KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
In fourteen years time, a mother will be twice as old as her son. Four years ago, the sum of their ages was 30 years. Find how old the mother was, when the son was born.
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Form 2 MathematicsForm 2 MathematicsForm 1 Mathematics
A square brass plate is 2 mm thick and has a mass of 1.05 kg. The density of the brass is 8.4 g/cm^3. Calculate the length of the plate in centimeters
Form 4 Mathematics
The gradient of the tangent to the curve y = ax3 + bx at the point ( 1,1) is -5
Calculate the values of a and b Form 1 Mathematics
A Kenyan businessman bought goods from Japan worth 2, 950 000 Japanese yen. On arrival in Kenya custom duty of 20% was charged on the value of the goods.
If the exchange rates were as follows 1 US dollar = 118 Japanese Yen 1 US dollar = 76 Kenya shillings Calculate the duty paid in Kenya shillings Form 2 Mathematics
The size of an interior angle of a regular polygon is 3x0 while its exterior angle is ( x- 20)0. Find the number of sides of the polygon
Form 4 Mathematics
A particle moves along straight line such that its displacement S metres from a given point is S = t3 – 5t2 + 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 20m2 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 Form 2 Mathematics
The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots The lengths BE and CD are 100m and 80m respectively. Angle ABE = 300,angle ACE = 450and angle ACD = 1000
Find to four significant figures:
(i) The length of AE (ii) The length of AD (iii) the perimeter of the piece of land (b) The plots are to be fenced with five strands of barbed wire leaving an entrance of 2.8 m wide to each plot. The type of barbed wire to be used is sold in rolls of lengths 480m. Calculate the number of rolls of barbed wire that must be bought to complete the fencing of the plots Form 3 Mathematics
A bus left Mombasa and traveled towards Nairobi at an average speed of 60km/hr. after 21/2 hours; a car left Mombasa and traveled along the same road at an average speed of 100km/ hr. If the distance between Mombasa and Nairobi is 500km, Determine
(a) (i) The distance of the bus from Nairobi when the car took off (ii) The distance the car traveled to catch up with the bus (b) Immediately the car caught up with the bus, the car stopped for 25 minutes. Find the new average speed at which the car traveled in order to reach Nairobi at the same time as the bus. Form 2 Mathematics
The diagram below ( not drawn to scale) represents the cross- section of a solid prism of height 8.0 cm
(a) Calculate the volume of the prism
(b) Given that the density of the prism is 5.75g/cm3, calculate its mass in grams (c) A second prism is similar to first one but is made of a different materials. The volume of the second is 246.24cm3 (i) calculate the area of the cross section of the second prism (ii) Given that the ratio of the mass of the first to that of the second is 2: 5 and the density of the second prism Form 2 Mathematics
On the Cartesian plane below, triangle PQR has vertices P(2, 3), Q ( 1,2) and R ( 4,1) while triangles P" Q" R" has vertices P" (-2, 3), Q" ( -1,2) and R" ( -4, 1)
(a) Describe fully a single transformation which maps triangle PQR onto triangle P"Q"R"
(b) On the same plane, draw triangle P"Q"R", the image of triangle PQR, under reflection in line y = -x (c) Describe fully a single transformation which maps triangle P"Q"R" onto triangle P"Q"R (d) Draw triangle P"Q"R" such that it can be mapped onto triangle PQR by a positive quarter turn about ( 0,0) (e) State all pairs of triangle that are oppositely congruent Form 1 Mathematics
In the year 2001, the price of a sofa set in a shop was Kshs 12,000
(a) Calculate the amount of money received from the sales of 240 sofa sets that year (b) (i) In the year 2002 the price of each sofa set increased by 25% while the number of sets sold decreased by 10% Calculate the percentage increase in the amount received from the sales (ii) If at the end of year 2002, the price of each sofa set changed in the ration 16:15, calculate the price of each sofa set in the year 2003 (c) The number of sofa sets sold in the year 2003 was P% less than the number sold in the year 200. Calculate the value of P, given that the amounts received from sales if the two years were equal. Form 3 MathematicsA circle centre O, ha the equation x2 + y2 = 4The area of the circle in the first quadrant is divided into 5 vertical strips of width 0.4 cm
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