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 80m^{2} 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 Form 3 Mathematics
Given that y is inversely proportional to x^{n} and k as the constant of proportionality;
(a) (i) Write down a formula connecting y, x, n and k (ii) If x = 2 when y = 12 and x = 4 when y = 3, write down two expressions for k in terms of n. Hence, find the value of n and k. (b) Using the value of n obtained in (a) (ii) above, find y when x = 5 1/3 Form 1 Mathematics
A tank has two inlet taps P and Q and an outlet tap R. when empty, the tank can be filled by tap P alone in 4 ½ hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R.
(a) The tank is initially empty. Find how long it would take to fill up the tank (i) If tap R is closed and taps P and Q are opened at the same time (ii) If all the three taps are opened at the same time (b) The tank is initially empty and the three taps are opened as follows P at 8.00 a.m Q at 8.45 a.m R at 9.00 a.m (i) Find the fraction of the tank that would be filled by 9.00 a.m (ii) Find the time the tank would be fully filled up Form 3 Mathematics
Find the radius and the coordinate of the centre of the circle whose equation is 2x^{2} + 2y^{2} – 3x + 2y + ½ = 0
Form 3 MathematicsForm 4 Mathematics
Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 118^{0}W and the longitude of B is 133^{0}E. The shorter distance between A and B measured along the circle of latitude is 5422 nautical miles.Find, to the nearest degree, the latitude on which A and B lie
Form 2 Mathematics
Vector q has a magnitude of 7 and is parallel to vector p. Given that
p= 3 i –j + 1 ½ k, express vector q in terms of I, j, and k. Form 3 MathematicsForm 1 Mathematics
A carpenter wishes to make a ladder with 15 cross pieces. The cross pieces are to diminish uniformly in length from 67 cm at the bottom to 32 cm at the top.
Calculate the length in cm, of the seventh cross piece from the bottom Form 2 Mathematics
Water and milk are mixed such that the ratio of the volume of water to that of milk is 4: 1. Taking the density of water as 1 g/cm^{3} and that of milk as 1.2g/cm^{3}, find the mass in grams of 2.5 litres of the mixture.

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