# HSC Mathematics: Exam Prep & Syllabus Final Exam

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#### Question 1 1. What is the probability of two mutually exclusive events occurring?

#### Question 2 2. Simplify the expression shown.

#### Question 3 3. Which graph(s) are indefinite quadratics?

#### Question 4 4. Find f'(x).

#### Question 5 5. Find arg (z) if z = -4 - 3i.

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Question 6
6.
Using our derivations, a simple harmonic oscillator is at its maximum velocity with sin(*ω***t* + *phi) = 1, and at its maximum acceleration when cos(*ω***t* + *&phi';') = 1. Find the spring constant for a weight on a spring with a mass of 0.2 kg, an amplitude of 5 m, and a maximum acceleration of - 2.5 m/s^2.

#### Question 7 7. Use Newton's method to find the root of f(x), starting at x=1.

#### Question 8 8. What is the simplified value of the expression below?

#### Question 9 9. Which of the following is not a quadratic equation?

#### Question 10 10. Solve for x using the image as a reference. The perimeter of the triangle is 36 units.

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Question 11
11.
Find the measure of the angle *x*.

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Question 12
12.
Which of the following statements are true?

a) d/dx f(x) = f'(x)

b) f'(x) is the derivative of the function f(x) with respect to x.

c) d/dx f(x) describes the instantaneous rate of change of f(x).

#### Question 13 13. How many arcs does a hyperbola have?

#### Question 14 14. Which of the following units would be correct for an acceleration?

#### Question 15 15. Which of the following equations represents a rectangular hyperbola?

#### HSC Mathematics: Exam Prep & Syllabus Final Free Practice Test Instructions

Choose your answer to the question and click 'Continue' to see how you did. Then click 'Next Question' to answer the next question. When you have completed the free practice test, click 'View Results' to see your results. Good luck!