Band 4 – Page 2

PHYSICS, M1 EQ-Bank 4 MC

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.

$20.5\ \text{ms}^{-1}$
$21.5\ \text{ms}^{-1}$
$22.5\ \text{ms}^{-1}$
$23.5\ \text{ms}^{-1}$

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$A$

Show Worked Solution

→ The increase in velocity of the truck will be equal to the area under the acceleration time graph.

→ Speed Increase $=\dfrac{1}{2} \times 7 \times 3 = 10.5\ \text{ms}^{-1}$

→ Final speed $=10.5 + 10 = 20.5\ \text{ms}^{-1}$

$\Rightarrow A$

PHYSICS, M1 EQ-Bank 12

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.

Calculate how far the skydiver has fallen after 4 seconds. (1 mark)

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What is the total distance the sound of their shout travelled in 4 seconds? (Hint: the speed of sound is 340 m/s) (1 mark)

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Determine the altitude from which the skydiver jumped if this scenario occurred. (2 marks)

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a. $78.4\ \text{m}$

b. $1360\ \text{m}$

c. $719.2\ \text{m}$

Show Worked Solution

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 $h\ \text{m}$.

→ When the skydiver hears the echo of their scream they would be at a height of $(h-78.4)\ \text{m}$.

→ As the sound of the scream travelled both of those distances:

$h+h-78.4$	$=1360$
$2h$	$=1438.4$
$h$	$=719.2\ \text{m}$

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.

In the space provided, sketch a velocity–time graph of the bus's journey, clearly marking the acceleration phase, the constant speed phase, and the deceleration phase with all key values. (3 marks)

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Calculate the total distance the bus covers during this trip. (2 marks)

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b. $1180\ \text{m}$

Show Worked Solution

b. Total distance travelled by the bus is equal to the area under the velocity-time graph.

$\text{Distance}$	$=(\dfrac{1}{2} \times 10 \times 20) + (50 \times 20) + (\dfrac{1}{2} \times 8 \times 20) $
	$=1180\ \text{m} $

PHYSICS, M1 EQ-Bank 2-3 MC

Using the velocity-time graph below

Part 1

Determine the magnitude of the displacement:

$32\ \text{m}$
$40\ \text{m}$
$48\ \text{m}$
$64\ \text{m}$

Part 2

Determine the average acceleration between 4 and 8 seconds:

$-4\ \text{ms}^{-2}$
$-2\ \text{ms}^{-2}$
$-1\ \text{ms}^{-2}$
$2\ \text{ms}^{-2}$

Show Answers Only

Part 1: $C$

Part 2: $B$

Show Worked Solution

Part 1

→ The displacement for the motion can be calculated by find the area under the velocity time graph.

→ By splitting the graph up into the square and triangle, the area under the curve is:

$\text{Area}\ =(4 \times 8) + (\dfrac{1}{2} \times 4 \times 8) = 32 +16 = 48\ \text{m}$

$\Rightarrow C$

Part 2

→ Average acceleration between t=4 and t=8 is:

$a= \dfrac{\Delta v}{\Delta t} = \dfrac{0-8}{8-4} = -2\ \text{ms}^{-2}$

$\Rightarrow B$

HMS, BM EQ-Bank 250

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. (7 marks)

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Sample Answer

Initial phase effectively utilises non-weight bearing aerobic training through upper body ergometer (3 x 10 minutes at 65-75% max HR) to maintain cardiovascular fitness while protecting injured knee.
Deep water running successfully maintains running-specific fitness through interval training (8 x 2 minutes at 80-85% max HR) without joint impact.
Stationary cycling appropriately progresses to include HIIT elements (6 x 1 minute at 85% max HR) as rehabilitation advances, maintaining anaerobic capacity.
Modified field-based training effectively reintroduces sport-specific movement through straight-line running before progressing to change of direction.
Final rehabilitation phase successfully integrates ball work with progressive intensity intervals (4 x 4 minutes at 80-90% max HR) to regain match fitness.

Show Worked Solution

Sample Answer

Initial phase effectively utilises non-weight bearing aerobic training through upper body ergometer (3 x 10 minutes at 65-75% max HR) to maintain cardiovascular fitness while protecting injured knee.
Deep water running successfully maintains running-specific fitness through interval training (8 x 2 minutes at 80-85% max HR) without joint impact.
Stationary cycling appropriately progresses to include HIIT elements (6 x 1 minute at 85% max HR) as rehabilitation advances, maintaining anaerobic capacity.
Modified field-based training effectively reintroduces sport-specific movement through straight-line running before progressing to change of direction.
Final rehabilitation phase successfully integrates ball work with progressive intensity intervals (4 x 4 minutes at 80-90% max HR) to regain match fitness.

HMS, BM EQ-Bank 248

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

Effectively incorporates continuous aerobic activity (10 minutes at 60-65% max HR) through structured court drills including dribbling and shooting to prepare cardiovascular system.

Main session

Successfully combines training methods through ‘wave’ loading pattern.
Example: 4 x 5 minute periods alternating between aerobic intensity full-court weave drills (70-75% max HR) and anaerobic intensity defensive sliding exercises (85-90% max HR).

Small-sided games (3v3)

Effectively integrate both energy systems through 4 x 4 minute games with 1-minute active recovery, maintaining high intensity while developing sport-specific skills.

Final round

Includes anaerobic power development through 6 x 20 second full-court sprint/dribble combinations with 40 seconds recovery.

Cool-down

Appropriately returns to aerobic intensity (60% max HR) through structured shooting drills for 5-10 minutes.

Show Worked Solution

Sample Answer

Warm-up

Incorporates continuous aerobic activity (10 minutes at 60-65% max HR) through structured court drills including dribbling and shooting to prepare cardiovascular system.

Main session

Combines training methods through ‘wave’ loading pattern.
Example: 4 x 5 minute periods alternating between aerobic intensity full-court weave drills (70-75% max HR) and anaerobic intensity defensive sliding exercises (85-90% max HR).

Small-sided games (3 v 3)

Integrate both energy systems through 4 x 4 minute games with 1-minute active recovery, maintaining high intensity while developing sport-specific skills.

Final round

Includes anaerobic power development through 6 x 20 second full-court sprint/dribble combinations with 40 seconds recovery.

Cool-down

Appropriately returns to aerobic intensity (60% max HR) through structured shooting drills for 5-10 minutes.

HMS, BM EQ-Bank 246

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

Effectively utilises SIT with repeated maximal sprints (6-8 x 40 m) with direction changes, reflecting game-specific movement patterns.
Rest periods (2-3 minutes) allow complete ATP-PCr recovery between efforts.
Effectively includes contact-specific HIIT through small-sided games (4 x 4 minutes) incorporating tackling at 90% intensity with 2-minute recovery periods.

Tennis player

Anaerobic training successfully incorporates court-specific movement patterns through shorter duration efforts (15-20 seconds) focusing on acceleration/deceleration.
Example: 6 x 4 point sequences at maximal intensity.
Tennis HIIT appropriately modifies work:rest ratios (1:3) to reflect match conditions, with 20-second maximal rallies followed by 60-second recovery, simulating time between points.

Both sports

Effectively utilise progressive overload by decreasing rest periods and increasing work intervals as fitness improves across the season.

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Sample Answer

Rugby league player

Effectively utilises SIT with repeated maximal sprints (6-8 x 40 m) with direction changes, reflecting game-specific movement patterns.
Rest periods (2-3 minutes) allow complete ATP-PCr recovery between efforts.
Effectively includes contact-specific HIIT through small-sided games (4 x 4 minutes) incorporating tackling at 90% intensity with 2-minute recovery periods.

Tennis player

Anaerobic training successfully incorporates court-specific movement patterns through shorter duration efforts (15-20 seconds) focusing on acceleration/deceleration.
Example: 6 x 4 point sequences at maximal intensity.
Tennis HIIT appropriately modifies work:rest ratios (1:3) to reflect match conditions, with 20-second maximal rallies followed by 60-second recovery, simulating time between points.

Both sports

Effectively utilise progressive overload by decreasing rest periods and increasing work intervals as fitness improves across the season.

HMS, BM EQ-Bank 245

Discuss how HIIT training can be modified for different fitness levels in a group fitness class. (6 marks)

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Sample Answer

Beginner

Modifications include longer active recovery periods (1:2 work:rest ratio) and lower intensity work intervals (75-80% max HR).
Example: 30 seconds work/60 seconds recovery.

Intermediate

Effectively train using 1:1 work:rest ratios with increased work intensity (80-85% max HR).
Example: 40 seconds work/40 seconds recovery.

Advanced

Successfully utilise shorter recovery periods (2:1 work:rest ratio) and near-maximal work intervals (85-95% max HR).
Example: 40 seconds work/20 seconds recovery.

Differing fitness levels

Exercise selection modifications effectively cater to different fitness levels.
Example: beginners perform step-ups while advanced participants perform box jumps.
Monitoring intensity through Rate of Perceived Exertion (RPE) proves effective for individual effort regulation within group setting.

Show Worked Solution

Sample Answer

Beginner

Modifications include longer active recovery periods (1:2 work:rest ratio) and lower intensity work intervals (75-80% max HR).
Example: 30 seconds work/60 seconds recovery.

Intermediate

Effectively train using 1:1 work:rest ratios with increased work intensity (80-85% max HR).
Example: 40 seconds work/40 seconds recovery.

Advanced

Successfully utilise shorter recovery periods (2:1 work:rest ratio) and near-maximal work intervals (85-95% max HR).
Example: 40 seconds work/20 seconds recovery.

Differing fitness levels

Exercise selection modifications effectively cater to different fitness levels.
Example: beginners perform step-ups while advanced participants perform box jumps.
Monitoring intensity through Rate of Perceived Exertion (RPE) proves effective for individual effort regulation within group setting.

HMS, BM EQ-Bank 242

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

Pre-Season (6-8 weeks)

Emphasises aerobic base development through continuous training methods.
Sessions include long slow distance running (45-60 minutes at 60-70% max HR) and fartlek training incorporating varied terrain and speeds.
This develops essential cardiovascular adaptations including increased stroke volume and improved oxygen utilisation.

Early competition phase

Introduces progressive integration of High Intensity Interval Training (HIIT).
Sessions include 4-6 sets of 4-minute high-intensity game-specific drills (85-90% max HR) with 2-minute active recovery periods.
This develops the anaerobic capacity needed for repeated sprint efforts during matches.

Mid-season training

Maintains aerobic fitness through modified continuous training (2 x 30 minutes at 70-75% max HR) while increasing anaerobic power through Sprint Interval Training (SIT).
SIT sessions include 8-10 repetitions of 30-second maximal effort sprints with ball control, with 2-minute rest periods.

Peak competition phase

Focuses on maintaining both energy systems through sport-specific combination training.
Example session includes 3 x 10 minute small-sided games (aerobic) interspersed with 4 x 30 second maximal sprint drills (anaerobic).

Show Worked Solution

Sample Answer

Pre-Season (6-8 weeks)

Emphasises aerobic base development through continuous training methods.
Sessions include long slow distance running (45-60 minutes at 60-70% max HR) and fartlek training incorporating varied terrain and speeds.
This develops essential cardiovascular adaptations including increased stroke volume and improved oxygen utilisation.

Early competition phase

Introduces progressive integration of High Intensity Interval Training (HIIT).
Sessions include 4-6 sets of 4-minute high-intensity game-specific drills (85-90% max HR) with 2-minute active recovery periods.
This develops the anaerobic capacity needed for repeated sprint efforts during matches.

Mid-season training

Maintains aerobic fitness through modified continuous training (2 x 30 minutes at 70-75% max HR) while increasing anaerobic power through Sprint Interval Training (SIT).
SIT sessions include 8-10 repetitions of 30-second maximal effort sprints with ball control, with 2-minute rest periods.

Peak competition phase

Focuses on maintaining both energy systems through sport-specific combination training.
Example session includes 3 x 10 minute small-sided games (aerobic) interspersed with 4 x 30 second maximal sprint drills (anaerobic).

HMS, BM EQ-Bank 241

Compare continuous training and High Intensity Interval Training (HIIT) methods and their application in basketball. (5 marks)

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Sample Answer

Continuous training

Maintains steady moderate intensity (60-75% max HR) for extended periods (20-60 minutes) without rest intervals.
In basketball, this could involve continuous court drills or off-court running focusing on developing the aerobic base needed for game endurance.
Early season continuous training builds fundamental cardiovascular adaptations including increased stroke volume, improved oxygen delivery to muscles, and enhanced mitochondrial density.
These adaptations provide the fitness foundation needed for more intense training phases.

High Intensity Interval Training (HIIT)

HIIT alternates high intensity work periods (85-95% max HR) with active recovery (60-70% max HR).
Basketball-specific HIIT might include 4 x 4 minute quarters of full-court pressing drills with 1-minute active recovery periods of walking or light jogging between sets.
HIIT better replicates actual game demands by training both aerobic and anaerobic energy systems simultaneously.
The high intensity periods mirror game situations like fast breaks and defensive pressure, while active recovery reflects lower intensity periods during free throws or time-outs.

Conclusion

Training program design should progress from predominantly continuous training in pre-season to increased HIIT sessions approaching competition phase.
This periodisation ensures players develop both the aerobic base and sport-specific anaerobic capacity needed for optimal game performance.

Show Worked Solution

Sample Answer

Continuous training

Maintains steady moderate intensity (60-75% max HR) for extended periods (20-60 minutes) without rest intervals.
In basketball, this could involve continuous court drills or off-court running focusing on developing the aerobic base needed for game endurance.
Early season continuous training builds fundamental cardiovascular adaptations including increased stroke volume, improved oxygen delivery to muscles, and enhanced mitochondrial density.
These adaptations provide the fitness foundation needed for more intense training phases.

High Intensity Interval Training (HIIT)

HIIT alternates high intensity work periods (85-95% max HR) with active recovery (60-70% max HR).
Basketball-specific HIIT might include 4 x 4 minute quarters of full-court pressing drills with 1-minute active recovery periods of walking or light jogging between sets.
HIIT better replicates actual game demands by training both aerobic and anaerobic energy systems simultaneously.
The high intensity periods mirror game situations like fast breaks and defensive pressure, while active recovery reflects lower intensity periods during free throws or time-outs.

Conclusion

Training program design should progress from predominantly continuous training in pre-season to increased HIIT sessions approaching competition phase.
This periodisation ensures players develop both the aerobic base and sport-specific anaerobic capacity needed for optimal game performance.

HMS, BM EQ-Bank 237 MC

The most appropriate training method for improving a rugby league player's ability to repeatedly sprint during a game would be:

Long slow distance training
Circuit training
Sprint Interval Training
Continuous aerobic training

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$C$

Show Worked Solution

Consider Option C: Sprint Interval Training

SIT develops repeat sprint ability needed in rugby league

Other Options:

A is incorrect: Too low intensity for game demands
B is incorrect: Not specific enough to sprint requirements
D is incorrect: Lacks high intensity needed for sprint development

$\Rightarrow C$

HMS, BM EQ-Bank 234 MC

A soccer team's pre-season program includes:

45 minutes continuous running
Heart rate maintained at 70% max
No rest intervals
Varied terrain and speeds based on coach signals

This training session would be classified as:

Continuous aerobic training
Sprint Interval Training (SIT)
Fartlek training
Circuit training

Show Answers Only

$C$

Show Worked Solution

Consider Option C: Fartlek training

Varied speeds/terrain while maintaining continuous movement is characteristic of fartlek training

Other Options:

A is incorrect: Continuous training doesn’t include speed variations
B is incorrect: SIT involves structured high intensity intervals
D is incorrect: Circuit training involves different exercise stations

$\Rightarrow C$

HMS, BM EQ-Bank 233 MC

A soccer player completes the following training session:

45 minutes continuous running
Heart rate maintained at 70% max
No rest intervals

This training session would be classified as:

Aerobic endurance training
Anaerobic power training
Speed endurance training
Resistance training

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$A$

Show Worked Solution

Consider Option A: Aerobic endurance training

Extended duration at moderate intensity targets aerobic system

Other Options:

B is incorrect: Anaerobic power requires high intensity short bursts
C is incorrect: Speed endurance involves intervals
D is incorrect: Resistance training involves external loads

$\Rightarrow A$

HMS, BM EQ-Bank 227

Describe how continuous training differs from interval training. Use examples to support your answer. (4 marks)

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Sample Answer

Continuous Training

Maintains a steady intensity throughout the entire session (typically 60-75% MHR).
Continuous training has no rest periods which forces ongoing aerobic system adaptation.

Interval Training

Deliberately alternates between high intensity work periods (85-95% MHR) and lower intensity recovery phases, creating varying physiological demands on the body.
Incorporates specific active or passive recovery periods between work efforts to allow partial ATP-PCr replenishment and lactate removal.

Examples

A 30-minute jog at 65% MHR for continuous training develops aerobic capacity through sustained oxygen demand, compared to 10 x 200m sprints with 2-minute recovery periods which develops both aerobic power and anaerobic capacity through alternating energy system use.

Energy systems are primarily targeted

Continuous training predominantly develops the aerobic system through sustained moderate intensity exercise.
Intervals develop both aerobic and anaerobic systems due to the varying intensities and inclusion of high-intensity efforts that require immediate energy.

Show Worked Solution

Sample Answer

Continuous Training

Maintains a steady intensity throughout the entire session (typically 60-75% MHR).
Continuous training has no rest periods which forces ongoing aerobic system adaptation.

Interval Training

Deliberately alternates between high intensity work periods (85-95% MHR) and lower intensity recovery phases, creating varying physiological demands on the body.
Incorporates specific active or passive recovery periods between work efforts to allow partial ATP-PCr replenishment and lactate removal.

Examples

A 30-minute jog at 65% MHR for continuous training develops aerobic capacity through sustained oxygen demand, compared to 10 x 200m sprints with 2-minute recovery periods which develops both aerobic power and anaerobic capacity through alternating energy system use.

Energy systems are primarily targeted

Continuous training predominantly develops the aerobic system through sustained moderate intensity exercise.
Intervals develop both aerobic and anaerobic systems due to the varying intensities and inclusion of high-intensity efforts that require immediate energy.

HMS, BM EQ-Bank 225 MC

Which row correctly shows the characteristics of continuous training?

Long duration, moderate intensity, no rest periods
Short duration, high intensity, frequent rest periods
Long duration, high intensity, no rest periods
Short duration, moderate intensity, frequent rest periods

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$A$

Show Worked Solution

Consider Option A: Long duration, moderate intensity, no rest periods

Continuous training is long duration, moderate intensity with no rest periods

Other Options:

B is incorrect: Describes interval training
C is incorrect: Not sustainable without rest
D is incorrect: Too short for aerobic adaptations

$\Rightarrow A$

HMS, BM EQ-Bank 217

Compare the hydration needs of sprinters versus endurance athletes. (3 marks)

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Sample Answer

Endurance athletes lose 2-3 litres fluid per hour requiring electrolyte replacement during activity to prevent performance decline
Sprinters lose minimal fluid through brief intense effort requiring basic pre/post hydration protocols
Timing of hydration varies significantly: endurance athletes need 150-300 millilitres every 15-20 minutes during activity while sprinters focus on achieving urine color of pale straw 4 hours pre-event to ensure optimal hydration status

Show Worked Solution

Sample Answer

Endurance athletes lose 2-3 litres fluid per hour requiring electrolyte replacement during activity to prevent performance decline
Sprinters lose minimal fluid through brief intense effort requiring basic pre/post hydration protocols
Timing of hydration varies significantly: endurance athletes need 150-300 millilitres every 15-20 minutes during activity while sprinters focus on achieving urine color of pale straw 4 hours pre-event to ensure optimal hydration status

HMS, BM EQ-Bank 216

Explain why timing of nutrient intake differs for a weightlifter versus a marathon runner. (3 marks)

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Sample Answer

Weightlifter needs high carbohydrate meal 3-4 hours pre-lift to ensure immediate ATP availability for explosive movements
Marathon runner requires carbohydrate loading 48 hours before and regular glucose intake during event for sustained energy
Recovery nutrition within 30 minutes post-exercise varies: protein focus for weightlifter, mixed macro recovery for runner

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Sample Answer

Weightlifter needs high carbohydrate meal 3-4 hours pre-lift to ensure immediate ATP availability for explosive movements
Marathon runner requires carbohydrate loading 48 hours before and regular glucose intake during event for sustained energy
Recovery nutrition within 30 minutes post-exercise varies: protein focus for weightlifter, mixed macro recovery for runner

HMS, BM EQ-Bank 213 MC

An endurance cyclist should prioritise which nutritional strategy during a 4-hour race?

High protein intake
High fat consumption
Protein shakes
Regular carbohydrate consumption

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$D$

Show Worked Solution

Consider Option D: Regular carbohydrate consumption

Maintains blood glucose for aerobic energy production

Other Options:

A is incorrect: Not primary fuel source
B is incorrect: Too slow to metabolise
C is incorrect: Not immediate energy source

$\Rightarrow D$

HMS, BM EQ-Bank 212 MC

A sprinter requires which micronutrient for optimal anaerobic energy production?

Vitamin D
Vitamin B
Vitamin C
Vitamin E

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$B$

Show Worked Solution

Consider Option B: Vitamin B

Essential for ATP production and energy metabolism

Other Options:

A is incorrect: Bone health primarily
C is incorrect: Immune function primarily
D is incorrect: Antioxidant primarily

$\Rightarrow B$

Statistics, EXT1 S1 2024 MET1 4

Let $X$ be a binomial random variable where $X \sim \operatorname{Bi}\left(4, \dfrac{9}{10}\right)$.

Find the standard deviation of $X$. (1 mark)

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Find $\operatorname{Pr}(X<2)$. (2 marks)

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a. $\operatorname{sd}(X)=\dfrac{3}{5}$

b. $\dfrac{37}{10\,000}$

Show Worked Solution

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.	$\operatorname{Pr}(X<2)$	$=\operatorname{Pr}(X=0)+\operatorname{Pr}(X=1)$
		$=\ ^4C _0\left(\dfrac{9}{10}\right)^0\left(\dfrac{1}{10}\right)^4+\ ^4C_1\left(\dfrac{9}{10}\right)^1\left(\dfrac{1}{10}\right)^3$
		$= 1 \times \dfrac {1}{10\,000} + 4 \times \dfrac{9}{10} \times \dfrac{1}{1000}$
		$=\dfrac{37}{10\,000}$

Mean mark (b) 51%.

Functions, 2ADV F2 2024 MET1 3*

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)

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Show Worked Solution

$\text{Find asymptotes:}$

$(x+3) \neq 0\ \ \Rightarrow\ \ \text{Asymptote at}\ x=-3$

$\text{As}\ x \rightarrow \infty, \ \dfrac{1}{(x+3)^2} \rightarrow 0\ \ \Rightarrow \ \ \text{Asymptote at}\ y=-2$

$y\text{-intercept:}\ x=0$

$y=\dfrac{1}{(0+3)^2}-2=-\dfrac{17}{9}$

$x\text{-intercepts:}\ y=0$

$\dfrac{1}{(x+3)^2}-2$	$=0$
$(x+3)^2$	$=\dfrac{1}{2}$
$x+3$	$=\pm\dfrac{1}{\sqrt{2}}$
$x$	$=-3\pm\dfrac{1}{\sqrt{2}}$

HMS, BM EQ-Bank 202

Explain why magnesium requirements increase during intense resistance training programs. (4 marks)

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Sample Answer

Essential for muscle contraction and relaxation cycles during heavy lifting sessions as magnesium regulates calcium uptake in muscle cells which directly impacts force production
Supports protein synthesis for muscle repair and growth following resistance training by activating enzymes required for building new muscle tissue
Helps regulate energy metabolism which is crucial during high-intensity exercise because magnesium is required for ATP production and glucose metabolism
Lost through sweat during intense training requiring increased intake for optimal recovery, with heavy training sessions potentially depleting up to 15-20% of daily magnesium stores

Show Worked Solution

Sample Answer

Essential for muscle contraction and relaxation cycles during heavy lifting sessions as magnesium regulates calcium uptake in muscle cells which directly impacts force production
Supports protein synthesis for muscle repair and growth following resistance training by activating enzymes required for building new muscle tissue
Helps regulate energy metabolism which is crucial during high-intensity exercise because magnesium is required for ATP production and glucose metabolism
Lost through sweat during intense training requiring increased intake for optimal recovery, with heavy training sessions potentially depleting up to 15-20% of daily magnesium stores

HMS, BM EQ-Bank 199 MC

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?

Simple carbohydrates
Vitamin A
Omega-3 fatty acids
Protein

Show Answers Only

$C$

Show Worked Solution

Consider Option C: Omega-3 fatty acids

Omega-3 fatty acids have anti-inflammatory properties that help reduce joint inflammation.

Other Options:

A is incorrect: Simple carbs don’t impact inflammation
B is incorrect: Vitamin A primarily affects vision
D is incorrect: Protein repairs tissue but doesn’t reduce inflammation

$\Rightarrow C$

HMS, BM EQ-Bank 195

Explain how carbohydrate loading can improve performance for a marathon runner. (4 marks)

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Sample Answer

Maximises muscle glycogen stores before competition through gradual increase in carbohydrate intake over 3-4 days
Provides sustained energy release during prolonged exercise by ensuring adequate fuel stores in working muscles
Delays onset of fatigue in later stages of race by maintaining blood glucose levels when glycogen stores deplete
Maintains blood glucose levels for optimal brain function which helps preserve technique and decision-making ability

Show Worked Solution

Sample Answer

Maximises muscle glycogen stores before competition through gradual increase in carbohydrate intake over 3-4 days
Provides sustained energy release during prolonged exercise by ensuring adequate fuel stores in working muscles
Delays onset of fatigue in later stages of race by maintaining blood glucose levels when glycogen stores deplete
Maintains blood glucose levels for optimal brain function which helps preserve technique and decision-making ability

HMS, BM EQ-Bank 192 MC

A triathlete has just completed the swimming leg of their event. Which macronutrient should they prioritise during their transition to cycling?

Protein
Essential fatty acids
Branch chain amino acids
Carbohydrates

Show Answers Only

$D$

Show Worked Solution

Consider Option D: Carbohydrates

Carbohydrates are essential to replenish glycogen stores for continued endurance performance.

Other Options:

A is incorrect: Protein not primary fuel source for immediate energy
B is incorrect: Fats too slow to metabolize for immediate energy
C is incorrect: BCAAs not primary energy source during exercise

$\Rightarrow D$

HMS, BM EQ-Bank 191

A swimmer performs a 200 m freestyle race.

Explain how TWO different energy systems contribute to fatigue during this event. (4 marks)

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Sample Answer

Any TWO of the following

In the first 10-15 seconds, the ATP-PCr system rapidly depletes its phosphagen stores, reducing the power output available for the explosive start and initial sprint phase.
The glycolytic system dominates through the middle section of the race, causing lactic acid accumulation in the working muscles which decreases the efficiency of muscle contractions.
The aerobic system becomes increasingly important in the final 50 m, but oxygen delivery may become limited, contributing to a reduction in ATP production and subsequent power output.

Show Worked Solution

Sample Answer

Any TWO of the following

In the first 10-15 seconds, the ATP-PCr system rapidly depletes its phosphagen stores, reducing the power output available for the explosive start and initial sprint phase.
The glycolytic system dominates through the middle section of the race, causing lactic acid accumulation in the working muscles which decreases the efficiency of muscle contractions.
The aerobic system becomes increasingly important in the final 50 m, but oxygen delivery may become limited, contributing to a reduction in ATP production and subsequent power output.

HMS, BM EQ-Bank 190

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

The depletion of muscle glycogen throughout multiple games reduces energy availability for explosive movements like jumping and diving, leading to decreased power output in attacking plays.
Progressive dehydration occurs during play in hot conditions, causing a decrease in blood plasma volume which reduces oxygen delivery to working muscles and impairs coordination for precise ball skills.

Show Worked Solution

Sample Answer

The depletion of muscle glycogen throughout multiple games reduces energy availability for explosive movements like jumping and diving, leading to decreased power output in attacking plays.
Progressive dehydration occurs during play in hot conditions, causing a decrease in blood plasma volume which reduces oxygen delivery to working muscles and impairs coordination for precise ball skills.

HMS, BM EQ-Bank 187

Outline TWO causes of fatigue when an athlete performs a 100 m sprint. (3 marks)

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Sample Answer

Any 2 of the following

The ATP-PCr system depletes quickly during the 100 m sprint as the phosphagen stores in the muscles are exhausted within the first 10 seconds of maximal effort.
The central nervous system experiences fatigue due to the rapid and continuous recruitment of fast-twitch muscle fibres required for explosive power throughout the sprint.
As the glycolytic system begins to engage towards the end of the race, lactic acid starts accumulating in the working muscles, contributing to performance decline.

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Sample Answer

Any 2 of the following

The ATP-PCr system depletes quickly during the 100 m sprint as the phosphagen stores in the muscles are exhausted within the first 10 seconds of maximal effort.
The central nervous system experiences fatigue due to the rapid and continuous recruitment of fast-twitch muscle fibres required for explosive power throughout the sprint.
As the glycolytic system begins to engage towards the end of the race, lactic acid starts accumulating in the working muscles, contributing to performance decline.

Calculus, 2ADV C3 2024 MET1 1b

Let $f(x)=\log _e\left(x^3-3 x+2\right)$.

Find $f^{\prime}(3)$ (2 marks)

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$\dfrac{6}{5}$

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	$f(x)$	$=\log_{e}(x^3-3x+2)$
	$f^{\prime}(x)$	$=\dfrac{3x^2-3}{x^3-3x+2}$
	$f^{\prime}(3)$	$=\dfrac{3(3)^2-3}{(3)^3-3(3)+2}=\dfrac{6}{5}$

HMS, BM EQ-Bank 181

Explain how the lactic acid system contributes to energy production during a 200 m sprint. (4 marks)

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Sample Answer

During the 200 m sprint, glucose is broken down without oxygen through glycolysis to produce ATP for sustained high-intensity muscle contractions.
This anaerobic process creates lactic acid as a by-product which accumulates in the working muscles causing fatigue.
The lactic acid system can maintain high-intensity performance for up to 60-90 seconds before waste products significantly impair muscle function.
As a 200 m sprint typically takes 20-25 seconds, this system provides the majority of energy required after the initial ATP-PCr stores are depleted at around 10 seconds.

Show Worked Solution

Sample Answer

During the 200 m sprint, glucose is broken down without oxygen through glycolysis to produce ATP for sustained high-intensity muscle contractions.
This anaerobic process creates lactic acid as a by-product which accumulates in the working muscles causing fatigue.
The lactic acid system can maintain high-intensity performance for up to 60-90 seconds before waste products significantly impair muscle function.
As a 200 m sprint typically takes 20-25 seconds, this system provides the majority of energy required after the initial ATP-PCr stores are depleted at around 10 seconds.

HMS, BM EQ-Bank 180

Outline how the ATP-PCr system provides energy for immediate muscle contraction. (3 marks)

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Sample Answer

When an impulse from the nervous system triggers muscle contraction, ATP rapidly splits into ADP and Pi releasing immediate energy.
During high-intensity activity, creatine phosphate breaks down to release a phosphate molecule which combines with ADP to replenish ATP stores.
This energy system can sustain maximal performance for approximately 10-15 seconds before creatine phosphate stores are depleted requiring 3-5 minutes for full recovery.

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Sample Answer

When an impulse from the nervous system triggers muscle contraction, ATP rapidly splits into ADP and Pi releasing immediate energy.
During high-intensity activity, creatine phosphate breaks down to release a phosphate molecule which combines with ADP to replenish ATP stores.
This energy system can sustain maximal performance for approximately 10-15 seconds before creatine phosphate stores are depleted requiring 3-5 minutes for full recovery.

HMS, BM EQ-Bank 179 MC

During a 400 m sprint race, an athlete's performance is most dependent on which combination of energy systems?

ATP-PCr and Aerobic
Lactic Acid and ATP-PCr
Aerobic and Lactic Acid
Equal contribution from all three systems

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$B$

Show Worked Solution

Consider Option B: Lactic Acid and ATP-PCr

A 400 m sprint typically takes 45-60 seconds requiring both immediate energy from ATP-PCr for the explosive start and lactic acid system for maintaining the high-intensity effort throughout the race.

Other Options:

A is incorrect: Aerobic system isn’t dominant in this duration
C is incorrect: Aerobic system isn’t significantly involved at this intensity/duration
D is incorrect: All systems don’t contribute equally in this event

$\Rightarrow B$

HMS, BM EQ-Bank 177

Explain how the rate of recovery differs between anaerobic energy systems and impacts performance. (4 marks)

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Sample Answer

ATP-PCr system demonstrates rapid initial recovery with 70% replenishment within 30 seconds, allowing repeated short bursts of maximal power output in sports like gymnastics or sprinting.
Glycolytic system requires significantly longer recovery periods of 3-5 minutes due to the need for lactate clearance, which directly affects an athlete’s ability to maintain intensity in events like 400 m running.
Recovery rates create distinct limitations for each system, where short recovery compromises ATP-PCr power output and insufficient glycolytic recovery leads to deteriorating performance through accumulated fatigue.
Both systems can improve recovery efficiency through specific training adaptations, with ATP-PCr enhancing phosphocreatine resynthesis and glycolytic developing better lactate buffering capacity.

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Sample Answer

ATP-PCr system demonstrates rapid initial recovery with 70% replenishment within 30 seconds, allowing repeated short bursts of maximal power output in sports like gymnastics or sprinting.
Glycolytic system requires significantly longer recovery periods of 3-5 minutes due to the need for lactate clearance, which directly affects an athlete’s ability to maintain intensity in events like 400 m running.
Recovery rates create distinct limitations for each system, where short recovery compromises ATP-PCr power output and insufficient glycolytic recovery leads to deteriorating performance through accumulated fatigue.
Both systems can improve recovery efficiency through specific training adaptations, with ATP-PCr enhancing phosphocreatine resynthesis and glycolytic developing better lactate buffering capacity.

Networks, STD2 N2 2024 GEN2 13*

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)

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HMS, BM EQ-Bank 173 MC

During high-intensity interval training, an athlete performs 400 m sprints. Which recovery period would be most appropriate to allow lactate clearance between efforts?

30 seconds active recovery
1 minute passive recovery
3 minutes active recovery
5 minutes passive recovery

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$C$

Show Worked Solution

Consider Option C: 3 minutes active recovery

Active recovery aids lactate removal within optimal timeframe

Other Options:

A is incorrect: Insufficient time for lactate clearance
B is incorrect: Passive recovery less effective for lactate removal
D is incorrect: Unnecessarily long recovery period

$\Rightarrow C$

HMS, BM EQ-Bank 171

Compare the duration limitations of the ATP-PCr and Glycolytic energy systems. (4 marks)

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Sample Answer

ATP-PCr system is limited to 0-10 seconds maximum duration before phosphocreatine stores deplete, making it suitable only for explosive actions like vertical jumps or short sprints.
Glycolytic system sustains high-intensity activity for 30-90 seconds before lactic acid accumulation causes fatigue, supporting activities like 400m sprints or intensive game sequences.
ATP-PCr requires approximately 3 minutes for full recovery between maximal efforts, with 70% regeneration occurring in the first 30 seconds due to efficient phosphate resynthesis.
Glycolytic system needs 5-8 minutes for complete recovery as lactate must be removed from muscles and blood pH restored, limiting repeated high-intensity efforts within this timeframe.
Both systems have specific duration constraints affecting training design.

Show Worked Solution

Sample Answer

ATP-PCr system is limited to 0-10 seconds maximum duration before phosphocreatine stores deplete, making it suitable only for explosive actions like vertical jumps or short sprints.
Glycolytic system sustains high-intensity activity for 30-90 seconds before lactic acid accumulation causes fatigue, supporting activities like 400m sprints or intensive game sequences.
ATP-PCr requires approximately 3 minutes for full recovery between maximal efforts, with 70% regeneration occurring in the first 30 seconds due to efficient phosphate resynthesis.
Glycolytic system needs 5-8 minutes for complete recovery as lactate must be removed from muscles and blood pH restored, limiting repeated high-intensity efforts within this timeframe.
Both systems have specific duration constraints affecting training design.

HMS, BM EQ-Bank 167 MC

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?

ATP-PCr
Glycolytic
Aerobic
ATP-PCr and Glycolytic combined

Show Answers Only

$A$

Show Worked Solution

Consider Option A: ATP-PCr

Duration exceeds ATP-PCr capacity

Other Options:

B is incorrect: 30s rallies heavily utilise glycolytic system
C is incorrect: Aerobic system aids recovery between rallies
D is incorrect: Both systems contribute significantly

$\Rightarrow A$

HMS, BM EQ-Bank 165

Compare and contrast how the ATP-PCr and Glycolytic energy systems respond to high intensity exercise. (4 marks)

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Sample Answer

ATP-PCr provides immediate energy for very high intensity but depletes rapidly within 10 seconds
Glycolytic system produces more ATP but takes longer to activate, sustaining high intensity for 30-90 seconds
ATP-PCr has no by-products while glycolytic produces lactic acid causing fatigue
Both systems can be trained for greater capacity but through different intensity protocols

Show Worked Solution

Sample Answer

ATP-PCr provides immediate energy for very high intensity but depletes rapidly within 10 seconds
Glycolytic system produces more ATP but takes longer to activate, sustaining high intensity for 30-90 seconds
ATP-PCr has no by-products while glycolytic produces lactic acid causing fatigue
Both systems can be trained for greater capacity but through different intensity protocols

HMS, BM EQ-Bank 162 MC

A tennis player is in a rally lasting 45 seconds at moderate-high intensity. Which energy system sequence best represents their energy production?

Glycolytic → ATP-PCr → Aerobic
Aerobic → ATP-PCr → Glycolytic
ATP-PCr → Aerobic → Glycolytic
ATP-PCr → Glycolytic → Aerobic

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$D$

Show Worked Solution

Consider Option D: ATP-PCr → Glycolytic → Aerobic

Shows the natural progression of energy systems as intensity/duration increases

Other Options:

A is incorrect: ATP-PCr is the initial energy system
B is incorrect: ATP-PCr is the initial energy system and aerobic takes longer to become predominant
C is incorrect: Glycolytic precedes Aerobic for moderate-high intensity

$\Rightarrow D$

HMS, BM EQ-Bank 161 MC

During a 400 m race at high intensity, an athlete experiences muscular fatigue. What is the main cause?

Depletion of glycogen stores
Accumulation of lactic acid
Lack of oxygen
Depletion of creatine phosphate

Show Answers Only

$B$

Show Worked Solution

Consider Option B: Accumulation of lactic acid

Lactic acid accumulation during high intensity glycolytic system use causes fatigue

Other Options:

A is incorrect: Glycogen depletion occurs over longer duration events
C is incorrect: Oxygen debt occurs after exercise completion
D is incorrect: CP depletion occurs in shorter activities under 10 seconds

$\Rightarrow B$

EXAMCOPY Algebra, STD2 A4 2019 HSC 33

The time taken for a car to travel between two towns at a constant speed varies inversely with its speed.

It takes 1.5 hours for the car to travel between the two towns at a constant speed of 80 km/h.

Calculate the distance between the two towns. (1 mark)

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By first plotting four points, draw the curve that shows the time taken to travel between the two towns at different constant speeds. (3 marks)

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`120\ text(km)`

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a.	`D`	`= S xx T`
		`= 80 xx 1.5`
		`= 120\ text(km)`

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ s\ \ \rule[-1ex]{0pt}{0pt} & 20 & 40 & 60 & 80 \\
\hline
\rule{0pt}{2.5ex} t \rule[-1ex]{0pt}{0pt} & 6 & 3 & 2 & 1.5 \\
\hline
\end{array}

EXAMCOPY Algebra, STD2 A4 2014 HSC 29a

The cost of hiring an open space for a music festival is $120 000. The cost will be shared equally by the people attending the festival, so that `C` (in dollars) is the cost per person when `n` people attend the festival.

Complete the table below by filling in the THREE missing values. (1 mark)
\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Number of people} (n) \rule[-1ex]{0pt}{0pt} & \ 500\ & \ 1000 \ & 1500 \ & 2000 \ & 2500\ & 3000 \ \\
\hline
\rule{0pt}{2.5ex}\text{Cost per person} (C)\rule[-1ex]{0pt}{0pt} & & & & 60 & 48\ & 40 \ \\
\hline
\end{array}
Using the values from the table, draw the graph showing the relationship between `n` and `C`. (2 marks)
What equation represents the relationship between `n` and `C`? (1 mark)

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Give ONE limitation of this equation in relation to this context. (1 mark)

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Is it possible for the cost per person to be $94? Support your answer with appropriate calculations. (1 mark)

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\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Number of people} (n) \rule[-1ex]{0pt}{0pt} & \ 500\ & \ 1000 \ & 1500 \ & 2000 \ & 2500\ & 3000 \ \\
\hline
\rule{0pt}{2.5ex}\text{Cost per person} (C)\rule[-1ex]{0pt}{0pt} & 240 & 120 & 80 & 60 & 48\ & 40 \ \\
\hline
\end{array}

ii.

iii. `C = (120\ 000)/n`

`n\ text(must be a whole number)`

iv. `text(Limitations can include:)`

`•\ n\ text(must be a whole number)`

`•\ C > 0`

v. `text(If)\ C = 94:`

`94`	`= (120\ 000)/n`
`94n`	`= 120\ 000`
`n`	`= (120\ 000)/94`
	`= 1276.595…`

`:.\ text(C)text(ost cannot be $94 per person,)`

`text(because)\ n\ text(isn’t a whole number.)`

Show Worked Solution

ii.

♦ Mean mark (iii) 48%

iii. `C = (120\ 000)/n`

♦♦♦ Mean mark (iv) 7%
COMMENT: When asked for limitations of an equation, look carefully at potential restrictions with respect to both the domain and range.

iv. `text(Limitations can include:)`

`•\ n\ text(must be a whole number)`

`•\ C > 0`

v. `text(If)\ C = 94`

`=> 94`	`= (120\ 000)/n`
`94n`	`= 120\ 000`
`n`	`= (120\ 000)/94`
	`= 1276.595…`

♦ Mean mark (v) 38%

`:.\ text(C)text(ost cannot be $94 per person,)`

`text(because)\ n\ text(isn’t a whole number.)`

EXAMCOPY Algebra, STD2 A4 2024 HSC 9 MC

The time taken to paint a school varies inversely with the number of painters completing the task.

It takes 6 painters a total of 20 days to paint a school.

How many days would it take 15 painters to paint the same school?

4.5
8
15.5
50

Show Answers Only

$B$

Show Worked Solution

$T \propto \dfrac{1}{N} \ \Rightarrow \ \ T=\dfrac{k}{N}$

$\text {Find}\ k\ \text{given}\ \ T=20\ \ \text {when}\ \ N=6 \text {:}$

$20=\dfrac{k}{6} \ \Rightarrow\ \ k=120$

$\therefore\ T=\dfrac{120}{N}$

$\text {Find}\ T \ \text {if}\ \ N=15:$

$T=\dfrac{120}{15}=8 \text { days }$

$\Rightarrow B$

PHYSICS, M1 EQ-Bank 9

An oil tanker is travelling eastward along a straight shipping route at an initial velocity of 30 ms$^{-1}$. The captain then applies the engines in reverse, causing the tanker to slow down at a constant rate until its velocity decreases to 12 ms$^{-1}$.

If it travelled 9000 metres while decelerating, determine

the magnitude and direction of the tanker's acceleration. (2 marks)

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the time over which the tanker changed its velocity. (2 marks)

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a. $a=-0.042\ \text{ms}^{-2}$

b. $674\ \text{sec}$

Show Worked Solution

a. $\Delta v = 30-12=-18\ \text{ms}^{-1}$

$s=9\ \text{km}\ = 9000\ \text{m}$

$\text{Since no time of deceleration is given,}$

$\text{Using}\ \ v^2=u^2-2as:$

$a=\dfrac{v^2-u^2}{2s} = \dfrac{12^2-30^2}{2 \times 9000} = -0.042\ \text{ms}^{-2}$

$\therefore a=0.042\ \text{ms}^{-2}\ \text{in the opposite direction to initial velocity.}$

b. $\text{Find time of deceleration:}$

$v$	$=u + at$
$t$	$=\dfrac{v-u}{a}$
	$=\dfrac{12-30}{-0.042}$
	$=428.6\ \text{sec (1 d.p.)}$

PHYSICS, M1 EQ-Bank 8

A drone is travelling in a straight line at 56 ms$^{-1}$ and then slows down at a constant rate until its velocity reaches 18 ms$^{-1}$.

If it travelled 400 metres while decelerating, determine

the magnitude and direction of the drone's acceleration. (2 marks)

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the time over which the drone changed its velocity. (2 marks)

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a. $a=-3.515\ \text{ms}^{-2}$

b. $10.8\ \text{sec}$

Show Worked Solution

a. $\Delta v = 56-18=-38\ \text{ms}^{-1}$

$\text{Since no time of deceleration is given,}$

$\text{Using}\ \ v^2=u^2-2as:$

$a=\dfrac{v^2-u^2}{2s} = \dfrac{18^2-56^2}{2 \times 400} = -3.515\ \text{ms}^{-2}$

$\therefore a=3.515\ \text{ms}^{-2}\ \text{in the opposite direction to initial velocity.}$

b. $\text{Find time of deceleration:}$

$v$	$=u + at$
$t$	$=\dfrac{v-u}{a}$
	$=\dfrac{18-56}{-3.515}$
	$=10.8\ \text{sec (1 d.p.)}$

Financial Maths, STD2 F4 2024 GEN1 21 MC

Lee took out a loan of $121 000, with interest compounding monthly. He makes monthly repayments of $2228.40 for five years until the loan is repaid in full.

The total interest paid by Lee is closest to

$4434
$5465
$10 539
$12 704

Show Answers Only

$D$

Show Worked Solution

$\text{Repayments}$	$ =2228.40\times 12\times 5$
	$=$133\,704$

$\text{Interest}$	$=133\,704-121\,000$
	$=$12\,704$

$\Rightarrow D$

Mean mark 56%.

Statistics, STD2 S5 2024 GEN1 7 MC

Fiona plays nine holes of golf each week, and records her score.

Her mean score for all rounds in 2024 is 55.7

In one round, when she recorded a score of 48, her standardised score was $z=-1.75$

The standard deviation for score in 2024 is

1.1
2.3
4.4
6.95

Show Answers Only

$C$

Show Worked Solution

$z$	$=\dfrac{x-\overline{x}}{s_x}$
$-1.75$	$=\dfrac{48-55.7}{s_x}$
$s_x$	$=\dfrac{48-55.7}{-1.75}$
	$=4.4$

$\Rightarrow C$

Statistics, STD2 S1 2024 GEN1* 6

More than 11 000 athletes from more than 200 countries competed in the Tokyo Summer Olympic Games.

An analysis of the number of athletes per country produced the following five-number summary.

\begin{array}{|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Minimum} \rule[-1ex]{0pt}{0pt}& \textbf{First quartile } & \textbf{Median } & \textbf{Third quartile} & \textbf{Maximum } \\
\hline
\rule{0pt}{2.5ex} 2 \rule[-1ex]{0pt}{0pt}& 5 & 11 & 48 & 613 \\
\hline
\end{array}

Find the smallest number of athletes per country that would display as an outlier on a boxplot of this dataset. (2 marks)

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$C$

Show Worked Solution

$IQR=48-5=43$

$\text{Upper boundary}$	$=Q_3+1.5\times IQR$
	$=48+1.5\times 43$
	$=112.5$

$\therefore\ \text{Smallest number of athletes to show as an outlier = 113.}$

HMS, BM EQ-Bank 157

Compare the efficiency of ATP production between the glycolytic and aerobic systems. (5 marks)

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Sample Answer

The glycolytic system rapidly produces 2-3 ATP molecules through anaerobic glucose breakdown, supporting high-intensity activities lasting 10-60 seconds.
The aerobic system yields 36-38 ATP molecules per glucose molecule through complete oxidation, but occurs at a slower rate for sustained activities.
Glycolytic efficiency is limited by lactic acid accumulation causing fatigue and restricting continuous high-intensity performance.
The aerobic system produces CO₂ and H₂O as by-products, allowing sustained energy production without causing fatigue.
While more efficient in ATP yield, the aerobic system requires constant oxygen availability and can only support submaximal exercise intensities.

Show Worked Solution

Sample Answer

The glycolytic system rapidly produces 2-3 ATP molecules through anaerobic glucose breakdown, supporting high-intensity activities lasting 10-60 seconds.
The aerobic system yields 36-38 ATP molecules per glucose molecule through complete oxidation, but occurs at a slower rate for sustained activities.
Glycolytic efficiency is limited by lactic acid accumulation causing fatigue and restricting continuous high-intensity performance.
The aerobic system produces CO₂ and H₂O as by-products, allowing sustained energy production without causing fatigue.
While more efficient in ATP yield, the aerobic system requires constant oxygen availability and can only support submaximal exercise intensities.

HMS, BM EQ-Bank 155 MC

Which statement best explains why the aerobic system produces the most ATP?

It has the fastest reaction rate
It uses more glucose molecules
It doesn't produce waste products
It completes glucose breakdown

Show Answers Only

$D$

Show Worked Solution

Consider Option D: It completes glucose breakdown

The aerobic system completely breaks down glucose and allows for maximum ATP extraction (36-38 ATP) from each glucose molecule. Other systems only partially break down glucose.

Other Options:

A is incorrect: Aerobic system has slowest reaction rate of all 3 energy systems. ATP-PCr is fastest, followed by glycolytic then aerobic.
B is incorrect: The amount of glucose molecules used is not the determining factor in ATP production. It’s the completeness of the breakdown process.
C is incorrect: Aerobic system produces waste products (CO₂ and H₂O).

$\Rightarrow D$

HMS, BM EQ-Bank 150

Explain how glucose is used differently as a fuel source in the glycolytic and aerobic energy systems. (4 marks)

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Sample Answer

Glycolytic System:

Breaks down glucose without oxygen in sarcoplasm
Produces 2 – 3 ATP molecules through rapid glycolysis
Results in lactic acid as by-product
Powers high-intensity exercise 10 – 60 seconds

Aerobic System:

Complete glucose breakdown with oxygen in mitochondria
Produces 36 – 38 ATP through Krebs cycle/electron transport chain
Results in CO₂ and H₂O as by-products
Powers prolonged exercise 2+ minutes

Show Worked Solution

Sample Answer

Glycolytic System:

Breaks down glucose without oxygen in sarcoplasm
Produces 2 – 3 ATP molecules through rapid glycolysis
Results in lactic acid as by-product
Powers high-intensity exercise 10 – 60 seconds

Aerobic System:

Complete glucose breakdown with oxygen in mitochondria
Produces 36 – 38 ATP through Krebs cycle/electron transport chain
Results in CO₂ and H₂O as by-products
Powers prolonged exercise 2+ minutes

HMS, BM EQ-Bank 148 MC

A marathon runner hits "the wall" after 30 km of running. Which fuel source has most likely been depleted?

Creatine phosphate
Blood glucose
Muscle glycogen
Plasma proteins

Show Answers Only

$C$

Show Worked Solution

Consider Option C: Muscle glycogen

Muscle glycogen depletion occurs in prolonged exercise

Other Options:

A is incorrect: CP depletion occurs in seconds
B is incorrect: Blood glucose is maintained through liver glycogen
D is incorrect: Proteins are not a primary fuel source

$\Rightarrow C$

HMS, BM EQ-Bank 144 MC

Which row correctly identifies the fuel source and duration of the ATP-PCr energy system?

\begin{align*}
\begin{array}{l}
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt}& \\
\rule{0pt}{2.5ex}\textbf{A.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{B.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\textbf{Fuel Source}\rule[-1ex]{0pt}{0pt}& \textbf{Duration} \\
\hline
\rule{0pt}{2.5ex}\text{Glucose}\rule[-1ex]{0pt}{0pt}&\text{30 - 60 seconds}\\
\hline
\rule{0pt}{2.5ex}\text{Creatine Phosphate}\rule[-1ex]{0pt}{0pt}& \text{0 - 10 seconds}\\
\hline
\rule{0pt}{2.5ex}\text{Fatty Acids}\rule[-1ex]{0pt}{0pt}& \text{2+ minutes} \\
\hline
\rule{0pt}{2.5ex}\text{Creatine Phosphate}\rule[-1ex]{0pt}{0pt}& \text{30 - 60 seconds} \\
\hline
\end{array}
\end{align*}

Show Answers Only

$B$

Show Worked Solution

Consider Option B: Creatine Phosphate 0 – 10 seconds

CP is the fuel source and system operates 0 – 10 seconds

Other Options:

A is incorrect: Glucose is fuel for glycolytic system
C is incorrect: Fatty acids fuel aerobic system
D is incorrect: Duration is wrong for ATP-PCr system

$\Rightarrow B$

HMS, BM EQ-Bank 143 MC

During a 400 m race, an athlete experiences heavy legs and reduced performance in the final 100m. Which statement best explains this occurrence?

Depletion of creatine phosphate stores
Accumulation of lactic acid
Insufficient oxygen supply
Depleted glycogen stores

Show Answers Only

$B$

Show Worked Solution

Consider Option B: Accumulation of lactic acid

The glycolytic system produces lactic acid as a by-product causing fatigue

Other Options:

A is incorrect: CP stores are depleted in first 10 seconds
C is incorrect: While oxygen debt occurs, it’s not the primary cause of fatigue
D is incorrect: Glycogen depletion occurs in much longer events

$\Rightarrow B$

HMS, BM EQ-Bank 140

Explain how the muscular and nervous systems are affected when a tennis player repeatedly serves with poor technique, and describe appropriate first aid responses. (5 marks)

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Sample Answer

Rotator cuff muscles strain from repetitive overuse and incorrect loading patterns during the serve action, leading to tissue damage.
Neural pathways activate a continuous pain response through the peripheral nervous system as protective feedback to prevent further damage.
Localised inflammation in the shoulder region compresses surrounding nerves, causing referred pain and potential movement limitations.
First aid requires ice application in 20-minute intervals and appropriate compression bandaging to reduce swelling and manage pain.
A 48-72 hour rest period from serving is needed while maintaining gentle mobility exercises to prevent joint stiffness.

Show Worked Solution

Sample Answer

Rotator cuff muscles strain from repetitive overuse and incorrect loading patterns during the serve action, leading to tissue damage.
Neural pathways activate a continuous pain response through the peripheral nervous system as protective feedback to prevent further damage.
Localised inflammation in the shoulder region compresses surrounding nerves, causing referred pain and potential movement limitations.
First aid requires ice application in 20-minute intervals and appropriate compression bandaging to reduce swelling and manage pain.
A 48-72 hour rest period from serving is needed while maintaining gentle mobility exercises to prevent joint stiffness.

HMS, BM EQ-Bank 136 MC

A swimmer presents with shoulder pain after repeatedly performing an inefficient freestyle arm pull. Which combination of systems is MOST likely to require first aid treatment?

Muscular and nervous systems
Circulatory and respiratory systems
Muscular and skeletal systems
Skeletal and nervous systems

Show Answers Only

$C$

Show Worked Solution

Consider Option C: Muscular and skeletal systems

Both muscular strain and joint stress occur from repetitive inefficient movement.

Other Options:

A is incorrect: While pain is present, muscle damage is primary concern
B is incorrect: These systems are not primarily impacted by the movement
D is incorrect: Joint stress occurs with muscle not nerve damage

$\Rightarrow C$

HMS, BM EQ-Bank 131 MC

During a 3-hour mountain bike ride in hot conditions, which sign indicates the digestive and endocrine systems require immediate first aid intervention?

Muscle cramping with normal sweating
Decreased urination with confusion
Rapid breathing with thirst
Fatigue with hunger

Show Answers Only

$B$

Show Worked Solution

Consider Option B: Decreased urination with confusion

Decreased urination shows digestive system stress while confusion indicates endocrine system involvement in blood glucose regulation.

Other Options:

A is incorrect: Primary muscular system involvement
C is incorrect: Respiratory system response
D is incorrect: Normal exercise response

$\Rightarrow B$

HMS, BM EQ-Bank 124

Analyse how the nervous system influences movement efficiency and discuss appropriate first aid interventions when neural responses are compromised. (8 marks)

--- 12 WORK AREA LINES (style=lined) ---

Show Answers Only

Sample Answer

Nervous System Function:

Controls muscle recruitment patterns
Coordinates movement through proprioception
Provides feedback during movement execution

Movement Efficiency Impact:

Determines timing of muscle activation
Controls force production
Maintains balance and coordination

Signs of Compromise:

Altered sensation or tingling
Loss of coordination
Muscle weakness or irregular activation

First Aid Interventions:

Immediate activity cessation
TOTAPS assessment focusing on sensation
Protection of affected areas
Medical referral if symptoms persist

Show Worked Solution

Sample Answer

Nervous System Function:

Controls muscle recruitment patterns
Coordinates movement through proprioception
Provides feedback during movement execution

Movement Efficiency Impact:

Determines timing of muscle activation
Controls force production
Maintains balance and coordination

Signs of Compromise:

Altered sensation or tingling
Loss of coordination
Muscle weakness or irregular activation

First Aid Interventions:

Immediate activity cessation
TOTAPS assessment focusing on sensation
Protection of affected areas
Medical referral if symptoms persist

HMS, BM EQ-Bank 120 MC

Which combination of symptoms indicates the musculoskeletal and nervous systems require immediate first aid intervention during movement?

Muscle spasm with tingling
General fatigue with sweating
Increased heart rate with thirst
Joint stiffness with warmth

Show Answers Only

$A$

Show Worked Solution

Consider Option A: Muscle spasm with tingling

Musculoskeletal and Nervous Systems

Combined muscular and neural symptoms indicate need for immediate assessment of both systems.

Other Options:

B is incorrect: Normal physiological response to exercise
C is incorrect: Normal cardiovascular response to exercise
D is incorrect: Normal musculoskeletal response to movement

$\Rightarrow A$

HMS, BM EQ-Bank 115

Analyse how the nervous and respiratory systems work together during high-intensity interval training. (8 marks)

--- 10 WORK AREA LINES (style=lined) ---

Show Answers Only

Sample Answer

Work Interval:

Nervous system increases motor unit recruitment while respiratory rate rapidly elevates
Neural signals increase breathing depth as oxygen demand peaks
Respiratory system responds to neural feedback about exercise intensity

Active Recovery:

Nervous system moderates motor signals while breathing rate partially decreases
Neural monitoring adjusts ventilation based on reduced oxygen demand
Respiratory pattern responds to neural signals for recovery preparation

Next Interval:

Nervous system reactivates high motor recruitment as breathing rate quickly elevates again
Neural pathways anticipate oxygen needs as respiratory rate increases
Respiratory system responds faster through neural preparation

Adaptation:

Nervous system becomes more efficient at coordinating breathing response
Neural pathways optimise respiratory patterns for work-recovery cycles
Both systems improve synchronisation of effort-recovery timing

Show Worked Solution

Sample Answer

Work Interval:

Nervous system increases motor unit recruitment while respiratory rate rapidly elevates
Neural signals increase breathing depth as oxygen demand peaks
Respiratory system responds to neural feedback about exercise intensity

Active Recovery:

Nervous system moderates motor signals while breathing rate partially decreases
Neural monitoring adjusts ventilation based on reduced oxygen demand
Respiratory pattern responds to neural signals for recovery preparation

Next Interval:

Nervous system reactivates high motor recruitment as breathing rate quickly elevates again
Neural pathways anticipate oxygen needs as respiratory rate increases
Respiratory system responds faster through neural preparation

Adaptation:

Nervous system becomes more efficient at coordinating breathing response
Neural pathways optimise respiratory patterns for work-recovery cycles
Both systems improve synchronisation of effort-recovery timing

\(h+h-78.4\)	\(=1360\)
\(2h\)	\(=1438.4\)
\(h\)	\(=719.2\ \text{m}\)

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.	\(\operatorname{Pr}(X<2)\)	\(=\operatorname{Pr}(X=0)+\operatorname{Pr}(X=1)\)
		\(=\ ^4C _0\left(\dfrac{9}{10}\right)^0\left(\dfrac{1}{10}\right)^4+\ ^4C_1\left(\dfrac{9}{10}\right)^1\left(\dfrac{1}{10}\right)^3\)
		\(= 1 \times \dfrac {1}{10\,000} + 4 \times \dfrac{9}{10} \times \dfrac{1}{1000}\)
		\(=\dfrac{37}{10\,000}\)

\(\dfrac{1}{(x+3)^2}-2\)	\(=0\)
\((x+3)^2\)	\(=\dfrac{1}{2}\)
\(x+3\)	\(=\pm\dfrac{1}{\sqrt{2}}\)
\(x\)	\(=-3\pm\dfrac{1}{\sqrt{2}}\)

	\(f(x)\)	\(=\log_{e}(x^3-3x+2)\)
	\(f^{\prime}(x)\)	\(=\dfrac{3x^2-3}{x^3-3x+2}\)
	\(f^{\prime}(3)\)	\(=\dfrac{3(3)^2-3}{(3)^3-3(3)+2}=\dfrac{6}{5}\)

\(v\)	\(=u + at\)
\(t\)	\(=\dfrac{v-u}{a}\)
	\(=\dfrac{12-30}{-0.042}\)
	\(=428.6\ \text{sec (1 d.p.)}\)

\(v\)	\(=u + at\)
\(t\)	\(=\dfrac{v-u}{a}\)
	\(=\dfrac{18-56}{-3.515}\)
	\(=10.8\ \text{sec (1 d.p.)}\)

\(\text{Repayments}\)	\( =2228.40\times 12\times 5\)
	\(=$133\,704\)

\(\text{Interest}\)	\(=133\,704-121\,000\)
	\(=$12\,704\)