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ENGINEERING, CS 2025 HSC 26a

Outline the importance of engineers working collaboratively during a construction project.   (2 marks)

Show Answers Only
  • Collaborative work practices allow engineers to coordinate with other professionals, such as architects and electricians, ensuring all aspects of a project meet safety and compliance requirements.
  • Teamwork helps identify and resolve problems early, preventing costly delays and ensuring the project is completed efficiently.
Show Worked Solution
  • Collaborative work practices allow engineers to coordinate with other professionals, such as architects and electricians, ensuring all aspects of a project meet safety and compliance requirements.
  • Teamwork helps identify and resolve problems early, preventing costly delays and ensuring the project is completed efficiently.

ENGINEERING, PPT 2025 HSC 8 MC

Which of the following is a key benefit of engineers adhering to AS 1100 when producing engineering drawings?

  1. It ensures consistency in drawings across different teams and industries.
  2. It reduces the cost of materials in design and manufacture of engineering parts.
  3. It simplifies the manufacturing process by eliminating the need for detailed drawings.
  4. It allows for the use of advanced 3D printing technologies in all stages of production.
Show Answers Only

\(A\)

Show Worked Solution
  • AS 1100 is the Australian Standard for technical drawing — it ensures all engineers interpret drawings the same way.
  • Consistency across teams and industries is the primary purpose of any drafting standard.
  • B, C and D relate to cost, manufacturing simplification and 3D printing — none are functions of a drawing standard.

\(\Rightarrow A\)

Proof, SPEC2 2025 VCAA 1 MC

A tiger is a type of cat.

Consider the following statement.

'If I have a tiger, then I have a cat.'

The contrapositive of this statement is

  1. if I do not have a tiger, then I do not have a cat.
  2. if I have a cat, then I have a tiger.
  3. if I do not have a cat, then I do not have a tiger.
  4. if I do not have a tiger, then I have a different type of cat.
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Statement: If} \ \ X \Rightarrow Y\)

\(\text{Contrapositive: If} \ \neg \ Y \ \Rightarrow \neg \ X\)

\(\text{If I don’t have a cat} \ \ \Rightarrow \ \ \text{I don’t have a tiger.}\)

\(\Rightarrow C\)

Vectors, SPEC1 2025 VCAA 5

The position vectors of particles \(P\) and \(Q\) at time \(t\) seconds are given by

\begin{align*}
{\underset{\sim}{r}}_P(t)=\left(t^3+a t^2\right) \underset{\sim}{i}-\underset{\sim}{j} \ \ \text {and} \ \  {\underset{\sim}{r}}_Q(t)=(b t+2 t) \underset{\sim}{i}+\left(2 t^2+c t+t\right) \underset{\sim}{j},
\end{align*}

where \(t \geq 0\)  and  \(a, b, c \in R\).

The particles collide when  \(t=1\).

  1. Show that for collision to occur when  \(t=1\), the value of \(c\) is \(-4\).   (1 mark)

When the particles collide, their velocities are at right angles to each other.

  1. Find the two possible values of \(a\) for collision to occur when  \(t=1\).   (2 marks)

  2. When the particles collide at  \(t=1\), the magnitudes of their accelerations are equal.
  3. Find the values of \(a\) and \(b\) for collision to occur when  \(t=1\).   (1 mark)

Show Answers Only

a.    \(\text{\(P\) and \(Q\) collide at \(\ t=1\).}\)

\(\text{Equate co-efficients of} \ \underset{\sim}{j}:\)

\(2+c+1=-1 \ \ \Rightarrow \ \ c=-4\)

b.    \(a=-\dfrac{3}{2},-1\)

c.    \(a=-1, \ b=-2\)

Show Worked Solution

a.    \(\text{\(P\) and \(Q\) collide at \(\ t=1\).}\)

\(\text{Equate co-efficients of} \ \underset{\sim}{j}:\)

\(2+c+1=-1 \ \ \Rightarrow \ \ c=-4\)
 

b.    \(r_P=\left(t^3+a t^2\right)\underset{\sim}{i}-\underset{\sim}{j} \ \ \Rightarrow \ \ \dot{r}_P=\left(3 t^2+2 a t\right) \underset{\sim}{i}\)

\(r_Q=(b t+2 t) \underset{\sim}{i}+\left(2 t^2-3 t\right)\underset{\sim}{j} \ \ \Rightarrow \ \ \dot{r}_Q=(b+2)\underset{\sim}{i}+(4 t-3)\underset{\sim}{j}\)

\(\text {Velocities are perpendicular at} \ \ t=1:\)

\(\displaystyle \dot{r}_p \cdot \dot{r}_Q=\binom{3+2 a}{0}\binom{b+2}{1}=(3+2 a)(b+2)=0\ \ldots\ (1)\)

♦ Mean mark (b) 49%.

\(\text{Equating co-efficients of \(\underset{\sim}{i}\) at \(\ t=1\):}\)

\(1+a=b+2\)

\(\text{Substitute into (1) above:}\)

\((3+2 a)(1+a)=0\)

\(a=-\dfrac{3}{2},-1\)
 

c.    \(\ddot{r}_P=(6 t+2 a)\underset{\sim}{i}, \ \ddot{r}_Q=4 \underset{\sim}{j}\)

\(\text{At \(\ t=1\), magnitudes of \(\ddot{r}_P\) and \(\ddot{r}_Q\) are equal.}\)

\(6+2 a=4 \ \ \Rightarrow \ \ a=-1\)

\(1-1=b+2 \ \ \Rightarrow \ \ b=-2\)

♦♦♦ Mean mark (c) 25%.

Financial Maths, STD2 F4 2025 GEN1 7

Declan is a filmmaker and content creator.

He has taken out a reducing balance loan to fund a new production.

Interest is calculated monthly and Declan makes monthly repayments.

Three rows of the amortisation table for Declan’s loan are shown below.

\begin{array}{|c|c|c|c|c|}
\hline
\hline \rule{0pt}{2.5ex}\quad \textbf{Payment} \quad & \quad\textbf{Payment} \quad & \quad\textbf{Interest} \quad& \textbf{Principal} & \quad\textbf{Balance}\quad\\
\textbf{number} & \textbf{(\$)}  \rule[-1ex]{0pt}{0pt}& \textbf{(\$)} & \quad\textbf{reduction (\$)} \quad& \textbf{(\$)}\\
\hline \hline \rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0.00 & 0.00 & 0.00 & 850\,000.00 \\
\hline \hline \rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & 15\,730.88 & 2975.00 & 12\,755.88 & 837\,244.12 \\
\hline \hline \rule{0pt}{2.5ex}2 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & 2930.35 & 12\,800.53 & 824\,443.59 \\
\hline
\end{array}

  1. What amount, in dollars, did Declan borrow?   (1 mark)
  2. Why is the interest associated with payment 2 lower than the interest associated with payment 1?   (1 mark)
  3. The interest rate on Declan’s loan is 4.2% per annum, compounding monthly.
  4. Using the values in the table, complete the table below.
  5. Round all values to the nearest cent.   (2 marks)

\begin{array}{|c|c|c|c|c|}
\hline
\hline \rule{0pt}{2.5ex}\quad \textbf{Payment} \quad & \quad\textbf{Payment} \quad & \quad\textbf{Interest} \quad& \textbf{Principal} & \quad\textbf{Balance}\quad\\
\textbf{number} & \textbf{(\$)}  \rule[-1ex]{0pt}{0pt}& \textbf{(\$)} & \quad\textbf{reduction (\$)} \quad& \textbf{(\$)}\\
\hline \hline \rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0.00 & 0.00 & 0.00 & 850\,000.00 \\
\hline \hline \rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & 15\,730.88 & 2975.00 & 12\,755.88 & 837\,244.12 \\
\hline \hline \rule{0pt}{2.5ex}2 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & 2930.35 & 12\,800.53 & 824\,443.59 \\
\hline \hline \rule{0pt}{2.5ex}3 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & & & \\
\hline
\end{array}

Show Answers Only

a.    \(\$ 850\,000\)

b.    \(\text{Interest is lower (payment 2 vs payment 1) because it is based on}\)

\(\text{a reduced balance.}\)

c.    \(\text{Interest}=\dfrac{4.2}{100} \times \dfrac{1}{12} \times 824\, 443.59=\$ 2885.55\)

\(\text{Principal reduction}=15\,730.88-2885.55=\$ 12\,845.33\)

\(\text{Balance}=824\,443.59-12\,845.33=\$811\,598.26\)

Show Worked Solution

a.    \(\$ 850\,000\)
 

b.    \(\text{Interest is lower (payment 2 vs payment 1) because it is based on}\)

\(\text{a reduced balance.}\)
 

c.    \(\text{Monthly interest}=\dfrac{4.2}{12}=0.35\%\)

\(\text{Calculating missing values in the table:}\)

\(\text{Interest}=\dfrac{0.35}{100} \times 824\, 443.59=\$ 2885.55\)

\(\text{Principal reduction}=15\,730.88-2885.55=\$ 12\,845.33\)

\(\text{Balance}=824\,443.59-12\,845.33=\$811\,598.26\)

♦ Mean mark (c) 40%.

Matrices, GEN2 2025 VCAA 11

An early learning centre contains three rooms, Nursery \((N)\), Toddler \((T)\) and Pre-kinder \((P)\).

The Nursery and Toddler rooms each have capacity for eight children and the Pre-kinder room has capacity for 20 children, as shown in matrix \(C\) below.

\begin{align*}
C=\left[\begin{array}{c}
8 \\
8 \\
20
\end{array}\right] \begin{aligned}
& N \\
& T \\
& P
\end{aligned}
\end{align*}

Matrix \(E\) shows enrolment numbers for each room for one week, Monday to Friday.

\begin{aligned}
& \quad \ \ \ Mon \quad Tue\quad Wed \ \ \ Thu \ \ \ Fri \\
E&=\begin{bmatrix}
6 & \quad 8 & \quad 8 & \quad 8 & \quad 5 \\
7 & \quad 8 & \quad 7 & \quad 8 & \quad 6 \\
18 & \ \ \ 18 &\ \ \ 17 &\ \ \ 15 &\ \ \ 13
\end{bmatrix}\begin{array}{l}
N \\
T \\
P 
\end{array}\\
\end{aligned}

  1. State the order of matrix \(E\).   (1 mark)
  3. The following matrix multiplication has been completed to determine a new matrix, \(W\).
    1. \begin{align*}
      \begin{bmatrix}
      1 & 1 & 1
      \end{bmatrix} \times E=W
      \end{align*}
  4. What information does matrix \(W\) provide regarding enrolments at the early learning centre?   (1 mark)

  5. It has been decided that the capacity of the Nursery room will be increased by 25% and the capacity of the Toddler room will be increased by 50%. The capacity of the Pre-kinder room will be reduced by 10%.
  6. The new capacities for the three rooms \((C_{\text {new}})\) can be determined from the matrix product
    1. \(C_{\text {new }}=F C\)
  7. where \(F\) is a diagonal matrix.
  8. Write down the matrix \(F\).   (1 mark)   
Show Answers Only

a.    \(\text{Order of matrix} \ \ E=3 \times 5\)

b.    \(\text { Total enrolments for each day of the week.}\)

c.

\(F=\begin{bmatrix}1.25 & 0 & 0 \\ 0 & 1.5 & 0 \\ 0 & 0 & 0.9\end{bmatrix}\)

Show Worked Solution

a.    \(\text{Order of matrix} \ \ E=3 \times 5\)
 

b.    \(\text { Total enrolments for each day of the week.}\)
  

c.

\(F=\begin{bmatrix}1.25 & 0 & 0 \\ 0 & 1.5 & 0 \\ 0 & 0 & 0.9\end{bmatrix}\)

♦ Mean mark (c) 44%.

Matrices, GEN1 2025 VCAA 28 MC

At a fast-food restaurant, team members use headsets to communicate.

There are six different headsets: \(A, B, C, D, E\) and \(F\).

These headsets work on different frequencies, which means some staff members cannot directly communicate with each other.

The matrix below shows which headsets can directly communicate with each other.

\begin{aligned}
& \quad \quad \quad \quad \textit{receiver} \\
& \quad \ \  A \ \ \  B \ \ \  C \ \ \  D \ \ \  E\ \ \ F \\
\textit{sender}\ \ & \begin{array}{l}
A \\
B \\
C \\
D \\
E \\
F
\end{array}\begin{bmatrix}
0 & 1 & 0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 0 & 1 \\
0 & 0 & 0 & 0 & 1 & 1 \\
1 & 1 & 0 & 0 & 1 & 0 \\
0 & 0 & 1 & 1 & 0 & 0 \\
1 & 1 & 1 & 0 & 0 & 0
\end{bmatrix}\\
\end{aligned}

 
In this matrix:

  • the '1' in row \(A\), column \(B\) indicates that headset \(A\) can directly communicate with headset \(B\)
  • the '0' in row \(A\), column \(E\) indicates that headset \(A\) cannot directly communicate with headset \(E\).

Which one of the following sequences allows a message to be communicated from headset \(A\) to headset \(E\) ?

  1. \(A-C-E\)
  2. \(A-D-B-E\)
  3. \(A-B-D-E\)
  4. \(A-F-D-E\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Option A: \(A\) cannot connect with \(C\) (elminate)}\)

\(\text{Option B: \(B\) cannot connect with \(E\) (eliminate)}\)

\(\text{Option C: All links work }\checkmark \)

\(\text{Option D: \(F\) cannot connect with \(D\) (eliminate)}\)

\(\Rightarrow C\)

Financial Maths, STD2 EQ-Bank 31

Chen earns an annual salary of $72 800. He is entitled to four weeks annual leave with 17.5% leave loading. A spreadsheet is used to calculate his total holiday pay.

Total holiday pay = 4 × weekly wage + 4 × weekly wage × 17.5%

A spreadsheet showing Chen's holiday pay calculation is shown.

  1. What value from the question should be entered in cell B5?   (1 mark)

  2. Write down the formula used in cell B9 to calculate the weekly wage, using appropriate grid references.   (2 marks)
  3. Verify the amount of Chen's total holiday pay using calculations.   (2 marks)
Show Answers Only

a.   \(4\)

b.   \(=\text{B4}/52\)

c.    \(\text{Total holiday pay}=\text{weekly wage}\times 4 +\ \text{weekly wage}\times 4\ \times 17.5\%\)

\(\text{Total holiday pay}=1400\times 4+1400\times 4\times\dfrac{17.5}{100}=5600+980=$6580\)

Show Worked Solution

a.    \(\text{Chen gets 4 weeks leave }\rightarrow\ 4\)
 

b.    \(\text{Weekly wage }=\dfrac{\text{Annual salary}}{52}\)

\(\text{Formula: }=\text{B4}/52\)
 

c.    \(\text{Total holiday pay}=\text{weekly wage}\times 4 +\ \text{weekly wage}\times 4\ \times 17.5\%\)

\(\text{Total holiday pay}=1400\times 4+1400\times 4\times\dfrac{17.5}{100}=5600+980=$6580\)

Probability, 2ADV EQ-Bank 13

Consider the universal set  \(U=\{x\) is a positive integer and  \(x \leqslant 24\}\)

Three sets are defined as

\begin{aligned}
& A=\{x \text { is a factor of } 24\} \\
& B=\{x \text { is a perfect square}\} \\
& C=\{x \text { is divisible by } 3\}
\end{aligned}

  1. List the elements of set \(A\).   (1 mark)

  2. Find \(A \cap B\).   (1 mark)

  3. Find \((A \cup B) \cap C^c\)   (2 marks)

Show Answers Only

a.    \(A=\{1,2,3,4,6,8,12,24\}\)

b.    \(A \cap B=\{1,4\}\)

c.    \((A \cup B) \cap C^c=\{1,2,4,8,16\}\)

Show Worked Solution

a.    \(A=\{1,2,3,4,6,8,12,24\}\)
 

b.    \(B=\{1,4,9,16\}\)

\(A \cap B=\{1,4\}\)
 

c.    \(A \cup B=\{1,2,3,4,6,8,9,12,16,24\}\)

\(C=\{3,6,9,12,15,18,21,24\}\)

\(C^c=\{1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23\}\)

\((A \cup B) \cap C^c=\{1,2,4,8,16\}\)

Probability, 2ADV EQ-Bank 12

Consider the universal set  \(U=\{x\) is a positive integer and \(x \leqslant 15\}\)

Three sets are defined as:

\begin{aligned}
& A=\{x \text { is a multiple of } 3\} \\
& B=\{x \text{ is a prime number}\} \\
& C=\{x \text{ is even}\}
\end{aligned}

  1. List the elements of set \(A\).   (1 mark)

  2.  Find  \(B \cap C\)   (1 mark)

  3. Find  \(A \cup \overline{C}\)   (2 marks)

Show Answers Only

a.    \(A=\{3,6,9,12,15\}\)

b.   \(B \cap C = \{2\} \)

c.    \(A \cup \overline{C}=\{1,3,5,6,7,9,11,12,13,15\}\)

Show Worked Solution

a.    \(A=\{3,6,9,12,15\}\)
 

b.    \(B=\{2,3,5,7,11,13\}\)

\(C=\{2,4,6,8,10,12,14\}\)

\(B \cap C = \{2\} \)
 

c.    \(\text{Find} \ \ A \cup \overline{C}:\)

\(\overline{C}=\{1,3,5,7,9,11,13\}\)

\(A \cup \overline{C}=\{1,3,5,6,7,9,11,12,13,15\}\)

Probability, 2ADV EQ-Bank 11

Consider the universal set  \(U=\{1,2,3,4,5,6,7,8,9,10\}\).

Two sets, \(A\) and \(B\), are given as

\(A= \{1,3,4,7,9\}\)

\(B =\{2,4,7,10\}\)

  1. Find \(A \cup B\)   (1 mark)

  2. Find \(A \cap \overline{B}\)   (2 marks)

Show Answers Only

a.    \(A \cup B = \{1,2,3,4,7,9,10\}\)

b.    \(A \cap \overline{B} = \{3, 4, 9\}\)

Show Worked Solution

a.    \(A= \{1,3,4,7,9\},\ \ B=\{2,4,7,10\}\)

\(A \cup B = \{1,2,3,4,7,9,10\}\)
 

b.     \(\overline{B} = \{1,3,5,6,8,9\}\)

\(A \cap \overline{B} = \{3, 4, 9\}\)

Functions, 2ADV EQ-Bank 11

Consider the function  \(f(x)=\dfrac{6}{x}\).

  1. State the equation(s) of any asymptotes of \(f(x)\).   (1 mark)

  2. Complete the table of values of  \(y=f(x)\)  below.   (1 mark)

  3. \begin{array}{|c|c|c|c|c|c|c|}
    \hline \rule{0pt}{2.5ex} \ \ \ x \ \ \ \rule[-1ex]{0pt}{0pt}& -\ 3 \ &   & \quad 1 \quad & \ \ \ 3 \ \ \ \\
    \hline \rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  & -6 &  & 2 \\
    \hline
    \end{array}
  4. Sketch the graph of  \(y=f(x)\), clearly showing any asymptote(s) and points from the table.   (2 marks)

Show Answers Only

a.    \(x=0, \ y=0\)

b.    \(\text{Table of values:}\)

\begin{array}{|c|c|c|c|c|c|c|}
\hline \rule{0pt}{2.5ex} \ \ \ x \ \ \ \rule[-1ex]{0pt}{0pt}& -\ 3 \ & \ -1 \ & \quad 1 \quad & \ \ \ 3 \ \ \ \\
\hline \rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -2 & -6 & 6 & 2 \\
\hline
\end{array} 

c.   
         

Show Worked Solution

a.    \(y=\dfrac{6}{x} \ \Rightarrow \ x \neq 0\)

\(\text{Vertical asymptote at} \ \ x=0.\)

\(\text{As}\ x \rightarrow \infty, \ y \rightarrow 0^{+}\)

\(\text{As}\ x \rightarrow -\infty, \ y \rightarrow 0^{-}\)

\(\text{Horizontal asymptote at} \ \ y=0.\)
 

b.    \(\text{Table of values:}\)

\begin{array}{|c|c|c|c|c|c|c|}
\hline \rule{0pt}{2.5ex} \ \ \ x \ \ \ \rule[-1ex]{0pt}{0pt}& -\ 3 \ & \ -1 \ & \quad 1 \quad & \ \ \ 3 \ \ \ \\
\hline \rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -2 & -6 & 6 & 2 \\
\hline
\end{array} 

c.   
         

HMS, HAG 2025 HSC 2 MC

Which of the following is an environmental factor that determines why some groups in Australia experience health inequities?

  1. Religion
  2. Genetics
  3. Employment
  4. Geographical location
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Geographical location determines access to healthcare services and facilities. Remote areas experience reduced access leading to health inequities.

Other Options:

  • A is incorrect: Religion does not determine health inequities.
  • B is incorrect: Genetics affects individuals, not group inequities.
  • C is incorrect: Employment is less fundamental than geographical access.

Financial Maths, STD2 EQ-Bank 18

Rachel is purchasing a new refrigerator priced at $3200. The store offers finance terms of 30% deposit and repayments of $65 per week for 40 weeks.

  1. What is the amount of the deposit?   (1 mark)
  2. Find the total cost of the repayments.   (1 mark)
  3. What is the total cost of purchasing the refrigerator using the finance package?   (1 mark)
Show Answers Only

a.   \($960\)

b.   \($2600\)

c.   \($3560\)

Show Worked Solution

a.    \(\text{Deposit}=\dfrac{30}{100}\times 3200=$960\)

b.    \(\text{Total repayments}=65\times 40=$2600\)

c.    \(\text{Total cost}\) \(=\text{Deposit}+\text{Total repayments}\)
    \(=960+2600=$3560\)

Financial Maths, STD2 EQ-Bank 25

George has constructed a yearly budget shown below.
  

               Income                      Expenses        
 Salary               $68 450.00   Groceries              $7280.00 
 Interest $825.60   Clothing $3960.00 
     Council Rates  $1740.00 
     Electricity $1890.00 
     Entertainment  $4320.00 
     Insurance $2650.00 
     Loan repayments  $15 840.00 
     Motor vehicle costs  $3180.00 
     Telephone $960.00 
     Work related costs $1250.00 
     Balance  
Total    Total   

 

  1. Calculate George's total income and total expenses.   (2 marks)
  2. Using the information from part (a), balance the budget.   (1 mark)
  3. What is the amount of George's weekly savings? Give your answer to the nearest dollar.   (1 mark)
Show Answers Only

a.   \(\text{Income}=$69\,275.60,\ \text{Expenses}=$43\,070.00\)

b.   \(\text{Balance}=$26\,205.60\)

c.   \(\text{Savings}=$504\ \text{(nearest dollar)}\)

Show Worked Solution

a.    \(\text{Income}=68\,450.00+825.60=$69\,275.60\)

\(\text{Expenses}\)

\(=7280.00+3960.00+1740.00+1890.00+4320.00\)

\(+2650.00+15840.00+3180.00+960.00+1250.00\)

\(=$43\,070.00\)
   

b.     \(\text{Balance}\) \(=\text{Income}-\text{Expenses}\)
    \(=$69\,275.60-$43\,070.00=$26\,205.60\)

  
c.    \(\text{Weekly savings}=\dfrac{$26\,205.60}{52}=$503.953…\ =$504\ \text{(nearest dollar)}\)

Measurement, STD2 EQ-Bank 10 MC

It is currently 2:17 pm. A train is due to arrive at 3:08 pm.

How long do you need to wait for the train?

  1. 49 minutes
  2. 51 minutes
  3. 1 hour 9 minutes
  4. 1 hour 51 minutes
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Method 1: Break into steps}\)

\(\rightarrow\text{From 2:17 pm to 3:00 pm: }\ 60-17 = 43 \text{ minutes} \)

\(\rightarrow\text{From 3:00 pm to 3:08 pm: }\  8 \text{ minutes} \)

\(\rightarrow\text{Total: }\  43+8 = 51 \text{ minutes} \)
  
\(\text{Method 2: Calculate directly}\)

\(\rightarrow 3:08-2:17 = 51 \text{ minutes} \)
  

\(\Rightarrow B\)

Functions, 2ADV 2011 HSC 3c

The diagram shows a line `l_1`, with equation  `3x + 4y-12 = 0`, which intersects the `y`-axis at `B`.

A second line `l_2`, with equation  `4x-3y = 0`, passes through the origin `O` and intersects `l_1` at `E`. 
 

  1. Show that the coordinates of `B` are `(0, 3)`.    (1 mark)
  2. Show that `l_1` is perpendicular to `l_2`.   (2 marks)
Show Answers Only

a.    `\text{See Worked Solution}`

b.    `\text{See Worked Solution}`

Show Worked Solution

a.    `B\ text(is)\ y text(-intercept of)\ l_1`

`text(When)\ x = 0:`

`(3 xx 0) + 4y-12=0\ \ =>\ \ y=3`

`:.\ B\ text(is)\ (0,3)`
 

b.    `l_1:\ \ 3x + 4y -12`  `= 0`
  `4y` `= -3x + 12`
  `y` `= -3/4x + 3`

`m(l_1)=-3/4`
 

`l_2:\ \ 4x-3y` `= 0`
`3y` `= 4x`
`y` `= 4/3 x`

`m(l_2)=4/3`
 

`m (l_1) xx m (l_2)= -3/4 xx 4/3= -1`

`:.\ l_1\ text(and)\ l_2\ text(are perpendicular)`

Algebra, STD2 EQ-Bank 22

Jerico is the manager of a weekend market in which there are 220 stalls for rent. From past experience, Jerico knows that if he charges \(d\) dollars to rent a stall. then the number of stalls, \(s\), that will be rented is given by:

\(s=220-4d\)

  1. How many stalls will be rented if Jerico charges $7.50 per stall .   (1 mark)

  2. Complete the following table for the function  \(s=220-4d\).   (1 mark)

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & \ & \ & \\
\hline
\end{array}

  1. Using an appropriate vertical scale and labelled axes, graph the function  \(s=220-4d\) on the grid below.   (2 marks)
  1. Does it make sense to use the formula  \(s=220-4d\)  to calculate the number of stalls rented if Jerico charges $60 per stall? Explain your answer.   (2 marks)

Show Answers Only
  

a.    \(190\ \text{stalls will be rented}\)

b.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & 180 \ & 100 \ & 20  \\
\hline
\end{array}

c.

d.    \(\text{When}\ d=60, s=220-4\times 60=-20\)

\(\therefore\ \text{It does not make sense to charge }$60\ \text{ per stall}\)

\(\text{as you cannot have a negative number of stalls.}\)

Show Worked Solution

a.    \(s=220-4d=220-4\times 7.50=190\)

\(\therefore 190\ \text{stalls will be rented}\)

b.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & 180 \ & 100 \ & 20  \\
\hline
\end{array}

c.

d.    \(\text{When}\ d=60, s=220-4\times 60=-20\)

\(\therefore\ \text{It does not make sense to charge }$60\ \text{ per stall}\)

\(\text{as you cannot have a negative number of stalls.}\)

CHEMISTRY, M6 2025 HSC 6 MC

What is the pH of a 0.25 mol L\(^{-1}\) solution of hydrochloric acid?

  1. \(-0.60\)
  2. \(-0.25\)
  3. \(0.25\)
  4. \(0.60\)
Show Answers Only

\(D\)

Show Worked Solution
  • Hydrochloric acid is a strong acid and will fully ionise in solution.
  • Therefore \(\ce{[HCl] = [H+] = 0.25\ \text{mol L}^{-1}}\).
\(\text{pH}\) \(=-\log_{10}(\ce{[H+]})\)  
  \(=-\log_{10}(0.25)\)  
  \(=0.60\)  

 

\(\Rightarrow D\)

Proof, EXT2 P1 2025 HSC 5 MC

Consider the statement:

If  \(x^2-2 x \geq 0\), then  \(x \leq 0\).

Which of the following is the contrapositive of the statement?

  1. If  \(x>0\), then  \(x^2-2 x<0\).
  2. If  \(x \leq 0\), then  \(x^2-2 x \geq 0\).
  3. If  \(x^2-2 x<0\), then  \(x<0\).
  4. If  \(x^2-2 x \leq 0\), then  \(x>0\).
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Statement: If}\ \ p\ \Rightarrow \ q\)

\(\text{Contrapositive statement: If}\ \ \neg\ q\ \Rightarrow \ \neg\ p\)

\(\therefore\ \text{If}\ \ x>0\ \ \Rightarrow\ \ x^2-2 x<0\).

\(\Rightarrow A\)

Vectors, EXT2 V1 2025 HSC 11d

  1. Force \({\underset{\sim}{F}}_1\) has magnitude 12 newtons in the direction of vector  \(2 \underset{\sim}{i}-2 \underset{\sim}{j}+\underset{\sim}{k}\).   
  2. Show that  \({\underset{\sim}{F}}_1=8 \underset{\sim}{i}-8 \underset{\sim}{j}+4 \underset{\sim}{k}\).   (1 mark)

  3. Force \({\underset{\sim}{F}}_1\) from part (i) and a second force,  \({\underset{\sim}{F}}_2=-6 \underset{\sim}{i}+12 \underset{\sim}{j}+4 \underset{\sim}{k}\), both act upon a particle.
  4. Show that the resultant force acting on the particle is given by:
  5.      \({\underset{\sim}{F}}_3=2 \underset{\sim}{i}+4 \underset{\sim}{j}+8 \underset{\sim}{k}.\)   (1 mark)

  6. Calculate  \({\underset{\sim}{F}}_3 \cdot \underset{\sim}{d}\), where \({\underset{\sim}{F}}_3\) is the resultant force from part (ii) and  \(\underset{\sim}{d}=\underset{\sim}{i}+\underset{\sim}{j}+2 \underset{\sim}{k}\).   (1 mark)

Show Answers Only

i.    \(\abs{2 \underset{\sim}{i}-2 \underset{\sim}{j}+\underset{\sim}{k}}=\sqrt{2^2+(-2)^2+1^2}=3\)

\({\underset{\sim}{F}}_1=\dfrac{12}{3}\left(\begin{array}{c}2 \\ -2 \\ 1\end{array}\right)=\left(\begin{array}{c}8 \\ -8 \\ 4\end{array}\right)\)

\({\underset{\sim}{F}}_1=8\underset{\sim}{i}-8 \underset{\sim}{j}+4 \underset{\sim}{k}\)
 

ii.    \({\underset{\sim}{F}}_3={\underset{\sim}{F}}_1+{\underset{\sim}{F}}_2=\left(\begin{array}{c}8 \\ -8 \\ 4\end{array}\right)+\left(\begin{array}{c}-6 \\ 12 \\ 4\end{array}\right)=\left(\begin{array}{l}2 \\ 4 \\ 8\end{array}\right)\)

\({\underset{\sim}{F}}_3=2 \underset{\sim}{i}+4 \underset{\sim}{j}+8 \underset{\sim}{k}\)
 

iii.  \({\underset{\sim}{F}}_3 \cdot d=\left(\begin{array}{l}2 \\ 4 \\ 8\end{array}\right)\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right)=2+4+16=22\)

Show Worked Solution

i.    \(\abs{2 \underset{\sim}{i}-2 \underset{\sim}{j}+\underset{\sim}{k}}=\sqrt{2^2+(-2)^2+1^2}=3\)

\({\underset{\sim}{F}}_1=\dfrac{12}{3}\left(\begin{array}{c}2 \\ -2 \\ 1\end{array}\right)=\left(\begin{array}{c}8 \\ -8 \\ 4\end{array}\right)\)

\({\underset{\sim}{F}}_1=8\underset{\sim}{i}-8 \underset{\sim}{j}+4 \underset{\sim}{k}\)
 

ii.    \({\underset{\sim}{F}}_3={\underset{\sim}{F}}_1+{\underset{\sim}{F}}_2=\left(\begin{array}{c}8 \\ -8 \\ 4\end{array}\right)+\left(\begin{array}{c}-6 \\ 12 \\ 4\end{array}\right)=\left(\begin{array}{l}2 \\ 4 \\ 8\end{array}\right)\)

\({\underset{\sim}{F}}_3=2 \underset{\sim}{i}+4 \underset{\sim}{j}+8 \underset{\sim}{k}\)
 

iii.  \({\underset{\sim}{F}}_3 \cdot d=\left(\begin{array}{l}2 \\ 4 \\ 8\end{array}\right)\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right)=2+4+16=22\)

Vectors, EXT2 V1 2025 HSC 1 MC

Points \(A\) and \(B\) are \((-3,1)\) and \((1,4)\) respectively.

Which of the following is a vector equation of the line \(A B\) with parameter \(\lambda\) ?

  1. \(\displaystyle \binom{x}{y}=\binom{1}{4}+\lambda\binom{3}{4}\)
  2. \(\displaystyle\binom{x}{y}=\binom{3}{4}+\lambda\binom{1}{4}\)
  3. \(\displaystyle\binom{x}{y}=\binom{4}{3}+\lambda\binom{-3}{1}\)
  4. \(\displaystyle\binom{x}{y}=\binom{-3}{1}+\lambda\binom{4}{3}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\overrightarrow{AB}=\displaystyle \binom{1}{4}-\binom{-3}{1}=\binom{4}{3}\)

\(\text{Line} \ \ AB:\)

\(\displaystyle \binom{x}{y}=\binom{-3}{1}+\lambda\binom{4}{3}\)

\(\Rightarrow D\)

BIOLOGY, M5 2025 HSC 1 MC

Amoeba reproduce by the process shown.
  

     

Which of the following is a characteristic of the daughter cells?

  1. Genetically different to parent amoeba
  2. Genetically identical to parent amoeba
  3. More organelles due to the cell division
  4. Fewer chromosomes than the parent amoeba
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Asexual reproduction produces genetically identical offspring.

Other Options:

  • A is incorrect: Sexual reproduction produces genetic variation, not asexual.
  • C is incorrect: Cell division distributes existing organelles between daughter cells.
  • D is incorrect: Mitosis maintains the same chromosome number in offspring.

Networks, STD1 N1 2025 HSC 14

The time, in minutes, it takes to travel by road between six towns is recorded and shown in the network diagram below.
 

  1. In this network the shortest path corresponds to the minimum travel time.
  2. What is the minimum travel time between towns \(A\) and \(F\), and what is the corresponding path?   (2 marks)

New roads are built to connect a town \(G\) to towns \(A\) and \(D\). The table gives the times it takes to travel by the new roads.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Town} \rule[-1ex]{0pt}{0pt} & \textit{Time} \text{(minutes)}  \rule[-1ex]{0pt}{0pt} & \textit{Town} \\
\hline
\rule{0pt}{2.5ex} A \rule[-1ex]{0pt}{0pt} & 8 \rule[-1ex]{0pt}{0pt} & G \\
\hline
\rule{0pt}{2.5ex} G \rule[-1ex]{0pt}{0pt} & 22 \rule[-1ex]{0pt}{0pt} & D \\
\hline
\end{array}

  1. Add the new roads and times to the network diagram below.   (2 marks)
     
      

     

  2. Explain whether the path in part (a) is still the shortest path from \(A\) to \(F\) after the new roads are added.   (1 mark)

Show Answers Only

a.    \(\text{Minimum travel time}\ = 15+20+10+5+8=58\ \text{minutes}\)

\(\text{Path: }A → B → C → D → E → F\)
 

b.    \(\text{New roads}\ A  → G\ \text{and }G → D \)
 

c.    \(\text{Using the new roads }A → G\ \text{and }G → D:\)

\(\text{Minimum travel time}\ =8+22+5+8=43\ \text{minutes.}\)

\(\text{Therefore the original path is no longer the shortest path.}\)

Show Worked Solution

a.    \(\text{Minimum travel time}\ = 15+20+10+5+8=58\ \text{minutes}\)

\(\text{Path: }A → B → C → D → E → F\)
 

b.    \(\text{New roads}\ A  → G\ \text{and }G → D \)
 

c.    \(\text{Using the new roads }A → G\ \text{and }G → D:\)

\(\text{Minimum travel time}\ =8+22+5+8=43\ \text{minutes.}\)

\(\text{Therefore the original path is no longer the shortest path.}\)

Probability, STD2 S2 2025 HSC 8 MC

A spinner made up of 4 colours is spun 100 times. The frequency histogram shows the results.
 

Which of these spinners is most likely to give the results shown?
 

Show Answers Only

\(A\)

Show Worked Solution
\(P(\text{White})\) \(=\dfrac{50}{100}=\dfrac{1}{2}\)
\(P(\text{Red})\) \(=\dfrac{25}{100}=\dfrac{1}{4}\)  
\(P(\text{Yellow})\) \(=\dfrac{15}{100}=\dfrac{3}{20}\)
\(P(\text{Green})\) \(=\dfrac{10}{100}=\dfrac{2}{20}=\dfrac{1}{10}\)

 
\(\text{Eliminate Options B and D as white}\ \neq \dfrac{1}{2}\ \text{of spinner.}\)

\(\text{Eliminate Option C as red}\ \neq \dfrac{1}{4}\ \text{of spinner.}\)

\(\Rightarrow A\)

Functions, 2ADV F1 2025 HSC 11

The graph of a quadratic function represented by the equation  \(h=t^2-8 t+12\)  is shown.
 

  1. Find the values of \(t\) and \(h\) at the turning point of the graph.   (2 marks)

  2. The graph shows  \(h=12\)  when  \(t=0\).
  3. What is the other value of \(t\) for which  \(h=12\)?   (1 mark)

Show Answers Only

a.   \(\text{Turning point at} \ \ (4,-4)\)

b.   \(t=8\)

Show Worked Solution

a.    \(\text{Strategy 1 (no calculus)}\)

\(\text{Axis of quadratic occurs when}\ \ t= \dfrac{2+6}{2} = 4\)

\(\text{At} \ \ t=4:\)

\(h=4^2-8 \times 4+12=-4\)

\(\therefore \ \text{Turning point at} \ \ (4,-4)\)
 

\(\text{Strategy 2 (using calculus)}\)

\(h=t^2-8 t+12\)

\(h^{\prime}=2 t-8\)

\(\text{Find \(t\) when} \ \ h^{\prime}=0:\)

\(2 t-8=0 \ \Rightarrow \ t=4\)
 

b.    \(\text {When} \ \ h=12:\)

\(t^2-8 t+12\) \(=12\)
\(t(t-8)\) \(=0\)

 
\(\therefore \ \text{Other value:} \ \ t=8\)

v1 Measurement, STD2 M7 2018 HSC 27a

Alex used a cloud storage service for one month.

The plan has a base monthly cost of $25. The service also charges 45 cents per GB uploaded and 12 cents per GB downloaded.

During the month, Alex uploaded 180 GB and downloaded 350 GB.

What was the total bill for the month?   (2 marks)

Show Answers Only

`$148.00`

Show Worked Solution

`text(Upload charge = 180 × 45c = $81.00)`

`text(Download charge = 350 × 12c = $42.00)`

`:.\ text(Total bill)` `= 25 + 81 + 42`
  `= $148.00`

HMS, TIP EQ-Bank 273

Describe why planning is crucial for athletes to meet their sleep, nutrition and hydration needs alongside their training commitments.   (3 marks)

Show Answers Only
  • Planning is crucial to ensure sleep, nutrition and hydration guidelines are met alongside demanding training schedules.
  • Athletes must coordinate meal preparation and timing with training sessions to optimise energy availability and recovery.
  • Sleep planning becomes essential for late games or events that can impact normal sleep patterns and recovery.
  • Hydration planning requires athletes to schedule drink breaks throughout the day based on weather conditions and training intensity.
  • Without proper planning, athletes may struggle to balance nutritional needs with training demands and competition schedules.
Show Worked Solution
  • Planning is crucial to ensure sleep, nutrition and hydration guidelines are met alongside demanding training schedules.
  • Athletes must coordinate meal preparation and timing with training sessions to optimise energy availability and recovery.
  • Sleep planning becomes essential for late games or events that can impact normal sleep patterns and recovery.
  • Hydration planning requires athletes to schedule drink breaks throughout the day based on weather conditions and training intensity.
  • Without proper planning, athletes may struggle to balance nutritional needs with training demands and competition schedules.

HMS, TIP EQ-Bank 270

Outline the general sleep guidelines recommended for athletes to reduce fatigue and support optimal recovery.   (3 marks)

Show Answers Only
  • Athletes should aim for 8-10 hours of sleep per night to allow for optimal rest and recovery from training demands.
  • Sleep duration may need to be increased during intense training periods when physical and mental stress levels are higher.
  • Deep sleep and REM sleep phases are particularly important for optimal recovery and cognitive functioning in athletes.
  • Consistent sleep and wake-up times help establish healthy sleep patterns for sustained performance.
  • Quality sleep helps reduce fatigue and supports the body’s natural recovery processes between training sessions.
Show Worked Solution
  • Athletes should aim for 8-10 hours of sleep per night to allow for optimal rest and recovery from training demands.
  • Sleep duration may need to be increased during intense training periods when physical and mental stress levels are higher.
  • Deep sleep and REM sleep phases are particularly important for optimal recovery and cognitive functioning in athletes.
  • Consistent sleep and wake-up times help establish healthy sleep patterns for sustained performance.
  • Quality sleep helps reduce fatigue and supports the body’s natural recovery processes between training sessions.

HMS, TIP EQ-Bank 267

Describe the general daily fluid intake recommendations for athletes and the indicators used to monitor hydration status.   (3 marks)

Show Answers Only
  • The general baseline recommendation for athletes is 3.7 litres per day for men and 2.7 litres per day for women.
  • However, fluid intake varies significantly with training intensity and climate conditions requiring individual adjustments.
  • Athletes should aim for pale yellow urine as a sign of good hydration status.
  • Urine colour monitoring helps assess hydration levels, with lighter colours indicating better hydration.
  • Darker urine colour indicates dehydration and the need for increased fluid intake.
Show Worked Solution
  • The general baseline recommendation for athletes is 3.7 litres per day for men and 2.7 litres per day for women.
  • However, fluid intake varies significantly with training intensity and climate conditions requiring individual adjustments.
  • Athletes should aim for pale yellow urine as a sign of good hydration status.
  • Urine colour monitoring helps assess hydration levels, with lighter colours indicating better hydration.
  • Darker urine colour indicates dehydration and the need for increased fluid intake.

HMS, TIP EQ-Bank 264

Outline the general principles of nutrient timing for endurance athletes before, during and after performance.   (3 marks)

Show Answers Only
  • Pre-performance nutrition should focus on carbohydrate intake several hours before activity to optimise glycogen stores for sustained exercise.
  • Food consumed prior to activity is useful only if digested and its energy made available to working muscles.
  • During longer endurance events, athletes need carbohydrate replacement to maintain blood glucose levels and delay fatigue.
  • Post-performance nutrition aims to quickly restore glycogen stores and return the body to its pre-event state.
  • Proper timing maximises energy availability while avoiding digestive issues during prolonged competition.
Show Worked Solution
  • Pre-performance nutrition should focus on carbohydrate intake several hours before activity to optimise glycogen stores for sustained exercise.
  • Food consumed prior to activity is useful only if digested and its energy made available to working muscles.
  • During longer endurance events, athletes need carbohydrate replacement to maintain blood glucose levels and delay fatigue.
  • Post-performance nutrition aims to quickly restore glycogen stores and return the body to its pre-event state.
  • Proper timing maximises energy availability while avoiding digestive issues during prolonged competition.

HMS, TIP EQ-Bank 261

Describe the main functions of the three macronutrients for athletes and how each contributes to athletic performance.   (3 marks)

Show Answers Only
  • Carbohydrates are required by all athletes to be broken down and stored as glycogen for energy production.
  • They provide the main fuel source for energy systems, particularly the aerobic energy system during endurance activities.
  • Fats are stored as triglycerides, similar to glycogen, and help produce energy during prolonged exercise.
  • Protein is used for muscle repair for all athletes, particularly weightlifters who require enhanced recovery.
  • Athletes have higher protein needs due to muscle repair requirements after training and competition.
Show Worked Solution
  • Carbohydrates are required by all athletes to be broken down and stored as glycogen for energy production.
  • They provide the main fuel source for energy systems, particularly the aerobic energy system during endurance activities.
  • Fats are stored as triglycerides, similar to glycogen, and help produce energy during prolonged exercise.
  • Protein is used for muscle repair for all athletes, particularly weightlifters who require enhanced recovery.
  • Athletes have higher protein needs due to muscle repair requirements after training and competition.

HMS, TIP EQ-Bank 258

Outline why athletes need to follow dietary guidelines specific to their sport to improve performance.   (3 marks)

Show Answers Only
  • Athletes need sport-specific dietary requirements because different sports require different energy intakes depending on their predominant energy system.
  • Marathon runners rely on the aerobic energy system requiring carbohydrates as the main fuel source for sustained performance.
  • Sprinters depend on the ATP/PCr energy system, requiring different nutritional support compared to endurance athletes.
  • Athletes must eat enough macronutrients and micronutrients suitable for their specific sport and training requirements.
  • Without proper nutrition, athletes will lack the energy needed to train effectively and sustain competition performance.
Show Worked Solution
  • Athletes need sport-specific dietary requirements because different sports require different energy intakes depending on their predominant energy system.
  • Marathon runners rely on the aerobic energy system requiring carbohydrates as the main fuel source for sustained performance.
  • Sprinters depend on the ATP/PCr energy system, requiring different nutritional support compared to endurance athletes.
  • Athletes must eat enough macronutrients and micronutrients suitable for their specific sport and training requirements.
  • Without proper nutrition, athletes will lack the energy needed to train effectively and sustain competition performance.

HMS, TIP EQ-Bank 257

Outline the main structural changes that occur in muscle fibres during the hypertrophy process following strength training.   (3 marks)

Show Answers Only
  • Muscle hypertrophy refers to the increase in muscle size due to growth in muscle fibres.
  • The process involves enlargement of cross-sectional muscle area following strength training demands.
  • Structural changes include an increase in actin and myosin filaments within the muscle cells.
  • Myofibrils within muscle fibres also enlarge to support enhanced muscle contraction.
  • Connective tissues that support muscle contraction strengthen during the hypertrophy process.
  • These adaptations occur when muscles are challenged beyond their normal capacity through progressive resistance training.
Show Worked Solution
  • Muscle hypertrophy refers to the increase in muscle size due to growth in muscle fibres.
  • The process involves enlargement of cross-sectional muscle area following strength training demands.
  • Structural changes include an increase in actin and myosin filaments within the muscle cells.
  • Myofibrils within muscle fibres also enlarge to support enhanced muscle contraction.
  • Connective tissues that support muscle contraction strengthen during the hypertrophy process.
  • These adaptations occur when muscles are challenged beyond their normal capacity through progressive resistance training.

HMS, TIP EQ-Bank 252

Outline the main characteristics that distinguish slow twitch muscle fibres from fast twitch muscle fibres in terms of their structure and function.   (3 marks)

Show Answers Only
  • Slow twitch fibres contract slowly and sustain activity for extended periods without fatigue.
  • They are efficient at using oxygen to generate energy through aerobic metabolism pathways.
  • Slow twitch fibres contain high numbers of mitochondria and increased myoglobin content for oxygen storage.
  • Fast twitch fibres contract quickly and generate high power output but fatigue rapidly.
  • They rely primarily on anaerobic energy systems for fuel during explosive movements.
  • Fast twitch fibres have lower mitochondrial density but greater glycolytic enzyme activity for rapid energy production.
Show Worked Solution
  • Slow twitch fibres contract slowly and sustain activity for extended periods without fatigue.
  • They are efficient at using oxygen to generate energy through aerobic metabolism pathways.
  • Slow twitch fibres contain high numbers of mitochondria and increased myoglobin content for oxygen storage.
  • Fast twitch fibres contract quickly and generate high power output but fatigue rapidly.
  • They rely primarily on anaerobic energy systems for fuel during explosive movements.
  • Fast twitch fibres have lower mitochondrial density but greater glycolytic enzyme activity for rapid energy production.

HMS, TIP EQ-Bank 246

Why are warm-up and cool-down components considered essential parts of every training session for both aerobic and strength training programs?   (3 marks)

Show Answers Only
  • Warm-up components prepare the body for training by gradually increasing heart rate and muscle temperature.
  • This process reduces injury risk through improved joint mobility and muscle elasticity before intense exercise.
  • Warm-up activities enhance performance by activating the cardiovascular system and preparing muscles for training demands.
  • Cool-down components help gradually lower heart rate and prevent blood pooling in extremities after exercise.
  • This enables better recovery by promoting lactic acid removal and reducing muscle stiffness post-training.
Show Worked Solution
  • Warm-up components prepare the body for training by gradually increasing heart rate and muscle temperature.
  • This process reduces injury risk through improved joint mobility and muscle elasticity before intense exercise.
  • Warm-up activities enhance performance by activating the cardiovascular system and preparing muscles for training demands.
  • Cool-down components help gradually lower heart rate and prevent blood pooling in extremities after exercise.
  • This enables better recovery by promoting lactic acid removal and reducing muscle stiffness post-training.

HMS, TIP EQ-Bank 243

A football player has been using the same strength training routine for 12 weeks, performing identical exercises, sets and repetitions in each session. Their coach suggests applying the variety principle to improve training effectiveness.

Outline three different ways the variety principle could be applied to the football player's strength training program.   (3 marks)

Show Answers Only
  • Equipment variety can be applied by alternating between free weights, fixed machines and elastic bands across different training sessions.
  • Exercise selection variety involves changing from bench press to push-ups or dumbbell flies to target chest muscles differently.
  • Session type variety includes incorporating supersets, drop sets or pyramid training methods instead of standard straight sets.
  • Training environment variety could involve outdoor training sessions, different gym locations or home-based body weight workouts.
  • These variety applications prevent training plateaus while maintaining athlete motivation and engagement.
Show Worked Solution
  • Equipment variety can be applied by alternating between free weights, fixed machines and elastic bands across different training sessions.
  • Exercise selection variety involves changing from bench press to push-ups or dumbbell flies to target chest muscles differently.
  • Session type variety includes incorporating supersets, drop sets or pyramid training methods instead of standard straight sets.
  • Training environment variety could involve outdoor training sessions, different gym locations or home-based body weight workouts.
  • These variety applications prevent training plateaus while maintaining athlete motivation and engagement.

HMS, TIP EQ-Bank 241

A 20-year-old athlete wants to train within their aerobic training zone to improve cardiovascular fitness. They calculate their maximum heart rate as 200 beats per minute and know that the aerobic threshold is approximately 70% of maximum heart rate.

Describe the characteristics of training at the aerobic threshold and what happens when the athlete exercises above this intensity level.   (3 marks)

Show Answers Only
  • Training at aerobic threshold involves exercising at approximately 140 beats per minute for sustained periods.
  • Aerobic threshold represents the minimum intensity required to achieve cardiovascular training adaptations and improvements.
  • Athletes can maintain steady-state exercise at this level using primarily aerobic energy systems for fuel.
  • Exercising above aerobic threshold but below anaerobic threshold places athletes in the aerobic training zone.
  • Training above anaerobic threshold results in rapid lactate accumulation and inability to sustain exercise intensity.
Show Worked Solution
  • Training at aerobic threshold involves exercising at approximately 140 beats per minute for sustained periods.
  • Aerobic threshold represents the minimum intensity required to achieve cardiovascular training adaptations and improvements.
  • Athletes can maintain steady-state exercise at this level using primarily aerobic energy systems for fuel.
  • Exercising above aerobic threshold but below anaerobic threshold places athletes in the aerobic training zone.
  • Training above anaerobic threshold results in rapid lactate accumulation and inability to sustain exercise intensity.

HMS, TIP EQ-Bank 238

A tennis coach uses drills and modified games to help players improve their backhand technique. The coach notices that players perform well during drills but struggle to use the backhand effectively during actual match play.

Explain why modified games might be more effective than drills for developing the backhand skill in competitive situations.   (3 marks)

Show Answers Only
  • Drills involve repetitive practice under controlled conditions without decision-making pressure or opposition.
  • This creates limited transfer to match situations where players face unpredictable ball placement and timing.
  • Modified games provide realistic match conditions with decision-making requirements and variable ball trajectories.
  • These conditions enable players to practice backhand technique while responding to changing game situations.
  • Therefore modified games better prepare players for competitive backhand execution under match pressure.
Show Worked Solution
  • Drills involve repetitive practice under controlled conditions without decision-making pressure or opposition.
  • This creates limited transfer to match situations where players face unpredictable ball placement and timing.
  • Modified games provide realistic match conditions with decision-making requirements and variable ball trajectories.
  • These conditions enable players to practice backhand technique while responding to changing game situations.
  • Therefore modified games better prepare players for competitive backhand execution under match pressure.

HMS, HAG EQ-Bank 82 MC

Which sector classification includes religious organisations and charity groups that operate health services?

  1. Federal government sector
  2. State government sector
  3. Local government sector
  4. Private sector
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Religious organisations and charity groups operate health services within the private sector.

Other Options:

  • A is incorrect: Religious and charity groups are not part of federal government operations.
  • B is incorrect: These organisations operate independently from state government structures.
  • C is incorrect: Local government doesn’t include religious organisations and charity groups.

HMS, HAG EQ-Bank 24 MC

Australia's Medicare system provides universal healthcare coverage to all citizens. Which factor explains why countries with similar universal healthcare systems might still have different health outcomes?

  1. All countries with universal healthcare have identical health outcomes
  2. Healthcare systems are the only factor influencing population health
  3. Universal coverage guarantees the highest life expectancy possible
  4. Social determinants and lifestyle factors also influence health beyond healthcare access
Show Answers Only

\(D\)

Show Worked Solution
  • D is correct: Health outcomes depend on multiple factors beyond just healthcare system design.

Other Options:

  • A is incorrect: Countries with universal systems still show varied health outcomes.
  • B is incorrect: Social, cultural, and environmental factors also influence population health.
  • C is incorrect: Universal coverage important but doesn’t guarantee optimal life expectancy.

HMS, HAG EQ-Bank 18 MC

According to Australia's Health 2024 data, which health indicator shows Australia performing BELOW the OECD average?

  1. Life expectancy at birth
  2. Daily tobacco smoking rates
  3. Overweight and obesity prevalence
  4. Cardiovascular disease mortality rates
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Australia’s obesity rate exceeds OECD average indicating below-average performance.

Other Options:

  • A is incorrect: Australia ranks fourth highest for life expectancy.
  • B is incorrect: Australia has fifth lowest smoking rates among OECD.
  • D is incorrect: Australia has fifth lowest cardiovascular mortality rates.

HMS, HIC 2012 HSC 4 MC

Which of the following is a modifiable risk factor of cardiovascular disease?

  1. Age
  2. Diet
  3. Gender
  4. Heredity
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Diet is a modifiable behavioural risk factor for cardiovascular disease.

Other Options:

  • A is incorrect: Age is a non-modifiable demographic risk factor.
  • C is incorrect: Gender is a non-modifiable biological risk factor.
  • D is incorrect: Heredity is a non-modifiable genetic risk factor.

HMS, TIP 2013 HSC 11 MC

Which principle of training refers to aligning training activities with the demands of a particular sport?

  1. Variety
  2. Specificity
  3. Reversibility
  4. Warm up and cool down
Show Answers Only

\(B\)

Show Worked Solution
  • B is correct: Specificity requires training to match sport-specific movement patterns.

Other Options:

  • A is incorrect: Variety prevents boredom, not sport-specific alignment.
  • C is incorrect: Reversibility refers to fitness loss without training.
  • D is incorrect: Warm-up/cool-down are preparation protocols, not alignment principles.

HMS, HAG 2013 HSC 8 MC

Which of the following best explains why breast cancer death rates are decreasing while incidence rates are increasing in Australia?

  1. Enhanced early detection and treatment
  2. Increased use and acceptance of alternative medicines
  3. Improved access to and delivery of immunisation programs
  4. Advances in understanding the role of family history in surviving breast cancer after diagnosis
Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: Early detection and treatment improve survival despite higher incidence.

Other Options:

  • B is incorrect: Alternative medicines not primary factor in survival improvement.
  • C is incorrect: No immunisation exists for breast cancer prevention.
  • D is incorrect: Family history understanding doesn’t explain incidence/mortality trends.

HMS, HAG 2013 HSC 6 MC

What is a benefit of emerging medical technologies?

  1. They are readily accessible for all patients.
  2. They are inexpensive for public and private hospitals.
  3. They can provide a means of early detection.
  4. They decrease the need for Medicare and the Pharmaceuticals Benefits Scheme.
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: New technologies enable earlier disease detection and diagnosis.

Other Options:

  • A is incorrect: Emerging technologies often have limited initial accessibility.
  • B is incorrect: New technologies typically expensive during early adoption.
  • D is incorrect: Technologies complement rather than replace Medicare/PBS systems.

HMS, HIC 2013 HSC 2 MC

Which of the following measures is NOT used to determine the health status of the population?

  1. Mortality
  2. Morbidity
  3. Quality of life
  4. Life expectancy
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Quality of life is subjective measure, not epidemiological indicator.

Other Options:

  • A is incorrect: Mortality is key health status measurement tool.
  • B is incorrect: Morbidity measures illness levels in populations effectively.
  • D is incorrect: Life expectancy is standard health status indicator.

HMS, HIC 2014 HSC 3 MC

What is the purpose of epidemiology?

  1. To identify causes and patterns of disease in a population
  2. To track hospital admission rates and ambulance response times
  3. To determine how health care budgets are managed by governments
  4. To monitor prescription medicines being administered by doctors to their patients
Show Answers Only

\(A\)

Show Worked Solution
  • A is correct: Epidemiology studies disease causes and patterns in populations.

Other Options:

  • B is incorrect: Hospital tracking is health service monitoring not epidemiology.
  • C is incorrect: Budget management is health economics not epidemiology.
  • D is incorrect: Prescription monitoring is pharmaceutical surveillance not epidemiology.

HMS, HAG 2015 HSC 1 MC

Which of the following is the main benefit of emerging treatments and technologies in health care

  1. Reduced costs for health care
  2.  Reduced dental health problems
  3. Improved early detection and screening procedures
  4. Improved waiting times for surgery in public hospitals
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: New technologies primarily enable earlier disease identification and screening.

Other Options:

  • A is incorrect: Technology typically increases rather than reduces healthcare costs.
  • B is incorrect: Too specific, not the main overall benefit.
  • D is incorrect: Technology doesn’t directly address surgical waiting times.

HMS, HAG 2016 HSC 17 MC

Which of the following best describes healthy ageing?

  1. Ageing at a healthy rate and trying to look younger
  2. Increasing the proportion of people who consume healthy foods throughout their life
  3. Reducing the risk of illness and disease when growing older by maintaining physical, dietary and mental health
  4. Reducing the number of people who die at a young age from illnesses related to hereditary and genetic factors
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: Healthy ageing involves maintaining wellness across all health dimensions.

Other Options:

  • A is incorrect: Focus on appearance rather than genuine health maintenance.
  • B is incorrect: Too narrow, only addresses nutrition not comprehensive health.
  • D is incorrect: Describes preventing premature death, not healthy ageing process.

HMS, HAG 2018 HSC 10 MC

Which of the following best describes Medicare?

  1. It is funded by taxpayers and covers the cost of ambulance services.
  2. It is funded by private contributions and covers the cost of physiotherapy.
  3. It is funded by insurance premiums and covers the cost of private hospitals.
  4. It is funded by a levy and subsidises the cost of visits to general practitioners.
Show Answers Only

\(D\)

Show Worked Solution

  • D is correct: Medicare is funded by a levy and subsidises GP visits through bulk billing.

Other Options:

  • A is incorrect: Ambulance services are typically state-funded, not covered by Medicare.
  • B is incorrect: Medicare is government-funded through levy, not private contributions.
  • C is incorrect: Private health insurance covers private hospitals, not Medicare.