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Probability 10 Probability 20 Probability 30 Differentiation 10 Differentiation 20 Differentiation 30 Integration 10 Integration 20 Integration 30 Vectors 10 Vectors 20 Vectors 30

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1. Given that a = i + 2j + k and b = 4i 3j + 2k a) Evaluate a.b b) What can you conclude from your answer to a)? Back to Menu

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x = 4i 3j + 2z and y = 5i +4j -7z. Find the cosine of the angle between the two vectors x and y. Back to Menu

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If f(x) = 3cos(2x-1) and g(x) = log(2x) a) Find f (x) b) Find g (x) Back to Menu

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Find the volume of revolution formed when y = sin(x) + 2 is turned through 360 degrees about the x-axis between 0 and 2. Back to Menu

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A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. (a)The first two apples are green. What is the probability that the third apple is red? (b)What is the probability that exactly two of the three apples are red? Back to Menu

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A box contains 35 red discs and 5 black discs. A disc is selected at random and its colour noted. The disc is then replaced in the box. (a)In eight such selections, what is the probability that a black disc is selected (i)exactly once? (ii)at least once? Back to Menu

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Intelligence Quotient (IQ) in a certain population is normally distributed with a mean of 100 and a standard deviation of 15. a) What percentage of the population has an IQ between 90 and 125? (b)If two persons are chosen at random from the population, what is the probability that both have an IQ greater than 125? Back to Menu