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Mathematics Extension 1

Stage 6 · HSC questions by topic

About this subject

Mathematics Extension 1

Atlas organises human-reviewed questions against the NSW Stage 6 Mathematics Extension 1syllabus. Every published question retains its exam source and page.

Syllabus: NESA Stage 6 (2017)
Explore the NESA Stage 6 (2017) syllabus topics

Functions

  • Further Work with Functions
  • Polynomials

Trigonometric Functions

  • Inverse Trigonometric Functions
  • Further Trigonometric Identities
  • Trigonometric Equations

Calculus

  • Rates of Change
  • Further Calculus Skills
  • Applications of Calculus

Combinatorics

  • Working with Combinatorics

Proof

  • Proof by Mathematical Induction

Vectors

  • Introduction to Vectors

Statistical Analysis

  • The Binomial Distribution
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5 questions found

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2023HSC
Q2

A standard six-sided die is rolled 12 times.

Let p^\hat pp^​ be the proportion of the rolls with an outcome of 2.

Which of the following expressions is the probability that at least 9 of the rolls have an outcome of 2?
A. P(p^≥34)P\left(\hat p\geq\frac{3}{4}\right) B. C. D.

P
(p^​≥43​)

P(p^≥16)P\left(\hat p\geq\frac{1}{6}\right)P(p^​≥61​)

P(p^≤34)P\left(\hat p\leq\frac{3}{4}\right)P(p^​≤43​)

P(p^≤16)P\left(\hat p\leq\frac{1}{6}\right)P(p^​≤61​)
1 mark
Multiple choice
2023HSC
Q11 (f) (i)

A recent census found that 30% of Australians were born overseas.

A sample of 900 randomly selected Australians was surveyed.

Let p^\hat pp^​ be the sample proportion of surveyed people who were born overseas.

A normal distribution is to be used to approximate P(p^≤0.31)P(\hat p\leq0.31)P(p^​≤0.31).

(i) Show that the variance of the random variable p^\hat pp^​ is

730 000.\frac{7}{30\,000}.300007​.
2 marks
Short answer
2023HSC
Q11 (f) (ii)

A recent census found that 30% of Australians were born overseas.

A sample of 900 randomly selected Australians was surveyed.

Let p^\hat pp^​ be the sample proportion of surveyed people who were born overseas.

A normal distribution is to be used to approximate P(p^≤0.31)P(\hat p\leq0.31)P(p^​≤0.31).

(ii) Use the standard normal distribution and the information on page 16 to approximate P(p^≤0.31)P(\hat p\leq0.31)P(p^​≤0.31), giving your answer correct to two decimal places.

2 marks
Short answer
2023HSC
Q12 (c) (i)

A gym has 9 pieces of equipment: 5 treadmills and 4 rowing machines.

On average, each treadmill is used 65% of the time and each rowing machine is used 40% of the time.

(i) Find an expression for the probability that, at a particular time, exactly 3 of the 5 treadmills are in use.

2 marks
Short answer
2023HSC
Q12 (c) (ii)

A gym has 9 pieces of equipment: 5 treadmills and 4 rowing machines.

On average, each treadmill is used 65% of the time and each rowing machine is used 40% of the time.

(ii) Find an expression for the probability that, at a particular time, exactly 3 of the 5 treadmills are in use and no rowing machines are in use.

1 mark
Short answer