KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 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.
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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 MathematicsForm 3 MathematicsA minor sector of a circle of radius 28cm includes an angle of 1350 at the center. a) (i) convert 1350 into radians. Hence of otherwise find the area of the sector. ii) Find the length of the minor arc. b) The sector is folded to form a right circular cone. Calculate the : i) Radius of the cone ii) Height of the cone. (Take the value of Ð to be 22/7) (8mks) Form 4 MathematicsA triangle T whose vertices are A (2,3) B(5,3) and C (4,1) is mapped onto triangle T1 whose vertices are A1 (-4,3) B1 (-1,3) and C1 (x,y) by a transformation Find the: (i) Matrix M of the transformation (ii) Coordinates of C1 b) Triangle T2 is the image of triangle T1 under a reflection in the line y = x. Find a single matrix that maps T and T2 (8mks) Form 1 Mathematics
In this question use a ruler and a pair of compasses
Line PQ drawn below is part of a triangle PQR. Construct the triangle PQR in which
a) < QPR = 300 and line PR = 8cm b) On the same diagram construct triangle PRS such that points S and Q are no the opposite sides of PR<PS = PS and QS = 8cm c) A point T is on the a line passing through R and parallel to QS.If <QTS =900, locate possible positions of T and label them T1 and T2, Measure the length of T1T2. Form 2 Mathematics
The figure below represents a right prism whose triangular faces are isosceles. The base and height of each triangular face are 12cm and 8cm respectively. The length of the prism is 20cm.
Calculate the:
Form 1 MathematicsForm 1 MathematicsForm 3 Mathematics
The average rate of depreciation in value of a water pump is 9% per annum. After three complete years its like value was sh 150,700. Find its value at the start of the three – year period.
Form 2 Mathematics
Solve the following inequalities and represent the solutions on a single number line:
3 – 2x < 5 4 – 3x ≥ -8 Form 1 Mathematics
A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 Deutsche Marks. Find the value of the watch in:
(a) Swiss Francs. (b) Kenya Shillings Use the exchange rates below: 1 Swiss Franc = 1.28 Deutsche Marks. 1 Swiss Franc = 45.21 Kenya Shillings Form 3 Mathematics
The position vectors of points X and Y are
x = 2i + j – 3k and y = 3i + 2j -2k respectively. Find xy; Form 3 Mathematics
Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
(a) If a ball is drawn at random from each bag, find the probability that both balls are of the same colour. (b) If two balls are drawn at random from each bag, one at a time without replacement, find the probability that: (i) The two balls drawn from bag A or bag B are red (ii) All the four balls drawn are red Form 4 Mathematics
The table below shows the values of the length X ( in metres ) of a pendulum and the corresponding values of the period T ( in seconds) of its oscillations obtained in an experiment.
(a) Construct a table of values of log X and corresponding values of log T,
correcting each value to 2 decimal places (b) Given that the relation between the values of log X and log T approximate to a linear law of the form m log X + log a where a and b are constants (i) Use the axes on the grid provided to draw the line of best fit for the graph of log T against log X.
(ii) Use the graph to estimate the values of a and b
(b) Find, to decimal places the length of the pendulum whose period is 1 second Form 4 Mathematics
A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below.
The company decided to install x machines of types A and y machines of type B(a) Write down the inequalities that express the following conditions
I. The number of operators available is 40 II. The floor space available is 80m2 III. The company is to install not less than 3 type of A machine IV. The number of type B machines must be more than one third the number of type A machines (b) On the grid provided, draw the inequalities in part ( a) above and shade the unwanted region (c) Draw a search line and use it to determine the number of machines of each type that should be installed to maximize the daily profit. Form 3 Mathematics
In this question use a ruler and a pair of compasses only
In the figure below, AB and PQ are straight lines
(a) Use the figure to:
(i) Find a point R on AB such that R is equidistant from P and Q (ii) Complete a polygon PQRST with AB as its line of symmetry and hence measure the distance of R from TS. (b) Shade the region within the polygon in which a variable point X must lie given that X satisfies the following conditions I: X is nearer to PT than to PQ II: RX is not more than 4.5 cm III. angle PXT > 90 Form 3 Mathematics
The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
(a) Find: (i) The equation of the curve (ii) The vales of x, at which the curve cuts the x- axis (b) Determine the area enclosed by the curve and the x- axis |
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