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Practice Exam 20230824

Question 1 (12 marks) Use a SEPARATE book clearly marked Question 1

(i) A die is rolled once. Find the probability that the number on the uppermost face is odd or less than 4.

(ii)	Find how many ways the letters of the word TWEETER can be arranged in a row: (a) without restriction. (b) with the letters W and R together.

(iii) Find the following indefinite integrals:

(a)

(b)

(iv) (a) Sketch the graph of y=x²-3x, showing all intercepts.

(b) Find the area bounded by the graph of y=x²-3x and the x-axis.

(v) The table below shows the probability distribution for a random variable X. If E(X)=3.6 find the values of a and b.

x	0	1	3	b
P(X=x)	0.1	0.15	0.45	a

Question 2 (12 marks) Use a SEPARATE book clearly marked Question 2

(i) Find the number of different ways 6 adults and 4 children can be seated in a row if:

(a) there are no restrictions.

(b) there must be an adult on each end of the row.

(d) there must be at least two adults seated between any two children.

(ii) A box contains 13 red marbles and 2 blue marbles. Three marbles are selected at

random without replacement from the box. Find the probability that all three of the selected marbles are red.

(iii) Consider the function

(a) Find the equation of the asymptote.

(b) Find any x-intercepts.

(d) Sketch the graph of y=f(x).

Question 3 (12 marks) Use a SEPARATE book clearly marked Question 3

(i) Find the number of different arrangements in a line of the letters of the place name

HONG KONG

(ii) A box contains 5 white cards and 4 black cards. Three cards are drawn in

succession at random without replacement. Find the probability of selecting:

(a) no white cards

(b) at least 2 black cards

(iii) Find the coefficient of x³ in the expansion of (5-2x)°

(iv)	Mr and Mrs Smith are a married couple. The probability that Mr Smith watches a certain TV show is 0.4 and the probability that Mrs Smith watches the show is 0.5. The conditional probability that Mr Smith watches the show, given that Mrs Smith does,is 0.7.