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CHEMISTRY, M7 2024 HSC 1 MC

Which two substances are members of the same homologous series?
 

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→ A homologous series refers to compounds with the same or similar functional group and same general formula.

→ Both substances in contain a hydroxyl group.

Matrices, GEN1 2024 VCAA 28 MC

A primary school is hosting a sports day.

Students represent one of four teams: blue , green , red or yellow .

Students compete in one of three sports: football , netball or tennis .

Matrix shows the number of students competing in each sport and the team they represent.

Matrix is multiplied by the matrix to produce matrix .

Element indicates that

  1. 210 students represent the blue team.
  2. 210 students compete in netball.
  3. 280 students compete in tennis.
  4. 280 students compete in football.
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Matrices, GEN1 2024 VCAA 26 MC

A market stall sells three types of candles.

The cost of each type of candle is shown in matrix below.

Towards the end of the day, the cost of each item is discounted by 15%.

Which one of the following expressions can be used to determine each discounted price?

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Extra close brace or missing open brace

Data Analysis, GEN1 2024 VCAA 5 MC

The number of siblings of each member of a class of 24 students was recorded.

The results are displayed in the table below.

A boxplot was constructed to display the spread of the data.

Which one of the following statements about this boxplot is correct?

  1. There are no outliers.
  2. The value of the interquartile range (IQR) is 1.5
  3. The value of the median is 1.5
  4. All of the five-number summary values are whole numbers.
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Data Analysis, GEN1 2024 VCAA 2 MC

Freddie organised a function at work. He surveyed the staff about their preferences.

He asked them about their payment preference (cash or electronic payment) and their budget preference (less than $50 or more than $50).

The variables in this survey, payment preference and budget preference, are

  1. both categorical variables.
  2. both numerical variables.
  3. categorical and numerical variables, respectively.
  4. numerical and categorical variables, respectively.
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Mechanics, EXT2 M1 2024 HSC 15c

A bar magnet is held vertically. An object that is repelled by the magnet is to be dropped from directly above the magnet and will maintain a vertical trajectory. Let be the distance of the object above the magnet.
 

The object is subject to acceleration due to gravity, , and an acceleration due to the magnet , so that the total acceleration of the object is given by

 

The object is released from rest at  .

  1. Show that  .   (2 marks)

  2. Find where the object next comes to rest, giving your answer correct to 1 decimal place.  (2 marks)

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ii.   

 
 
 

 

♦♦♦ Mean mark (ii) 24%.

 
   
   
   

 
 

Vectors, EXT2 V1 2024 HSC 14e

The diagram shows triangle .

The point lies on so that  .

The point lies on so that  .

The point is the intersection of and .

The point is chosen on so that and are collinear.
 

Let    and    where is a real number.

  1. Show that  .   (2 marks)

Writing  , where is a real number, it can be shown that  .  (Do NOT prove this.)

  1. Show that  .   (2 marks)

  2. Find in terms of and .   (2 marks)

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ii.   

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iii.    

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iii.   

♦ Mean mark (iii) 45%.
 

 
 
   

 

 
 
 

 

ENGINEERING, TE 2024 HSC 4 MC

Which row of the table correctly identifies characteristics of analogue and digital communications?

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→ Analog signals are continuous and more susceptible to degradation while digital signals are discrete (binary) and less susceptible to degradation since they can be regenerated and error-corrected during transmission.

ENGINEERING, CS 2024 HSC 1 MC

A common house brick is shown.
 

Which forming process was used to manufacture the brick?

  1. Forging
  2. Extrusion
  3. Slip casting
  4. Shell moulding
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→ Common house bricks are manufactured through extrusion, where clay is forced through a die to create a rectangular column that is then cut into individual brick lengths before drying and firing.

Mechanics, EXT2 M1 2024 HSC 13c

A particle of unit mass moves horizontally in a straight line. It experiences a resistive force proportional to , where m s is the speed of the particle, so that the acceleration is given by  .

Initially the particle is at the origin and has a velocity of 40 m s to the right. After the particle has moved 15 m to the right, its velocity is 10 m s (to the right).

  1. Show that  .   (3 marks)

  2. Show that  .   (1 mark)

  3. At what time will the particle's velocity be 30 m s to the right?   (3 marks)

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ii.  

 
 
 
 
 

iii. 

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Vectors, EXT2 V1 2024 HSC 13a

The point has position vector  . The line has vector equation

.

The point lies on and has position vector  .

  1. Show that  .   (1 mark)

  2. Hence, or otherwise, determine the shortest distance between the point and the line .  (2 marks)

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ii.   

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ii.   

♦ Mean mark (ii) 45%.

Vectors, EXT2 V1 2024 HSC 12e

The line passes through the points and .

  1. Find a vector equation of the line .   (1 mark)

  2. Determine, giving reasons, whether the point lies on the line .   (2 marks)

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ii.   

 

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ii.   

 

Calculus, EXT1 C3 2024 HSC 13a

In an experiment, the population of insects, , was modelled by the logistic differential equation

where is the time in days after the beginning of the experiment.

The diagram shows a direction field for this differential equation, with the point representing the initial population.
 

  1. Explain why the graph of the solution that passes through the point cannot also pass through the point .   (1 mark)

  2. Clearly sketch the graph of the solution that passes through the point .   (1 mark)

  3. Find the predicted value of the population, , at which the rate of growth of the population is largest.   (2 marks)

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 i.   

ii.    
       

iii. 

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 i.   

ii.    
       

iii. 

♦ Mean mark (iii) 51%.

CHEMISTRY, M2 EQ-Bank 2

In an experiment, calcium carbonate is heated strongly to produce calcium oxide and carbon dioxide according to the reaction below:

A student starts with 50.0 g of calcium carbonate. After heating, they collect 28.0 g of calcium oxide.

  1. Using the law of conservation of mass, calculate the mass of carbon dioxide gas produced in this reaction.   (2 marks)
  1. Explain how the law of conservation of mass applies to this reaction.   (2 marks)
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a.   

b.    The law of conservation of mass states that the mass of reactants in a chemical reaction must equal the mass of the products.

→ Here, the 50.0 g of calcium carbonate decomposes into 28.0 g of calcium oxide and 22.0 g of carbon dioxide gas.

→ The total mass of products (28.0 g + 22.0 g) equals the initial mass of reactants (50.0 g), confirming that mass is conserved in this reaction.

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a.    Law of conservation of mass:

→ The total mass of reactants must equal the total mass of products.

 
   
   

 

b.    Application of law to reaction:

→ The mass of reactants in a chemical reaction must equal the mass of the products.

→ Here, the 50.0 g of calcium carbonate decomposes into 28.0 g of calcium oxide and 22.0 g of carbon dioxide gas.

→ The total mass of products (28.0 g + 22.0 g) equals the initial mass of reactants (50.0 g), confirming that mass is conserved in this reaction.

CHEMISTRY, M2 EQ-Bank 1 MC

What numbers are required to correctly balance this equation?

__ __ __ __

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Balancing the iron atoms:

→ There are 2 Fe atoms in , so we place a 2 in front of  on the product side.


 

Balancing the oxygen atoms:

→ has 3 oxygen atoms. To balance equation, we need 3 molecules on the reactant side to balance the 3 molecules on the product side.

CHEMISTRY, M2 EQ-Bank 13

  1. Calculate the volume of solution needed to obtain 0.6 moles of solute from a solution of concentration 1.2 mol/L.   (1 mark)
  1. Explain the significance of accurate volume measurements when preparing solutions of specific concentrations in the laboratory.   (2 marks)
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a.   

b.    The exact volumes of solutions must be known as:

→ The concentration of each solution must be precise, as it affects the molar ratios and yields.

→ Miscalculating volume would lead to incorrect concentrations, impacting experimental results and validity.

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a.   
 

b.    The exact volumes of solutions must be known as:

→ The concentration of each solution must be precise, as it affects the molar ratios and yields.

→ Miscalculating volume would lead to incorrect concentrations, impacting experimental results and validity.

CHEMISTRY, M2 EQ-Bank 12

  1. Calculate the amount (in moles) of a solute in a 2.0 L solution with a concentration of 0.75 mol/L.   (1 mark)
  1. Using your answer from part a, determine the mass of the solute if the solute is .   (2 marks)
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b.   

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b.   

Trigonometry, EXT1 T1 2024 HSC 5 MC

Consider the function  .

Which transformations have been applied to   to obtain ?

  1. Vertical dilation by a factor of and a horizontal dilation by a factor of
  2. Vertical dilation by a factor of and a horizontal dilation by a factor of 3
  3. Vertical dilation by a factor of 2 and a horizontal dilation by a factor of
  4. Vertical dilation by a factor of 2 and a horizontal dilation by a factor of 3
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CHEMISTRY, M2 EQ-Bank 5 MC

A standard solution is best described as:

  1. A solution prepared to an approximate concentration for general use.
  2. A solution with a precisely known concentration, used in quantitative chemical analysis.
  3. A solution containing only one type of solute molecule.
  4. A solution prepared by dissolving a solid solute in a small volume of solvent.
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→ A standard solution is a solution with a precise and known concentration, allowing accurate calculations in quantitative chemical analysis.

→ It is prepared by dissolving an exact amount of a primary standard in a specific volume of solvent.

CHEMISTRY, M2 EQ-Bank 7

  1. 4.56 g of potassium chloride is dissolved in 250 mL of water. What is the concentration of this solution?   (2 marks)
  1. How many grams of calcium chloride will be needed to make 1.50 L of a 0.250 M solution?   (2 marks)
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b.   

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b.   

Probability, STD1 S2 2024 HSC 17

A wheel is shown with the numbers 0 to 19 marked.

A game is played where the wheel is spun until it stops.

When the wheel stops, a pointer points to the winning number. Each number is equally likely to win.
 

  1. List all the even numbers on the wheel that are greater than 7.   (1 mark)

  2. What is the probability that the winning number is NOT an even number greater than 7?   (2 marks)

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b.   

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b.   

♦♦ Mean mark (b) 32%.

Networks, STD1 N1 2024 HSC 15

A network of towns and the distances between them in kilometres is shown.
 

  1. What is the shortest path from to ?   (2 marks)

  2. A truck driver needs to travel from to but knows that the road from to is closed.
  3. What is the length of the shortest path the truck driver can take from to after the road closure?  (2 marks)

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a.   

b. 

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b.   

Algebra, STD2 A1 2024 HSC 24

Sarah, a 60 kg female, consumes 3 glasses of wine at a family dinner over 2.5 hours.

Note: there are 1.2 standard drinks in one glass of wine.

The blood alcohol content for females can be estimated by

  where  = number of standard drinks
   = number of hours drinking
   = mass in kilograms
 
  1. Calculate Sarah's at the end of the dinner, correct to 3 decimal places.   (2 marks)

  2. The time it takes a person's BAC to reach zero is given by   

                 

    Calculate the time it takes for Sarah's BAC to return to zero, assuming she stopped drinking after 2.5 hours. Give your answer to the nearest minute.  (2 marks)

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b.   

 

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b.    
   
   
COMMENT: Use calculator degrees/minutes function for part (b).

Financial Maths, STD2 F1 2024 HSC 23

Zazu works a 38-hour week and is paid at an hourly rate of $45. Any overtime hours worked are paid at time-and-a-half.

In a particular week, Zazu worked the regular 38 hours and some overtime hours. In that week Zazu earned $2790.

How many hours of overtime did Zazu work in that week?   (3 marks)

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Networks, STD2 N2 2024 HSC 16

A network of towns and the distances between them in kilometres is shown.
 

  1. What is the shortest path from to ?   (2 marks)

  2. A truck driver needs to travel from to but knows that the road from to is closed.
  3. What is the length of the shortest path the truck driver can take from to after the road closure?  (2 marks)

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a.   

b. 

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b.   

Statistics, 2ADV S2 2024 HSC 21

A researcher is studying anacondas (a type of snake).

A dataset recording the age (in years) and length (in cm) of female and male anacondas is displayed on the graph.

Anacondas reach maturity at about 4 years of age.
 

Write THREE observations about anacondas that may be made from the scatterplot. (Note: No calculations are required.)   (3 marks)

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Calculus, 2ADV C3 2024 HSC 17

In a particular electrical circuit, the voltage (volts) across a capacitor is given by

,

where is a positive constant and is the number of seconds after the circuit is switched on.

  1. Draw a sketch of the graph of , showing its behaviour as increases.   (2 marks)
     

  1. When , the voltage across the capacitor is 2.6 volts.
  2. Find the value of , correct to 3 decimal places.   (2 marks)
  1. Find the rate at which the voltage is increasing when , correct to 3 decimal places.   (2 marks)

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♦ Mean mark (a) 49%.

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CHEMISTRY, M2 EQ-Bank 8 MC

  represents which gas law?

  1. Boyle’s Law
  2. Charles’ Law
  3. Avogadro’s Law
  4. Gay-Lussac’s Law
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→ The equation  represents Charles’ Law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure and amount of gas remain constant.

CHEMISTRY, M2 EQ-Bank 7 MC

According to Gay-Lussac's Law, the pressure of a gas is directly proportional to which quantity, assuming the volume and the number of moles are constant?

  1. Volume
  2. Temperature
  3. Moles
  4. Pressure
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→ Gay-Lussac’s Law states that the pressure of a gas is directly proportional to its temperature, provided the volume and number of moles remain constant. 

→ This can be written mathematically like  .