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
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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
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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.
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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
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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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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
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Form 3 Mathematics
Find the radius and the coordinate of the centre of the circle whose equation is 2x2 + 2y2 – 3x + 2y + ½ = 0
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Form 3 Mathematics
The figure below is a sketch of the graph of the quadratic function y = k
( x+1) (x-2) 
Find the value of k
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Form 4 Mathematics
Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 1180W and the longitude of B is 1330E. 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
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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.
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Form 3 Mathematics
In the figure below AB is a diameter of the circle. Chord PQ intersects AB at N. A tangent to the circle at B meets PQ produced at R.
Given that PN = 14cm, NB = 4 cm and BR = 7.5 cm, calculate the length of:
(a) NR (b) AN
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Form 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
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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/cm3 and that of milk as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture.
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Form 3 Mathematics
A rectangular block has a square base whose side is exactly 8 cm. Its height measured to the nearest millimeter is 3.1 cm
Find in cubic centimeters, the greatest possible error in calculating its volume.
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Form 2 Mathematics
Find the equation of a straight line which is equidistant from the points ( 2,3) and ( 6, 1), expressing it in the form ax + by = c where a, b and c are constants
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Form 1 Mathematics
The cash price of a T.V set is Kshs 13, 800. A customer opts to buy the set on Hire purchase terms by paying a deposit of Kshs 2, 280
If simple interest of 20% p.a is charged on the balance and the customer is required to repay by 24 equal monthly installments, calculate the amount of each installment.
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Related Questions and Answers on Commercial Arithmetic IForm 4 Mathematics
A particle moves in a straight line through a point P. Its velocity v m/s is given by v= 2 -1, where t is time in seconds, after passing P. The distance s of the particle from P when t = 2 is 5 metres. Find the expression for s in terms of t.
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Form 4 Mathematics
The diagram on the grid below represents as extract of a survey map showing two adjacent plots belonging to Kazungu and Ndoe.
The two dispute the common boundary with each claiming boundary along different smooth curves coordinates ( x, y) and (x, y2) in the table below, represents points on the boundaries as claimed by Kazungu Ndoe respectively.
(a) On the grid provided above draw and label the boundaries as claimed by Kazungu and Ndoe
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Form 4 Mathematics
(b) In a certain week a businessman bought 36 bicycles and 32 radios for total of Kshs 227 280. In the following week, he bought 28 bicycles and 24 radios for a total of Kshs 174 960
Using matrix method, find the price of each bicycle and each radio that he bought (c) In the third week, the price of each bicycle was reduced by 10% while the price of each radio was raised by 10%. The businessman bought as many bicycles and as many radios as he had bought in the first two weeks. Find by matrix method, the total cost of the bicycles and radios that the businessman bought in the third week.
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Form 1 Mathematics
Two cylindrical containers are similar. The larger one has internal cross- section area of 45cm2 and can hold 0.945 litres of liquid when full. The smaller container has internal cross- section area of 20cm2
(a) Calculate the capacity of the smaller container (b) The larger container is filled with juice to a height of 13 cm. Juice is then drawn from is and emptied into the smaller container until the depths of the juice in both containers are equal. Calculate the depths of juice in each container. (c) On fifth of the juice in the larger container in part (b) above is further drawn and emptied into the smaller container. Find the difference in the depths of the juice in the two containers.
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Form 3 Mathematics
In the figure below, OQ = q and OR = r. Point X divides OQ in the ratio 1: 2 and Y divides OR in the ratio 3: 4 lines XR and YQ intersect at E.
(a) Express in terms of q and r
(i) XR (ii) YQ (b) If XE = m XR and YE = n YQ, express OE in terms of: (i) r, q and m (ii) r, q and n (c) Using the results in (b) above, find the values of m and n.
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