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Questions and Answers
What is the simplified form of $\left( \frac{8}{3} \right)^{-1}$?
What is the simplified form of $\left( \frac{8}{3} \right)^{-1}$?
What is the value of $\sin\left( \frac{3\pi}{2} \right)$?
What is the value of $\sin\left( \frac{3\pi}{2} \right)$?
What is the turning point of the parabola defined by $y = x^2 - 2x - 6$?
What is the turning point of the parabola defined by $y = x^2 - 2x - 6$?
If $3^{x + 1} = 9\sqrt{3}$, what is the value of $x$?
If $3^{x + 1} = 9\sqrt{3}$, what is the value of $x$?
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In the equation $x^2 - 2x - 6 = 0$, what are the roots?
In the equation $x^2 - 2x - 6 = 0$, what are the roots?
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What materials are students allowed to bring into the examination room?
What materials are students allowed to bring into the examination room?
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Which of the following statements about the examination is true?
Which of the following statements about the examination is true?
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How many questions must students answer in this examination?
How many questions must students answer in this examination?
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Which item is specifically excluded from the permitted examination materials?
Which item is specifically excluded from the permitted examination materials?
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What is the duration of writing time for the examination?
What is the duration of writing time for the examination?
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During Part A of the examination, which of the following is NOT allowed?
During Part A of the examination, which of the following is NOT allowed?
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What type of devices are students prohibited from bringing into the examination room?
What type of devices are students prohibited from bringing into the examination room?
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What should students do if they need to write down their answers?
What should students do if they need to write down their answers?
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What should be used to mark answers on the multiple choice answer sheet?
What should be used to mark answers on the multiple choice answer sheet?
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What will happen if more than one answer is completed for a question?
What will happen if more than one answer is completed for a question?
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What are the solutions to the equation $8x^2 - 14x + 3 = 0$?
What are the solutions to the equation $8x^2 - 14x + 3 = 0$?
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Which of the following statements is true regarding incorrect answers?
Which of the following statements is true regarding incorrect answers?
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Which expression is equivalent to $4\sqrt{5}$?
Which expression is equivalent to $4\sqrt{5}$?
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What should you do if you make a mistake on your answer sheet?
What should you do if you make a mistake on your answer sheet?
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What are the two possible angles for $∠A$ in triangle ABC, rounded to two decimal places?
What are the two possible angles for $∠A$ in triangle ABC, rounded to two decimal places?
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What does the instruction suggest about shading the box for your answer?
What does the instruction suggest about shading the box for your answer?
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Which graph could represent the equation $y = -2^{-x} + 2$?
Which graph could represent the equation $y = -2^{-x} + 2$?
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Which of the following is NOT a valid property of triangle angles?
Which of the following is NOT a valid property of triangle angles?
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What is the value of $ ext{cos}(180^ ext{°} + heta)$ when $ ext{cos}( heta) = rac{2}{3}$?
What is the value of $ ext{cos}(180^ ext{°} + heta)$ when $ ext{cos}( heta) = rac{2}{3}$?
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Which of the following statements about the cosine function is true for $0 \leq \theta \leq 90^ ext{°}$?
Which of the following statements about the cosine function is true for $0 \leq \theta \leq 90^ ext{°}$?
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If $\cos(\theta) = \frac{2}{3}$, what is $\theta$ approximately in degrees?
If $\cos(\theta) = \frac{2}{3}$, what is $\theta$ approximately in degrees?
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In the function $\cos(180^ ext{°} + \theta)$, what type of angle does the addition of $180^ ext{°}$ represent?
In the function $\cos(180^ ext{°} + \theta)$, what type of angle does the addition of $180^ ext{°}$ represent?
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Which value would cause $\cos(\theta)$ to be undefined?
Which value would cause $\cos(\theta)$ to be undefined?
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If $\theta$ is an angle such that $\cos(\theta) = \frac{2}{3}$, which of the following is true about $\theta$?
If $\theta$ is an angle such that $\cos(\theta) = \frac{2}{3}$, which of the following is true about $\theta$?
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The cosine of which angle is equal to the negative cosine of another angle in the specified range?
The cosine of which angle is equal to the negative cosine of another angle in the specified range?
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What results from evaluating $\cos(180^ ext{°} + \theta)$ if $\theta$ is a positive acute angle?
What results from evaluating $\cos(180^ ext{°} + \theta)$ if $\theta$ is a positive acute angle?
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What is the equation representing the population of the Siamese Fireback after $t$ years?
What is the equation representing the population of the Siamese Fireback after $t$ years?
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What are the x-intercepts of the cubic function that models the tunnel?
What are the x-intercepts of the cubic function that models the tunnel?
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Which is the correct form of the cubic equation passing through $(0, \frac{9}{5})$?
Which is the correct form of the cubic equation passing through $(0, \frac{9}{5})$?
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At what coordinates do the two tunnels intersect?
At what coordinates do the two tunnels intersect?
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What does the term 'cubic function' refer to in the context of modeling the tunnel?
What does the term 'cubic function' refer to in the context of modeling the tunnel?
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Study Notes
Year 10 Extension Mathematics Practice Exam
- Exam Structure: Part A (CAS Free) and Part B (CAS Active)
- Reading Time: 10 minutes for both parts
- Writing Time: 30 minutes
- Part A Structure: 5 questions, 20 marks
- Part B Structure: 3 questions, 15 marks
Exam Information
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Permitted Items (Part A): Pens, pencils, highlighters, erasers, sharpeners, rulers, the bound reference, lecture pad of notes
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Not Permitted Items (Part A): Blank sheets of paper, white out, calculators
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Permitted Items (Part B): Pens, pencils, highlighters, erasers, sharpeners, rulers, one bound reference, one approved CAS calculator, and (if desired) one scientific calculator
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Not Permitted Items (Part B): Blank sheets of paper, white out, calculators during reading time, dictionaries
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General Instructions:
- Answer all questions in the provided space.
- Show appropriate working for multi-mark questions.
- Diagrams are not drawn to scale unless stated otherwise.
Section A Questions (Multiple Choice)
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Instructions: Answer all questions on a separate answer sheet. Each correct answer is worth 1 mark. Incorrect or multiple answers will not be penalized.
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Question 1: Finding the value of a in a sinusoidal function with period 5π/2.
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Question 2: Finding the solutions to a quadratic equation expressed as 8x^2 - 14x + 3=0.
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Question 3: Determining an equivalent expression to 4√5. (√100, √80, 2√10, √40).
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Question 4: Finding possible angles for a triangle. Relevant information: Triangle ABC, c=10, a=12, ∠A is unknown.
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Question 5: Identifying a graph of a function. The function is y = -2^x + 2.
Section B Questions (Extended Response)
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Instructions: Answer all questions in the provided space. Show all your working. Exact answers are required unless stated otherwise.
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Question 1 (Part B): Solving a trigonometric equation 8=10 + 4 cos(x) where 0 ≤ x ≤ 2π. Sketching the graph of y = 10 + 4 cos(x) for 0 ≤ x ≤ 2π (labeling intercepts, endpoints, and turning points).
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Question 2 (Part B): Two bird populations (Siamese Firebacks and Tufted Puffins) are described. Using equations, determine when the number of Tufted Puffins will exceed the number of Siamese Firebacks. Also, a third bird's population (Pūteketeke) P = Po × k^t, is modeled using the different populations/initial population data, find and solve for the constants k and Po.
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Question 3 (Part B): A tunnel is modeled using a cubic function y = ax^3 + bx^2 + cx + d. Determine the x intercepts. Given the function passes through a point (0,3), determine the equation of the cubic function. Finding the point where two tunnels meet.
Additional Notes
- Mobile phones and other electronic devices capable of storing, receiving, or transmitting information are not permitted in the examination room.
- Students are not allowed to disclose the examination contents; doing so is a breach of guidelines.
- Ensure that all written work is in English.
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Description
Prepare for your Year 10 Extension Mathematics exam with this comprehensive practice exam. The exam consists of two parts: a CAS Free section and a CAS Active section, covering essential mathematical concepts and problem-solving skills. Make sure to review the permitted items and instructions for each part to achieve the best results.
