Calculate the average acceleration of an airplane during landing if it touches down with a velocity of 60 m/s north and comes to a complete stop over a distance of 350 m. (2 marks)
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Aussie Maths & Science Teachers: Save your time with SmarterEd
Calculate the average acceleration of an airplane during landing if it touches down with a velocity of 60 m/s north and comes to a complete stop over a distance of 350 m. (2 marks)
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\(5.14\ \text{ms}^{-2}\) to the south.
| \(v^2\) | \(=u^2 +2as\) | |
| \(a\) | \(=\dfrac{v^2-u^2}{2s}\) | |
| \(=\dfrac{0-60^2}{2 \times 350}\) | ||
| \(=-5.14\ \text{ms}^{-2}\) |
Outline an experimental procedure to determine the acceleration of a falling steel ball. Your explanation should include all the measurements that must be recorded, the calculations needed to compute the acceleration, and an identification of any potential sources of error in the experiment. (6 marks)
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Procedure and Measurements:
Sources of Error:
Procedure and Measurements:
Sources of Error:
If \( { \displaystyle \int_a^b f(x) d x=-5 } \) and \( { \displaystyle \int_a^c f(x) d x=3 } \), where \(a<b<c\).
Find \( { \displaystyle \int_b^c 2 f(x) d x } \). (2 marks)
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\(16\)
| \({ \displaystyle \int_a^b f(x) d x} +{ \displaystyle \int_b^c f(x) d x}\) | \(={ \displaystyle \int_a^c f(x) d x} \) | |
| \(-5+{ \displaystyle \int_b^c f(x) d x}\) | \(=3\) | |
| \({ \displaystyle \int_b^c f(x) d x}\) | \(=3+5=8\) |
\(\therefore{ \displaystyle \int_b^c 2f(x) d x}=16\)
A discrete random variable \(X\) is defined using the probability distribution below, where \(k\) is a positive real number.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & \ \ \ \ \text{0}\ \ \ \ \rule[-1ex]{0pt}{0pt} & \ \ \ \ \text{1}\ \ \ \ \rule[-1ex]{0pt}{0pt} & \ \ \ \ \text{2}\ \ \ \ \rule[-1ex]{0pt}{0pt} & \ \ \ \ \text{3}\ \ \ \ \rule[-1ex]{0pt}{0pt} & \ \ \ \ \text{4}\ \ \ \ \\
\hline
\rule{0pt}{2.5ex} \text{Pr} \ (X = x) \rule[-1ex]{0pt}{0pt} & 2k \rule[-1ex]{0pt}{0pt} & 3k \rule[-1ex]{0pt}{0pt} & 5k \rule[-1ex]{0pt}{0pt} & 3k \rule[-1ex]{0pt}{0pt} & 2k \\
\hline
\end{array}
Find \(\operatorname{Pr}(X<4 \mid X>1)\) (3 marks)
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\(C\)
\(2k+3k+5k+3k+2k=1\ \Rightarrow\ k=\dfrac{1}{15}\)
| \(\operatorname{Pr}(X<4 \mid X>1)\) | \(=\dfrac{\operatorname{Pr}(X>1)\ \cap \ \operatorname{Pr}(X<4)}{\operatorname{Pr}(X>1)}\) |
| \(=\dfrac{\operatorname{Pr}(1<X<4)}{\operatorname{Pr}(X>1)}\) | |
| \(=\dfrac{\frac{5}{15}+\frac{3}{15}}{\frac{5}{15}+\frac{3}{15}+\frac{2}{15}}\) | |
| \(=\dfrac{\frac{8}{15}}{\frac{10}{15}}\) | |
| \(=\dfrac{4}{5}\) |
A function \(g(x)\) has the derivative \( { \displaystyle g^{\prime}(x)=x^3-x } \).
Given that \(g(0)=5\), the value of \(g(2)\) is
\(D\)
| \({ \displaystyle g^{\prime}(x)}\) | \(=x^3-x\) |
| \(g(x)\) | \(=\dfrac{x^4}{4}-\dfrac{x^2}{2}+c\) |
\(\text{Given }g(0)=5,\ c=5\)
\(g(x)=\dfrac{x^4}{4}-\dfrac{x^2}{2}+5\)
\(\therefore\ g(2)=\dfrac{2^4}{4}-\dfrac{2^2}{2}+5=7\)
\(\Rightarrow D\)
The asymptote(s) of the graph of \(y=\log _e(x+1)-3\) are
\(A\)
\(\text{Asymptotes occur when}\ \ x+1=0\)
\(\therefore\ \text{Only one asymptote at}\ \ x=-1\)
\(\Rightarrow A\)
Consider the function `f`, where `f:\left(-\frac{1}{2}, \frac{1}{2}\right) \rightarrow R, f(x)=\log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right).`
Part of the graph of `y=f(x)` is shown below.
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| a. | `R` |
| b.i | `f^{\prime}(0)=4` |
| b.ii | `\left(-\frac{1}{2}, \frac{1}{2}\right)` |
| c. | `0` |
| d. | `x \in \mathbb{R}` |
| e.i | ` k > 4` |
| e.ii | No bounded area for `0<k \leq 4` |
a. `R` is the range.
| b.i | `f(x)` |
`= \log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right)` | |
| `f^{\prime}(x)` | `= \frac{1}{x+\frac{1}{2}}+\frac{1}{\frac{1}{2}-x}` | ||
| `= \frac{2}{2 x+1}-\frac{2}{2 x-1}` | |||
| `f^{\prime}(0)` | `= \frac{2}{2 xx 0+1}-\frac{2}{2 xx 0-1}` | ||
| `= 4` |
b.ii `\left(-\frac{1}{2}, \frac{1}{2}\right)`
| c. `f(x)+f(-x)` | `= \log _e\left(x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-x\right)+\log _e\left(-x+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}+x\right)` | |
| `= 0` |
d. To find the inverse swap `x` and `y` in `y=f(x)`
| `x` | `= \log _e\left(y+\frac{1}{2}\right)-\log _e\left(\frac{1}{2}-y\right)` | |
| `x` | `= \log _e\left(\frac{y+\frac{1}{2}}{\frac{1}{2}-y}\right)` | |
| `e^x` | `=\frac{y+\frac{1}{2}}{\frac{1}{2}-y}` | |
| `y+\frac{1}{2}` | `= e^x\left(-y+\frac{1}{2}\right)` | |
| `y+\frac{1}{2}` | `= -e^x y+\frac{e^x}{2}` | |
| `y\left(e^x+1\right)` | `= \frac{e^x-1}{2}` | |
| `:.\ f^(-1)(x)` | `= \frac{e^x-1}{2(e^x + 1)}` |
`:.` Domain: `x \in \mathbb{R}`
e.i The vertical dilation factor of `f(x)` is `1/k`
For `A(k)>=0` , `h^{\prime}(0)<1`
`\frac{1}{k}(4)<1` [Using CAS]
`:.\ k > 4`
e.ii When `h \geq h^{-1}` for `x>0` (or `h \leq h^{-1}` for `x<0`) there is no bounded area.
`:.` There will be no bounded area for `0<k \leq 4`.
A truck is driving along a straight road travelling at 10 ms\(^{-1}\). He then accelerates according to the acceleration time graph below:
Determine the final speed of the truck after it accelerates for 7 seconds.
\(A\)
\(\Rightarrow A\)
A skydiver jumps from a stationary aircraft and yells as soon as she starts falling. Four seconds later, while still falling, she hears the echo of her shout from the ground below.
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a. \(78.4\ \text{m}\)
b. \(1360\ \text{m}\)
c. \(719.2\ \text{m}\)
a. \(u=0,\ \ t=4,\ \ a=9.8\)
Using the formula \(s=ut + \dfrac{1}{2}at^2\)
\(s = (0 \times 4) + (\dfrac{1}{2} \times 9.8 \times 4^2) = 78.4\ \text{m}\)
b. \(d=vt = 340 \times 4 = 1360\ \text{m}\)
c. Let initial height of the skydiver be \(h\ \text{m}\).
| \(h+h-78.4\) | \(=1360\) | |
| \(2h\) | \(=1438.4\) | |
| \(h\) | \(=719.2\ \text{m}\) |
A bus departs from its depot, starting from rest and accelerating uniformly at 2.0 ms\(^{-2}\) for 10 seconds until it reaches a speed of 20 ms\(^{-1}\). It then travels at this constant speed for 50 seconds before decelerating uniformly at – 2.5 ms\(^{-2}\) until coming to a complete stop at the next bus stop. --- 6 WORK AREA LINES (style=blank) --- --- 4 WORK AREA LINES (style=lined) ---
Using the velocity-time graph below
Part 1
Determine the magnitude of the displacement:
Part 2
Determine the average acceleration between 4 and 8 seconds:
Part 1: \(C\)
Part 2: \(B\)
Part 1
\(\text{Area}\ =(4 \times 8) + (\dfrac{1}{2} \times 4 \times 8) = 32 +16 = 48\ \text{m}\)
\(\Rightarrow C\)
Part 2
\(a= \dfrac{\Delta v}{\Delta t} = \dfrac{0-8}{8-4} = -2\ \text{ms}^{-2}\)
\(\Rightarrow B\)
Explain how different training methods could be modified to maintain fitness during a 6-week injury rehabilitation period for a soccer player with a knee injury. (6 marks)
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Sample Answer
Sample Answer
Evaluate the benefits and limitations of Fartlek training compared to structured interval training for a team sport of your choice. (8 marks)
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Sample Answer – Touch Football
Evaluation Statement:
Game Simulation:
Precision and Progression:
Training Phase Application:
Final Evaluation:
Sample Answer
Evaluation Statement:
Game Simulation:
Precision and Progression:
Training Phase Application:
Final Evaluation:
Describe how aerobic and anaerobic training methods can be combined effectively in a basketball training session. (6 marks)
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Sample Answer
Warm-up
Main session
Small-sided games (3v3)
Final round
Cool-down
Sample Answer
Warm-up
Main session
Small-sided games (3v3)
Final round
Cool-down
Compare how anaerobic training methods would differ between a rugby league player and a tennis player. (6 marks)
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Sample Answer
Rugby league player
Tennis player
Both sports
Sample Answer
Rugby league player
Tennis player
Both sports
Discuss how HIIT training can be modified for different fitness levels in a group fitness class. (6 marks)
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Sample Answer
Benefits of HIIT modifications:
However, challenges of HIIT modifications include:
Sample Answer
Benefits of HIIT modifications:
However, challenges of HIIT modifications include:
Evaluate the effectiveness of different training methods for a 400 metre track athlete throughout a competition season. (8 marks)
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Sample Answer
Evaluation Statement:
Pre-Season Foundation:
Early Competition Phase:
Mid-Season Power:
Competition Preparation:
Final Evaluation:
Sample Answer
Evaluation Statement:
Pre-Season Foundation:
Early Competition Phase:
Mid-Season Power:
Competition Preparation:
Final Evaluation:
Analyse how contemporary training methods like HIIT and SIT have evolved from traditional aerobic and anaerobic training approaches. Use examples from two different sports. (8 marks)
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Sample Answer (Note other sports could be chosen)
Traditional v Contemporary training – Aerobic
Example 1: Swimming
Traditional v Contemporary training – Anaerobic
Example 2: Rugby league
Conclusions
Sample Answer (Note other sports could be chosen)
Traditional v Contemporary training – Aerobic
Example 1: Swimming
Traditional v Contemporary training – Anaerobic
Example 2: Rugby league
Conclusions
Explain how different training methods would be used across a soccer season to develop both aerobic and anaerobic fitness. (6 marks)
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Sample Answer
Sample Answer
Compare continuous training and High Intensity Interval Training (HIIT) methods and their application in basketball. (5 marks)
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Sample Answer
Similarities:
Differences:
Sample Answer
Similarities:
Differences:
Compare aerobic and anaerobic training methods. (5 marks)
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Sample Answer
Similarities:
Differences:
Sample Answer
Similarities:
Differences:
The most appropriate training method for improving a rugby league player's ability to repeatedly sprint during a game would be:
\(C\)
Other Options:
A soccer team's pre-season program includes:
This training session would be classified as:
\(C\)
Other Options:
A soccer player completes the following training session:
This training session would be classified as:
\(A\)
Other Options:
Compare how continuous training would be applied differently for an individual sport athlete versus a team sport athlete. (6 marks)
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Sample Answer
Similarities:
Differences:
Sample Answer
Similarities:
Differences:
Explain how a soccer player could use continuous training to improve their aerobic capacity during pre-season. (5 marks)
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Sample Answer
Sample Answer
Describe how continuous training differs from interval training. Use examples to support your answer. (4 marks)
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Sample Answer
Continuous Training
Interval Training
Examples
Energy systems are primarily targeted
Sample Answer
Continuous Training
Interval Training
Examples
Energy systems are primarily targeted
Which row correctly shows the characteristics of continuous training?
\(A\)
Other Options:
Outline the hydration needs of sprinters versus endurance athletes. (3 marks)
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Sample Answer
Sample Answer
Explain why timing of nutrient intake differs for a weightlifter versus a marathon runner. (3 marks)
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Sample Answer
Sample Answer
An endurance cyclist should prioritise which nutritional strategy during a 4-hour race?
\(D\)
Other Options:
A sprinter requires which micronutrient for optimal anaerobic energy production?
\(B\)
Other Options:
Let \(X\) be a binomial random variable where \(X \sim \operatorname{Bi}\left(4, \dfrac{9}{10}\right)\). --- 4 WORK AREA LINES (style=lined) --- --- 8 WORK AREA LINES (style=lined) --- a. \(\operatorname{sd}(X)=\dfrac{3}{5}\) b. \(\dfrac{37}{10\,000}\)
a.
\(\operatorname{sd}(X)\)
\(=\sqrt{np(1-p)}\)
\(=\sqrt{4\times\dfrac{9}{10}\times\dfrac{1}{10}}\)
\(=\sqrt{\dfrac{36}{100}}\)
\(=\dfrac{3}{5}\)
b.
\(\operatorname{Pr}(X<2)\)
\(=\operatorname{Pr}(X=0)+\operatorname{Pr}(X=1)\)
\(=\ ^4C _0\left(\dfrac{9}{10}\right)^0\left(\dfrac{1}{10}\right)^4+\ ^4C_1\left(\dfrac{9}{10}\right)^1\left(\dfrac{1}{10}\right)^3\)
\(= 1 \times \dfrac {1}{10\,000} + 4 \times \dfrac{9}{10} \times \dfrac{1}{1000}\)
\(=\dfrac{37}{10\,000}\)
Let \(f(x)=\dfrac{1}{(x+3)^2}-2\). On the axes below, sketch the graph of \(y=f(x)\), labelling all asymptotes with their equations and axis intercepts with their coordinates. (4 marks) --- 4 WORK AREA LINES (style=lined) ---
\(\text{Find asymptotes:}\) \((x+3) \neq 0\ \ \Rightarrow\ \ \text{Asymptote at}\ x=-3\) \(\text{As}\ x \rightarrow \infty, \ \dfrac{1}{(x+3)^2} \rightarrow 0\ \ \Rightarrow \ \ \text{Asymptote at}\ y=-2\)
Compare pre and post-training nutrition requirements for a triathlete. (5 marks)
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Sample Answer
Similarities:
Differences:
Specific Needs:
Sample Answer
Similarities:
Differences:
Specific Needs:
Compare how carbohydrates and fats contribute to energy production during a marathon. (5 marks)
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Sample Answer
Similarities:
Differences:
Key Relationship:
Sample Answer
Similarities:
Differences:
Key Relationship:
Explain why iron requirements differ between endurance athletes and recreational athletes. (4 marks)
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Sample Answer
Sample Answer
A volleyball player has increased their intake of nuts and seeds during off-season training. Which nutrient in these foods is most likely to assist with reducing inflammation in their jumping knee?
\(C\)
Other Options:
Compare the nutritional requirements of a sprinter versus a marathon runner in preparation for competition. (5 marks)
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Sample Answer
Similarities:
Differences:
Sample Answer
Similarities:
Differences:
Assess the importance of iron intake for female endurance athletes. (5 marks)
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Sample Answer
Judgment Statement:
Oxygen Transport Efficiency:
Menstruation and Depletion Risks:
Overall Assessment:
Sample Answer
Judgment Statement:
Oxygen Transport Efficiency:
Menstruation and Depletion Risks:
Overall Assessment:
Explain how carbohydrate loading can improve performance for a marathon runner. (4 marks)
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Sample Answer
Sample Answer
A triathlete has just completed the swimming leg of their event. Which macronutrient should they prioritise during their transition to cycling?
\(D\)
Other Options:
A swimmer performs a 200 metre freestyle race.
Explain how TWO different energy systems contribute to fatigue during this event. (4 marks)
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Sample Answer
ATP-PCr System
Glycolytic System
Sample Answer
ATP-PCr System
Glycolytic System
During a summer time beach volleyball tournament, an athlete begins to experience fatigue during their third game of the day.
Identify TWO causes of fatigue and explain their impact on performance. (3 marks)
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Sample Answer – Any TWO of the following
Glycogen depletion
Dehydration
Electrolyte imbalance
Lactic acid accumulation
Sample Answer – Any TWO of the following
Glycogen depletion
Dehydration
Electrolyte imbalance
Lactic acid accumulation
Outline TWO causes of fatigue when an athlete performs a 100 metre sprint. (3 marks)
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Sample Answer
Any 2 of the following
Sample Answer
Any 2 of the following
Let \(f(x)=\log _e\left(x^3-3 x+2\right)\). Find \(f^{\prime}(3)\) (2 marks) --- 6 WORK AREA LINES (style=lined) --- \(\dfrac{6}{5}\)
\(f(x)\)
\(=\log_{e}(x^3-3x+2)\)
\(f^{\prime}(x)\)
\(=\dfrac{3x^2-3}{x^3-3x+2}\)
\(f^{\prime}(3)\)
\(=\dfrac{3(3)^2-3}{(3)^3-3(3)+2}=\dfrac{6}{5}\)
Describe how the three energy systems interact during a 3-minute boxing round. (5 marks)
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Sample Answer
Sample Answer
Explain how the lactic acid system contributes to energy production during a 200 m sprint. (4 marks)
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Sample Answer
Sample Answer
Outline how the ATP-PCr system provides energy for immediate muscle contraction. (3 marks)
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Sample Answer
Sample Answer
During a 400 metre sprint race, an athlete's performance is most dependent on which combination of energy systems?
\(B\)
Other Options:
Explain how the rate of recovery differs between anaerobic energy systems, and impacts performance. (4 marks)
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Sample Answer
Sample Answer
A supermarket has five departments, with areas allocated as shown on the floorplan below. The floorplan is represented by the network diagram below. On this network diagram, vertices represent departments and edges represent boundaries between two departments. This network diagram is incomplete. Draw the missing vertex and missing edges on the diagram above. Include a label. (2 marks) --- 0 WORK AREA LINES (style=lined) ---
During high-intensity interval training, an athlete performs 400 metre sprints. Which recovery period would be most appropriate to allow lactate clearance between efforts?
\(C\)
Other Options:
Compare the duration limitations of the ATP-PCr and Glycolytic energy systems. (4 marks)
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Keyword – “Compare”: Show how things are similar or different.
Sample Answer
Keyword – “Compare”: Show how things are similar or different.
Sample Answer
How does the rate of recovery between energy systems influence substitution strategies in team sports? (5 marks)
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Sample Answer
Sample Answer
A volleyball player performs six 30-second rallies with 2-minute rest periods between each rally. Which system would be LEAST relied upon for energy production?
\(A\)
Other Options:
Compare and contrast how the ATP-PCr and Glycolytic energy systems respond to high intensity exercise. (4 marks)
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Sample Answer
Similarities:
Differences:
Sample Answer
Similarities:
Differences:
Analyse how different intensities of training can affect energy system adaptations. (5 marks)
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Sample Answer
Sample Answer
A tennis player is in a rally lasting 45 seconds at moderate-high intensity. Which energy system sequence best represents their energy production?
\(D\)
Other Options:
During a 400 m race at high intensity, an athlete experiences muscular fatigue. What is the main cause?
\(B\)
Other Options: