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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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a.   

b.   

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a.   
 

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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Show Worked Solution

→ 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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a.   

b.   

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a.   

 

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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a.   

b.   

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a.   
 

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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a.   


 

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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a.   

b.   

 

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a.     

 
   

 

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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Show Worked Solution

 
 
 
 
   

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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a.   


 

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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a.   
       

b.  

c. 

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a.   
       
♦ Mean mark (a) 49%.

b.   

 
 
 
 
 
   

 
c.   

 
   
   

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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Show Worked Solution

→ 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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Show Worked Solution

→ 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  .

CHEMISTRY, M2 EQ-Bank 6

A piece of zinc weighing 3.20 grams is placed into a beaker containing 300.0 mL of 0.7500 mol/L hydrochloric acid.

  1. Determine the limiting reagent (show all working).   (2 marks)
  1. Calculate the volume of gas produced in this reaction at 25°C and 100 kPa.   (2 marks)
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a.    Zinc is the limiting reagent.

b.    

Show Worked Solution

a.    

→ Based on the mole ratio, of Zinc would require of hydrochloric acid. 

→ As there is excess hydrochloric acid, Zinc is the limiting reagent.

 

b.    The Mole ratio of is

→ of is produced.

→ At and , mole of gas

→

Calculus, 2ADV C4 2024 HSC 15

Initially there are 350 litres of water in a tank. Water starts flowing into the tank.

The rate of increase of the volume of water in litres is given by  , where is the time in hours.

Find the volume of water in the tank when  .   (3 marks)

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Calculus, 2ADV C4 2024 HSC 14

The curves    and    intersect at two points, as shown in the diagram.
 

  1. Find the -coordinates of the points of intersection of the two curves.   (1 mark)

  2. Find the area enclosed by the two curves.   (3 marks)

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a.  

b.   

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a.  

 
 
 
 

 

 

b.     
   
   
   
   
   
   

BIOLOGY, M2 EQ-Bank 17

The image below shows a dinosaur fossil found in South Africa believed to be 200 million years old.

  1. What type of diet did this dinosaur likely consume? Explain your answer.   (1 mark)
  2. Discuss two features that could be observed in the dinosaur’s digestive tract.   (3 marks)
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a.   Diet: herbivore

→ The presence of flat teeth in a dinosaur species strongly indicates a herbivorous diet, as these teeth are well-suited for grinding and processing plant material.
 

b.   Digestive tract features:

→ Herbivorous dinosaurs likely possessed specialised digestive tracts adapted for processing plant material.

→ One key feature would be an enlarged caecum, a pouch-like structure connected to the large intestine, which housed symbiotic bacteria to break down cellulose through fermentation. This process would have allowed dinosaurs to extract more nutrients from tough plant matter.

→ Additionally, these dinosaurs may have had elongated intestines to increase the surface area for nutrient absorption and provide more time for the digestion of fibrous plant material.

Show Worked Solution

a.   Diet: herbivore

→ The presence of flat teeth in a dinosaur species strongly indicates a herbivorous diet, as these teeth are well-suited for grinding and processing plant material.
 

b.   Digestive tract features:

→ Herbivorous dinosaurs likely possessed specialised digestive tracts adapted for processing plant material.

→ One key feature would be an enlarged caecum, a pouch-like structure connected to the large intestine, which housed symbiotic bacteria to break down cellulose through fermentation. This process would have allowed dinosaurs to extract more nutrients from tough plant matter.

→ Additionally, these dinosaurs may have had elongated intestines to increase the surface area for nutrient absorption and provide more time for the digestion of fibrous plant material.

BIOLOGY, M4 EQ-Bank 7

Examine the diagram provided, which depicts the biological relationships within an ecosystem.
 

  1. Describe how food webs differ from food chains in representing the flow of energy within an ecosystem.   (2 marks)

  2. Name a consumer from the second trophic level in the diagram.   (1 mark)
  3. Poaching has pushed impala populations towards extinction in certain African regions. Describe the potential ecological consequences for other species in the food web shown.   (2 marks)
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a.   Food webs vs food chains:

→ Food webs and food chains both represent energy flow in ecosystems, but differ in complexity and scope.

→ While a food chain shows a single, linear path of energy transfer from one organism to another, a food web illustrates multiple interconnected food chains within an ecosystem.

→ Food webs thus provide a more comprehensive and realistic depiction of the complex feeding relationships and energy transfers that occur among various species.
 

b.   Second trophic level  (\Rightarrow\)  first order consumer

Zebra or Impala
 

c.   Ecological consequences:

→ The decline or extinction of impalas would impact lions and vultures as they are an important food source of both.

→ Zebras would benefit from increased available vegetation due to reduced competition from impalas, leading to potential population growth.

→ The potential increase in zebra population would provide a more abundant food source for lions and vultures eventually, mitigating but not replacing the loss of impalas to these predator.

→ This scenario illustrates the complex interdependencies within the ecosystem and the cascading effects of species loss on different trophic levels.

Show Worked Solution

a.   Food webs vs food chains:

→ Food webs and food chains both represent energy flow in ecosystems, but differ in complexity and scope.

→ While a food chain shows a single, linear path of energy transfer from one organism to another, a food web illustrates multiple interconnected food chains within an ecosystem.

→ Food webs thus provide a more comprehensive and realistic depiction of the complex feeding relationships and energy transfers that occur among various species.
 

b.   Second trophic level  (\Rightarrow\)  first order consumer

Zebra or Impala
 

c.   Ecological consequences:

→ The decline or extinction of impalas would impact lions and vultures as they are an important food source of both.

→ Zebras would benefit from increased available vegetation due to reduced competition from impalas, leading to potential population growth.

→ The potential increase in zebra population would provide a more abundant food source for lions and vultures eventually, mitigating but not replacing the loss of impalas to these predator.

→ This scenario illustrates the complex interdependencies within the ecosystem and the cascading effects of species loss on different trophic levels.

BIOLOGY, M4 EQ-Bank 3

Consider a grassland ecosystem with a population of rabbits, foxes, and various grass species.

  1. Describe one example of predation in this ecosystem.   (1 mark)
  2. Explain two ways in which competition might occur between the rabbits.   (2 marks)
  3. Evaluate how the removal of foxes might affect both the rabbit population and the grass species.   (1 mark)
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a.   → Predation occurs when foxes hunt and eat rabbits.
 

b.   Competition among rabbits could result from (choose two):

→ limited resources such as food or water

→ suitable burrow sites

→ mating partners
 

c.   Removing foxes:

→ could lead to an increase in the rabbit population.

→ this growing population might then overgraze the grass species, potentially causing a decline in grass biodiversity and altering the ecosystem’s structure.

Show Worked Solution

a.   → Predation occurs when foxes hunt and eat rabbits.
 

b.   Competition among rabbits could result from (choose two):

→ limited resources such as food or water

→ suitable burrow sites

→ mating partners
 

c.   Removing foxes:

→ could lead to an increase in the rabbit population.

→ this growing population might then overgraze the grass species, potentially causing a decline in grass biodiversity and altering the ecosystem’s structure.

BIOLOGY, M4 EQ-Bank 2

  1. Is soil pH a biotic or abiotic factor?   (1 mark)
  2. Describe how soil pH can affect plant growth.   (1 mark)
  3. Explain one way in which plants might alter soil pH.   (1 mark)
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a.   Abiotic factor
 

b.   Soil pH:

→ Affects plant growth by influencing nutrient availability and solubility.

→ Most plants thrive in slightly acidic to neutral soils (pH 6.0-7.0) where essential nutrients are most accessible.
 

c.   Plants alter soil pH (choose 1):

→ through root exudates, which release organic acids into the soil.

→ through the decomposition of their leaf litter, which can increase soil acidity over time.

Show Worked Solution

a.   Abiotic factor
 

b.   Soil pH:

→ Affects plant growth by influencing nutrient availability and solubility.

→ Most plants thrive in slightly acidic to neutral soils (pH 6.0-7.0) where essential nutrients are most accessible.
 

c.   Plants alter soil pH (choose 1):

→ through root exudates, which release organic acids into the soil.

→ through the decomposition of their leaf litter, which can increase soil acidity over time.

BIOLOGY, M4 EQ-Bank 2

Our actions as a human species are inadvertently altering the evolutionary trajectories of countless organisms.

Explain two distinct mechanisms by which human activities exert selection pressures on other species. For each mechanism, provide a specific example of a species affected by this pressure.   (4 marks)

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Answers could include two of the following.

Mechanism: urbanisation

→ Human activities exert selection pressure on other species through urbanisation. As cities expand, isolated pockets of natural habitat are created, forcing species to adapt to smaller, disconnected areas.

→ For example, the San Diego deer mouse has shown rapid evolution in its size and fur colour to better camouflage against urban environments, with urban mice becoming larger and darker than their rural counterparts.
 

Mechanism: pollution from fossil fuel burning

→ Humans exert selection pressure on other species through pollution from fossil fuel burning.

→ The emission of sulfur-dioxide from coal-burning power plants has led to acid rain, which changes soil and water pH levels. This has resulted in strong selection pressure on aquatic organisms.

→ For instance, in some Scandinavian lakes, the European perch has evolved increased tolerance to acidic conditions in order to survive.
 

Mechanism: use of pesticides

→ Another mechanism is the widespread use of pesticides, which creates strong selection pressures for resistance. In agriculture, the overuse of pesticides has led to the evolution of resistance in many insect pest species.

→ A specific example is the green peach aphid, which has developed resistance to multiple classes of insecticides. This adaptation makes it increasingly difficult to control these crop pests without resorting to even more potent chemicals.

Show Worked Solution

Answers could include two of the following.

Mechanism: urbanisation

→ Human activities exert selection pressure on other species through urbanisation. As cities expand, isolated pockets of natural habitat are created, forcing species to adapt to smaller, disconnected areas.

→ For example, the San Diego deer mouse has shown rapid evolution in its size and fur colour to better camouflage against urban environments, with urban mice becoming larger and darker than their rural counterparts.
 

Mechanism: pollution from fossil fuel burning

→ Humans exert selection pressure on other species through pollution from fossil fuel burning.

→ The emission of sulfur-dioxide from coal-burning power plants has led to acid rain, which changes soil and water pH levels. This has resulted in strong selection pressure on aquatic organisms.

→ For instance, in some Scandinavian lakes, the European perch has evolved increased tolerance to acidic conditions in order to survive.
 

Mechanism: use of pesticides

→ Another mechanism is the widespread use of pesticides, which creates strong selection pressures for resistance. In agriculture, the overuse of pesticides has led to the evolution of resistance in many insect pest species.

→ A specific example is the green peach aphid, which has developed resistance to multiple classes of insecticides. This adaptation makes it increasingly difficult to control these crop pests without resorting to even more potent chemicals.

CHEMISTRY, M3 EQ-Bank 7 MC

Which of the following observations indicates a chemical change has occurred?

  1. Dissolving sugar in water
  2. Change in temperature when two solutions are mixed
  3. Melting of ice into water
  4. Mixing sand with iron filings
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→ A chemical change is one where a new substance is created and cannot be reversed.

→ The changing temperature of a mixed solution is the result of bonds breaking and forming new products thus indicating a chemical change.

→ All other options can be reversed by physical processes and therefore represent physical changes only.

BIOLOGY, M4 EQ-Bank 10

Ecosystems are dynamic, shaped not only by physical forces but also by the living organisms within them. Including a specific example, explain one biotic factor that has significantly impacted past ecosystems:

  1. Over a relatively short timescale (within a few decades or centuries)   (2 marks)
  2. Over an extended geological timescale (millions of years)   (2 marks)
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a.   Short timescale biotic factor: introduction of invasive species

→ The introduction of cane toads in Australia in 1935 has rapidly altered local ecosystems within decades.

→ Cane toads have caused declines in native predator populations that attempt to eat the toxic toads, leading to cascading effects throughout the food web.
 

b.   Geological timescale biotic factor: evolution of land plants

→ The development of land plants around 470 Mya led to increased oxygen production, soil formation, and the creation of new habitats.

→ This gradual but profound change altered atmospheric composition and weather patterns. This reshaped terrestrial ecosystems and paved the way for the evolution of terrestrial animal life.

Show Worked Solution

a.   Short timescale biotic factor: introduction of invasive species

→ The introduction of cane toads in Australia in 1935 has rapidly altered local ecosystems within decades.

→ Cane toads have caused declines in native predator populations that attempt to eat the toxic toads, leading to cascading effects throughout the food web.
 

b.   Geological timescale biotic factor: evolution of land plants

→ The development of land plants around 470 Mya led to increased oxygen production, soil formation, and the creation of new habitats.

→ This gradual but profound change altered atmospheric composition and weather patterns. This reshaped terrestrial ecosystems and paved the way for the evolution of terrestrial animal life.

CHEMISTRY, M3 EQ-Bank 17

A student tested how soluble silver salts are by reacting a 0.1 mol L silver nitrate solution with 0.1 mol L solutions of calcium hydroxide, calcium chloride, and calcium sulfate. The results are shown below:

  1. Write a balanced chemical equation for the reaction with calcium chloride.   (2 marks)
  1. Name the white precipitate.   (1 mark)
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a.    

b.    The white precipitate is → silver chloride.

Show Worked Solution

a.    
 

b.    The white precipitate is → silver chloride.

BIOLOGY, M4 EQ-Bank 6

The graph below shows the concentration of in the earth's atmosphere over the last 800 years.

  1. How would scientists obtain these historical levels of ?   (1 mark)

  2. Explain the shape of the graph over the 800 years of data presented.   (3 marks)

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a.   Data would be obtained by gas analysis within ice cores.

b.   Graph shape over the past 800 years:

→ Atmospheric levels of were very steady between the period 1200-1800 at approximately 280 ppm.

→ In the period 1800-2000, levels increased exponentially from 280 ppm to 370 ppm.

→ This increase coincided with industrialisation which saw the widespread use of fossil fuels like coal, oil, and natural gas for energy.

→ The use of these energy sources released large amounts of (\ce{CO2}\) into the atmosphere and is regarded as a major contributing factor to rise in atmospheric levels over this period.

Show Worked Solution

a.   Data would be obtained by gas analysis within ice cores.

b.   Graph shape over the past 800 years:

→ Atmospheric levels of were very steady between the period 1200-1800 at approximately 280 ppm.

→ In the period 1800-2000, levels increased exponentially from 280 ppm to 370 ppm.

→ This increase coincided with industrialisation which saw the widespread use of fossil fuels like coal, oil, and natural gas for energy.

→ The use of these energy sources released large amounts of (\ce{CO2}\) into the atmosphere and is regarded as a major contributing factor to rise in atmospheric levels over this period.

BIOLOGY, M4 EQ-Bank 5

Scientists analyse the ratio of to isotopes in various geological samples to reconstruct past climatic conditions.

  1. Describe one method used to obtain oxygen isotope data from ancient samples.   (1 mark)

  2. Explain how the relationship between and ratios provides evidence of past changes in ecosystems.   (3 marks)

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a.   Scientists analyse gas trapped within ice cores.

b.    ratios

→ The ratio of in geological samples reflects past temperature and precipitation patterns, which are crucial factors in shaping ecosystems.

→ During warmer periods, there is a higher proportion of the heavier isotope in precipitation.

→ During cooler periods, there is a relative increase in lighter .

→ These isotopic signatures allow scientists to reconstruct past climate conditions and infer associated ecosystem changes.

Show Worked Solution

a.   Scientists analyse gas trapped within ice cores.

b.    ratios

→ The ratio of in geological samples reflects past temperature and precipitation patterns, which are crucial factors in shaping ecosystems.

→ During warmer periods, there is a higher proportion of the heavier isotope in precipitation.

→ During cooler periods, there is a relative increase in lighter .

→ These isotopic signatures allow scientists to reconstruct past climate conditions and infer associated ecosystem changes.

CHEMISTRY, M3 EQ-Bank 3 MC

Which of the following are the products of the complete combustion of propane, ?

  1. Carbon monoxide, soot and water
  2. Carbon dioxide, carbon monoxide, soot and water
  3. Carbon monoxide and water
  4. Carbon dioxide and water
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Show Worked Solution

→ A reaction which under goes complete combustion will produce carbon dioxide and water.

→ Carbon monoxide is a product of incomplete combustion which occurs when there is a lack of oxygen available.

CHEMISTRY, M3 EQ-Bank 2 MC

Which of the following equations involving sulfur compounds represents a synthesis reaction?

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Show Worked Solution

→ A synthesis reaction is one where two or more reactants (sulfur dioxide and oxygen) combine to form a more complex product (sulfur trioxide).