Year 10 Sem1Exam P1 Final - WordPress.com

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01. (a) Given

f(x) = 2x – 1 g(x) = 3x2 + 1 h(x) = – 7 . (i) Find fg(1).

Answer: ....................................................................... [1] (ii) Find g(f(x)), in simplest form.

Answer: ...................................................................... [2]

(iii) Find h-1(x), the inverse of h(x).

Answer: ...................................................................... [3] (iv) Solve for x, if f-1(x) = 3.

Answer: ...................................................................... [2]

8 x

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(b) Which of the following functions are shown by the graphs below? In each case, k > 1. Write the letter of the function under each graph.

A y = D y = kx B y = k-x E y =

C y = kx3 F y = kx2

[3]

………………………

k x

k x2

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02. Two hundred (200) people recorded the number of hours they work in a week. The results are shown in the table below.

(a) Write down the median class.

Answer: ...................................................................... [1]

(b) Calculate the estimated mean number of hours that workers spent for work, giving your answers correct to 2 decimal places.

Answer: ...................................................................... [3]

Amount (x hours)

No. of workers

Mid-Value Mid-Value × Frequency

0 < x ≤ 10 12 5

10 < x ≤ 20 34 510

20 < x≤ 30 36 25 900

30 < x ≤ 40 30

40 < x ≤ 50 38 45

50 < x ≤ 60 30 1650

60 < x ≤ 70 16 65 1040

70 < x ≤ 80 4

Total 200

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(c) The cumulative frequency graph of the 200 workers and the amount of hours they spent for work is shown below.

Use the graph to find (i) the median number of hours,

Answer: ...................................................................... [1]

(ii) the 65% percentile,

Answer: ...................................................................... [1]

(iii) the upper quartile,

Answer: ...................................................................... [1] (iv) the interquartile range,

Answer: ...................................................................... [1] (v) the number of people who work more than 60 hours in a week.

Answer: ...................................................................... [1]

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03. Mario must choose a ball from Bag A or from Bag B. Bag A contains 5 white balls and 3 black balls. Bag B contains 6 white balls and 2 black balls. The probability that he chooses Bag A is #$. The tree diagram below shows some of his information.

(a) Calculate, in simplest form, the values of p, q, r, and s.

Answer: ...................................................................... [2]

(b) Find the probability that Mario chooses a black ball.

Answer: ...................................................................... [2]

(c) Determine the probability that Mario chooses a white ball or any ball from Bag A.

Answer: ...................................................................... [2] (d) If he chose a black ball, he chooses another ball from the same bag without replacing the first one. What is the probability that he chooses two black balls from Bag A?

Answer: ...................................................................... [2]

Bag A

Bag B

white ball

white ball

black ball

black ball

q

r

s

p

23

58

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04. (a) Show, by shading the unwanted regions, the region T, containing the points which satisfy

the three inequalities y ≥ 2x, x + y ≤ 10 and 2x + y > 10. [4]

(b) Using the graphs in (a), find the greatest value of x in the region T, such that x is an integer

Answer: ...................................................................... [1]

(c) The point (x, y) is in the region T. Write down all pairs of integer values of x and y such 2x + y = 11.

Answer: ...................................................................... [2]