KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 Mathematics
In a uniformly accelerated motion the distance, s metres, travelled in time t seconds varies partly as the time and partly as the square of the time. When the time is 2 seconds, the distance travelled is 80 metres and when the time is 3 seconds, the distance travelled is 135 metres.
(a) Express s in terms of t. (b) Find: (i) the distance travelled in 5 seconds; (ii) the time taken to travel a distance of 560 metres.
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Form 2 Mathematics
A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm2.
(a) Express in terms of x: (i) the internal height h, of the box; (ii) the internal volume V, of the box. (b) Find: (i) the value of x for which the volume V is maximum; (ii) the maximum internal volume of the box. Form 2 MathematicsForm 2 Mathematics
In the figure below, ABCD is a square. Points P, Q, R and S are the midpoints of AB, BC, CD and DA respectively.
(a) Describe fully:
(i) a reflection that maps triangle QCE onto triangle SDE; (ii) an enlargement that maps triangle QCE onto triangle SAE; (iii) a rotation that maps triangle QCE onto triangle SED. (b) The triangle ERC is reflected on the line BD. The image of ERC under the reflection is rotated clockwise through an angle of 90° about P. Determine the images of R and C: (i) under the reflection; (ii) after the two successive transformations. Form 2 Mathematics
Motorbike A travels at 10 km/h faster than motorbike B whose speed is x km/h.Motorbike A takes 1 1/2 hours less than motorbike B to cover a 180 km journey.
(a) Write an expression in terms of x for the time taken to cover the 180 km journey by: (i) motorbike A; (ii) motorbike B. (b) Use the expressions in (a) above to determine the speed, in km/h, of motorbike A. (c) For a journey of 48 km, motorbike B starts 10 minutes ahead of motorbike A. Calculate, in minutes, the difference in the time of their arrival at the destination. Form 2 Mathematics
A carpenter constructed a closed wooden box with internal measurements 1.5 metres long, 0.8 metres wide and 0.4 metres high. The wood used in constructing the box was 1.0 cm thick and had a density of 0.6 gcm3.
(a) Determine the: (i) volume, in cm3, of the wood used in constructing the box; (ii) mass of the box, in kilograms, correct to 1 decimal place. (b) Identical cylindrical tins of diameter 10 cm, height 20cm with a mass of 120 g each were packed in the box. Calculate the: (i) maximum number of tins that were packed; (ii) total mass of the box with the tins. Form 2 MathematicsForm 2 Mathematics
A cylindrical solid whose radius and height are equal has a surface area of 154 cm2. Calculate its diameter, correct to 2 decimal places. (Take π = 3.142)
Form 2 Mathematics
A triangular flower garden has an area of 28m2. Two of its edges are 14 metres and 8 metres. Find the angle between the two edges.
Form 2 Mathematics
A bus left a petrol station at 9.20 a.m. and travelled at an average speed of 75 km/h to a town N. At 9.40 a.m. a taxi, travelling at an average speed of 95 km/h, left the same
petrol station and followed the route of the bus. Determine the distance, from the petrol station, covered by the taxi at the time it caught up with the bus. Form 2 Mathematics
A straight line l passes through the point (3, —2) and is perpendicular to a line whose equation is 2y-4x= 1.
Find the equation of l in the form y = mx + c, where m and c are constants. Form 4 Mathematics
Triangle PQR shown on the grid has vertices p(5,5), Q(10, 10) and R(10,15)
a) Find the coordinates of the points p‟, Q‟ and R‟ and the images of P, Q and R respectively under transformation M whose matrix is
b) Given that M is a reflection;
i) draw triangle P‟Q‟R‟ and the mirror line of the reflection; ii) Determine the equation of the mirror line of the reflection c) Triangle P” Q” R” is the image of triangle P‟Q‟R‟ under reflection N is a reflection in the y-axis. i) draw triangle P”Q”R” ii) Determine a 2 x2 matrix equivalent to the transformation NM iii) Describe fully a single transformation that maps triangle PQR onto triangle P”Q”R” Form 2 MathematicsForm 2 Mathematics
A glass, in the form of a frustum of a cone, is represented by the diagram below.
The glass contains water to a height of 9 cm,. The bottom of the glass is a circle of radius 2 cm while the surface of the water is a circle of radius 6 cm.
a) Calculate the volume of the water in the glass
b) When a spherical marble is submerged into the water in the glass, the water level rises by 1 cm. Calculate: i) The volume of the marble; ii) The radius of the marble Form 2 Mathematics
In the figure below (not drawn to scale), AB = 8cm, AC= 6cm, AD= 7cm, CD= 2.82 cm and angle CAB =500
Calculate, to 2 decimal places
a) The length BC, b) The size of angle ABC, c) The size of angle CAD, d) The area of triangle ACD b) Express vector NM in terms of OB
OP = OM + 2 MN, find the coordinates of P.
Form 2 MathematicsForm 2 Mathematics
An electric pole is supported t stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 metres from the foot of the pole as shown.
The angle which the wire makes with the ground is three times the angle it makes with the pole.
Calculate the length of the wire to the nearest centimeter. Form 2 Mathematics
The size of an interior angle of a regular polygon is 6 ½ times that of its exterior angle determine the number of sides of the polygon.
Form 2 Mathematics
A line which joins the points a (3, k) and B (-2, 5) is parallel to another line whose equation is 5y + 2x = 10
Find the value of k. Form 2 MathematicsForm 2 Mathematics
A bus traveling at an average speed of 63 km/h left a station at 8.15 a.m. find the average speed of the car.
Form 2 Mathematics
Two policemen were together at a road junction. Each had a walkie talkie. The maximum distance at which one could communicate with the other was 2.5 km.
One of the policemen walked due East at 3.2 km/h while the other walked due North at 2.4 km/h the policeman who headed East traveled for x km while the one who headed North traveled for y km before they were unable to communicate. (a) Draw a sketch to represent the relative positions of the policemen. (b) (i) From the information above form two simultaneous equations in x and y. |
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