B towards D. At point P, the angle of depression of the car from point A is 11.3. Calculate the distance BP to 4 significant figures.
b) If the car takes 5 seconds to move from P to Q at an average speed of 36 km/h, calculate the angle of depression of Q from A to 2 decimal places c) Given that QC=50.9m, calculate; (i) The height of CD in meters to 2 decimal places; (ii) The angle of elevation of A from C to the nearest degree. Form 3 MathematicsForm 4 Mathematics
The figure below is a sketch of the curve whose equation is y=x2+x+5.
It cuts the line y=11 at points P and Q.
a) Find the area bounded by the curve = x2+x+5 and the line y=11 using the trapezium rule with 5 strips.
b) Calculate the difference in the area if the mid-ordinate rule with 5 ordinates was used instead of the trapezium rule. Form 1 Mathematics
a) The ratio of Juma's and Akinyi's earnings was 5:3 Juma's earnings rose to Ksh 8400 after an increase of 12%.
Calculate the percentage increase in Akinyi's earnings given that the sum of their new earnings was Ksh. 14100. b) Juma and Akinyi contributed all the new earnings to buy maize at Ksh 1175 per bag. The maize was then sold at Ksh 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got. Form 2 Mathematics
The equation of line L1 is 2y-5x-8=0 and line L2 passes through the points (-5, 0) and (5,-4). Without drawing the lines L1 and L2 show that the two lines are perpendicular to each other.
Form 2 Mathematics
Given that log 4=0.6021 and log 6=0.7782, without using mathematical tables or a calculator, evaluate log 0.096.
Form 2 Mathematics
A rectangular and two circular cut-outs of metal sheet of negligible thickness are used to make a closed cylinder. The rectangular cut-out has a height of 18cm. Each circular cu-out has a radius of 5.2cm. Calculate in terms of pi, the surface area of the cylinder
Form 4 MathematicsForm 2 Mathematics
Three vertices of a rhombus ABCD are; A(-4,-3), B(1,-1) and c are constants.
a) Draw the rhombus on the grid provided below. b) Find the equation of the line AD in the form y = mx + c, where and c are constants. Form 2 Mathematics
An angle of 1.8 radians at the centre of a circle subtends an area of length 23.4cm
Find; a) The radius of the circle b) The area of the sector enclosed by the arc and the radii. Form 1 Mathematics
A solid metal sphere of radius 4.2 cm was melted and the molten material used to make a cube. Find to 3 significant figures the length of the side of the cube.
Form 1 MathematicsRelated Questions and Answers on Geometric ConstructionsForm 2 Mathematics
A liquid spray of mass 384g is packed in a cylindrical container of internal radius 3.2cm. Given that the density of the liquid is 0.6g/cm3, calculate to 2 decimal places the height of the liquid in the container.
Form 1 Mathematics
A fuel dealer makes a profit of Kshs. 520 for every 1000 litres of petrol sold and Ksh. 480 for every 1000 litres of diesel sold.
In a certain month the dealer sold twice as much diesel as petrol. If the total fuel sold that month was 900,000 litres, find the dealer‟s profit for the month. Form 1 MathematicsForm 2 Mathematics
Mapesa traveled by train from Butere to Nairobi. The train left Butere on a Sunday at 23 50 hours and traveled for 7 hours 15 minutes to reach Nakuru. After a 45 minutes stop in Nakuru, the train took 5 hours 40 minutes to reach Nairobi.
Find the time, in the 12 hours clock system and the day Mapesa arrived in Nairobi. Form 2 Mathematics |
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