Sample assessment 2020 Multiple choice question book

Mathematical Methods Paper 1 — Technology-free

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Section 1

Instructions • Answer all questions in the question and response book.

• This book will not be marked.

QUESTION 1 The random variable 𝑋𝑋 is binomially distributed with 10 trials and a probability of success equal to 0.25 at each attempt. The value of P(𝑋𝑋 ≥ 1) is equal to

(A) �14�10

(B) �34�10

(C) 1 − �14�10

(D) 1 − �34�10

QUESTION 2 The approximate area under the curve 𝑦𝑦 = 2𝑥𝑥2 between 𝑥𝑥 = 1 and 𝑥𝑥 = 4 is found using rectangles (of width equal to one unit) as shown in the diagram.

What is the approximate area found using these rectangles?

(A) 58 units2

(B) 45 units2

(C) 42 units2

(D) 28 units2

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QUESTION 3

If 𝑦𝑦 = cos2(3𝑥𝑥), then 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

=

(A) −6 sin(3𝑥𝑥) cos(3𝑥𝑥)

(B) −2 sin(3𝑥𝑥) cos(3𝑥𝑥)

(C) 2 sin(3𝑥𝑥) cos(3𝑥𝑥)

(D) 6 sin(3𝑥𝑥) cos(3𝑥𝑥)

QUESTION 4 If ∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = 40

−2 and ∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = −10,30 which of the following is true?

∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = −143−2 (A)

(B) ∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = −63−2

(C) ∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = 63−2

(D) ∫ 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑥𝑥 = 143−2

QUESTION 5 The slope of the tangent to the graph of 𝑦𝑦 = ln(𝑥𝑥2) at 𝑥𝑥 = 𝑒𝑒2 is

(A) 1𝑒𝑒2

(B) 2𝑒𝑒2

(C) 4𝑒𝑒4

(D) 1𝑒𝑒4

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QUESTION 6

Calculate ∫ 𝑑𝑑𝑑𝑑�(2+𝑑𝑑)

7−1

(A) 1

(B) 43

(C) 2

(D) 4

QUESTION 7 The distribution of marks in three subjects is given below. The mark received by a student in each of the subjects is also shown.

Subject Mean Standard deviation Student mark

Science 60 15 70

Mathematics 68 6 72

Music 65 9 72

Standardised 𝑧𝑧-scores were used to compare the results and showed that the student

(A) performed equally well in mathematics and science.

(B) performed equally well in mathematics and music.

(C) performed better in mathematics than in science.

(D) performed better in mathematics than in music.

QUESTION 8

Given 𝑦𝑦 = 5𝑒𝑒2𝑑𝑑, rearrange the function to make 𝑥𝑥 the subject.

(A)

(B)

(C)

(D)

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QUESTION 9 An equilateral triangle has side lengths of 9 m. The area of the triangle is

(A) 814

m2

(B) 81√24

m2

(C) 81√34

m2

(D) 812

m2

QUESTION 10 If the sample size is decreased, but the sample proportion and the confidence level remain the same, the width of the confidence interval

(A) will increase.

(B) will decrease.

(C) remains unchanged.

(D) may increase or decrease.

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