Evaluate
--- 6 WORK AREA LINES (style=lined) ---
Aussie Maths & Science Teachers: Save your time with SmarterEd
Evaluate
--- 6 WORK AREA LINES (style=lined) ---
A country has five states,
A graph can be drawn with vertices to represent each of the states.
Edges represent a border shared between two states.
--- 1 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
a.
b.i.
b.ii.
c.
a.
b.i.
b.ii.
c.
Arthur borrowed $30 000 to buy a new motorcycle.
Interest on this loan is charged at the rate of 6.4% per annum, compounding quarterly.
Arthur will repay the loan in full with quarterly repayments over six years.
--- 1 WORK AREA LINES (style=lined) ---
The balance of the loan, in dollars, after
--- 4 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
a.
b.
c.
a.
b.
c.
The scatterplot below plots the average monthly ice cream consumption, in litres/person, against average monthly temperature, in °C. The data for the graph was recorded in the Northern Hemisphere.
When a least squares line is fitted to the scatterplot, the equation is found to be:
consumption = 0.1404 + 0.0024 × temperature
The coefficient of determination is 0.7212
--- 0 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
a.
b.
c.
d.
e.
f.
a.
b.
c.
d.
e.
f.
Consider the following statement.
'If my football team plays badly, then they are not training enough.'
Which one of the following statements is the contrapositive of the statement above?
Consider the following statement.
'If my football team plays badly, then they are not training enough.'
Which one of the following statements is the contrapositive of the statement above?
The network below shows the distances, in kilometres, along a series of roads.
The vertices
Prim's algorithm can be used to find the
Prim’s algorithm is used to find the minimum spanning tree.
The communication matrix below shows the communication links between five people: Steph
In this matrix:
Ursula needs to communicate with Steph.
The sequence of communication links that will successfully allow Ursula to communicate with Steph is
By elimination:
Option A:
Option B:
Option C:
Option D:
Option E:
A bike rental business rents road bikes
Matrix
The element in row
Question 1
The daily cost of renting an adult mountain bike is shown in element
Question 2
On Sundays, the business increases the daily rental price for each type of bike by 10%.
To determine the rental cost for each type of bike on a Sunday, which one of the following matrix calculations needs to be completed?
The balance of a loan,
Question 18
The balance of the loan first falls below $398 000 after how many months?
Question 19
With a small change to the final payment, the loan is expected to be repaid in full in
Butanoic acid is the simplest carboxylic acid that is also classified as a fatty acid. Butanoic acid may be synthesised as outlined in the following reaction flow chart.
--- 0 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i.
ii.
iii. butan-1-ol or 1-butanol
iv.
v.
i.
iii. butan-1-ol or 1-butanol
iv.
v.
Draw the full structural formula of an isomer of butan-2-ol. (1 mark)
--- 5 WORK AREA LINES (style=lined) ---
Possible images include:
Possible images include:
A reaction pathway is designed for the synthesis of the compound that has the structural formula shown below.
The table below gives a list of available organic reactants and reagents.
Complete the reaction pathway design flow chart below. Write the corresponding letter for the structural formula of all organic reactants in each of the boxes provided. The corresponding letter for the formula of other necessary reagents should be shown in the boxes next to the arrows. (5 marks)
--- 0 WORK AREA LINES (style=lined) ---
What is the name of the product formed when chlorine,
→ Product is 1,2-dichlorobutane
Which one of the following statements best defines a renewable energy resource?
→ Renewable energy sources have the potential to be replenished at the same rate as their consumption.
A boy on a bike is travelling at 8 ms
--- 4 WORK AREA LINES (style=blank) ---
--- 4 WORK AREA LINES (style=blank) ---
10 ms
a.
b.
By separating the vector, shown below, into its constituent horizontal and vertical elements, express each component in terms of theta
Horizontal component:
Vertical component:
Horizontal component:
Vertical component:
Below is a description of the motion of a runner. The motion can be divided into three stages.
Stage 1: Runner travels 120 metres south taking 20 seconds.
Stage 2: Runner turns west and travels at 5 ms
Stage 3: Runner travels directly back to their starting position.
--- 2 WORK AREA LINES (style=blank) ---
--- 6 WORK AREA LINES (style=blank) ---
a.
b.
a. | ||
b. Stage 1 and Stage 2 displacement diagram:
Using Pythagoras:
Table 1 summarises the results of a study that compared the effectiveness of individual and group instruction (instructional method) when training future basketball referees.
In this table, test grade is the response variable and instructional method is the explanatory variable.
Question 9
The variables test grade (A, B, C, D, E) and instructional method (individual, group) are
Question 10
Of the students who received an A grade, the percentage who were instructed individually is closest to
Question 11
To become a qualified referee, a grade of A or B on the test is required. Those who receive a C, a D or an E will not qualify.
Using column percentages, a new two-way percentage frequency table is constructed from the data in Table 1.
In this new table, qualified to be a referee (yes, no) is the response variable and instructional method (individual, group) is the explanatory variable.
Which one of the following tables correctly displays the data from Table 1?
The possum population of a large city park is 2498.
The body lengths of this species of possum are known to be approximately normally distributed with a mean of 88 cm and a standard deviation of 4 cm.
Using the 68–95–99.7% rule, the number of possums in this park with a body length between 84 cm and 96 cm is closest to
The histogram below displays the distribution of skull width, in millimetres, for 46 female possums.
Question 1
The shape of the distribution is best described as
Question 2
The percentage of the 46 possums with a skull width of less than 55 mm is closest to
Question 3
The third quartile
The distribution’s centre is in the 56–57 group and if the possible outlier is disregarded, the tail of the distribution is spread more to the left → i.e. negatively skewed with possible outlier.
The 34.5th score lies between 57 and 58, therefore, 57.7.
A truck travelling in a straight line with a speed of 60 ms
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
a.
b.
a. | ||
b. | ||
A bipartite graph is typically used to display which one of the following?
Consider option A:
Individuals or groups can be represented by a column of nodes and tasks can be represented by a second column, allowing for edges to indicate the allocation of tasks.
The daily maximum temperature at a regional town for two weeks is displayed in the table below.
This information can also be represented by matrix
Element
Let
--- 8 WORK AREA LINES (style=lined) ---
The vertices of a triangle can be labelled
Three complex numbers
--- 8 WORK AREA LINES (style=lined) ---
--- 8 WORK AREA LINES (style=lined) ---
i.
ii.
iii.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i.
ii. One example (of many possible answers):
→ Magnesium reacts with hydrochloric acid to produce magnesium chloride and hydrogen gas
i.
ii. One example (of many possible answers):
→ Magnesium reacts with hydrochloric acid to produce magnesium chloride and hydrogen gas
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i.
ii. One possible example (of many correct answers):
i.
ii. One possible example (of many correct answers):
Write the generalised equation for reactions between metals and water. (2 marks)
--- 3 WORK AREA LINES (style=lined) ---
Data was collected to investigate the use of electronic images to automate the sizing of oysters for sale. The variables in this study were:
The data collected for a sample of 15 oysters is displayed in the table.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
a.
b.i.
b.ii.
c.i.
c.ii.
d.
e.
a.
b.i.
b.ii.
c.i.
c.ii.
d.
e.
A sequence of numbers is generated by the recurrence relation shown below.
The value of
A block is being dragged along a flat surface with a horizontal force of 30
The mass of the block is 6 kilograms.
If the block is travelling at a constant velocity, determine the magnitude of the frictional forces acting on the block, giving reasons for your answer. (2 marks)
--- 3 WORK AREA LINES (style=blank) ---
→ As the block is travelling at a constant velocity, the sum of all the forces acting on the block must add to 0.
→ The frictional forces must be equal in magnitude and opposite to the applied force.
→ Therefore, the magnitude of the frictional forces is 30
→ As the block is travelling at a constant velocity, the sum of all the forces acting on the block must add to 0.
→ The frictional forces must be equal in magnitude and opposite to the applied force.
→ Therefore, the magnitude of the frictional forces is 30
List three properties of a bar magnet. (3 marks)
--- 5 WORK AREA LINES (style=blank) ---
Answers could include three of the following properties:
→ They have a north and a south pole.
→ The magnetic field lines run from north to south.
→ The magnetic field lines leave and enter the magnet at right angles to the surface.
→ They are permanent magnets.
→ Like poles repel and opposite poles attract.
Answers could include three of the following properties:
→ They have a north and a south pole.
→ The magnetic field lines run from north to south.
→ The magnetic field lines leave and enter the magnet at right angles to the surface.
→ They are permanent magnets.
→ Like poles repel and opposite poles attract.
The following circuit has 4 resistors and a 24 V DC supply with a switch.
--- 3 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
a.
b.
c.
a. | ||
b.
Circuit current:
Potential difference across the 15
c. Potential difference across the 5
Current through the
Some physics students are conducting an experiment investigating both electrostatic and gravitational forces. They suspend two equally charged balls, each of mass 4.0 g, from light, non-conducting strings suspended from a low ceiling.
The charged balls repel each other with the strings at an angle of 60°, as shown in Figure 1.
There are three forces acting on each ball:
--- 0 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
--- 6 WORK AREA LINES (style=lined) ---
a.
b. System is in an equilibrium state:
→ The sum of the forces must add to zero as seen in the triangle below.
→
c. Using the same triangle as part (b):
a.
b. System is in an equilibrium state:
→ The sum of the forces must add to zero as seen in the triangle below.
→
c. Using the same triangle as part (b):
Water waves travelling at constant speed and hitting a barrier can change direction, as shown in the diagram below.
Which one of the following best identifies this phenomenon?
→ Diffraction is the phenomena that can describe when waves bend around a corner after they pass a barrier, as can be observed in the diagram.
Two ambulances,
Ambulance
Which one of the following best describes the frequency of each siren as measured by the stationary observer, compared to the frequency the observer would measure if the ambulances were stationary?
→ By the doppler effect, as the sound waves move towards the person the frequency of the sound waves increase.
→ As the sound waves move away from the person, the frequency of the sound waves will decrease.
A physics student hears a clap of thunder shortly after observing a flash of lightning.
Which one of the following statements best describes the sound associated with the clap of thunder and the visible light associated with the flash of lightning?
→ Sound is a longitudinal wave where the particles travel parallel to the direction of motion and require a medium.
→ Light is a transverse wave of alternating electric and magnetic fields and therefore doesn’t require a medium.
What is the primary benefit of placing a satellite in a low earth orbit rather than a higher earth orbit?
→ Low earth orbit (LEO) satellites’ primary benefit is faster data transmission (low communication latency).
→ Another major benefit of LEO satellites is accessibility for servicing, although this was not given as an option.
Why were steam trains replaced with electric trains in underground rail systems?
→ The use of steam trains in the small, unvented tubular tunnels of deep-level underground systems was impractical due to the lack of ventilation.
--- 1 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
--- 6 WORK AREA LINES (style=lined) ---
a. Grass, carrots and grain.
b. Carnivore: Owl or fox
Herbivore: Bird
c. Extinction of the grasshopper effects:
→ Will result in a greater availability of the grass and grain they (previously) ate.
→ Subsequently, there will be less competition for food among the other species which also eat grass and grain. These species will thrive and an increase in the bird, mouse and rabbit populations would be expected.
→ The grasshoppers’ extinction will also cause its consumers, the bird and the owl, to have to find other food sources.
→ Population fluctuations of birds and owls would be expected as they adapt to new hunting or grazing habits to replace their lost food source.
→ The complexity of nature in such extinction events can be seen particularly on birds who benefit from more grain availability but lose grasshoppers as a direct food source.
a. Grass, carrots and grain.
b. Carnivore: Owl or fox
Herbivore: Bird
c. Extinction of the grasshopper effects:
→ Will result in a greater availability of the grass and grain they (previously) ate.
→ Subsequently, there will be less competition for food among the other species which also eat grass and grain. These species will thrive and an increase in the bird, mouse and rabbit populations would be expected.
→ The grasshoppers’ extinction will also cause its consumers, the bird and the owl, to have to find other food sources.
→ Population fluctuations of birds and owls would be expected as they adapt to new hunting or grazing habits to replace their lost food source.
→ The complexity of nature in such extinction events can be seen particularly on birds who benefit from more grain availability but lose grasshoppers as a direct food source.
Four types of lines are shown.
Which row of the table correctly identifies the typical application of each line type according to AS 1100 ?
A team of engineers is working together to develop a new aeronautical device for a company. An engineer takes the design and produces the device without permission.
Describe the implications for the individual engineer and the company. (3 marks)
--- 7 WORK AREA LINES (style=lined) ---
→ The device design is the intellectual property of the company that created it.
→ Taking the design without permission is stealing and would have legal implications for the individual.
→ The engineer is also not working ethically from a professional basis.
→ The production of the device will also have serious financial implications for the company involved as they are not the intellectual property owners and would likely be prohibited from selling the product.
Other answers could include:
→ Health and safety factors.
→ Financial ramifications, particularly through legal action.
→ Employment ramifications given the ethical breach of the professional.
→ The device design is the intellectual property of the company that created it.
→ Taking the design without permission is stealing and would have legal implications for the individual.
→ The engineer is also not working ethically from a professional basis.
→ The production of the device will also have serious financial implications for the company involved as they are not the intellectual property owners and would likely be prohibited from selling the product.
Other answers could include:
→ Health and safety factors.
→ Financial ramifications, particularly through legal action.
→ Employment ramifications given the ethical breach of the professional.
One of several fail-safe systems incorporated into a roller coaster design uses the following safety protocol.
Before a roller coaster car brake can be released to allow the roller coaster to commence its ride, ALL of the following conditions must be met:
A logic gate schematic is shown.
--- 5 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
i. NAND gate purpose:
→ Ensures that if any or all of the inputs are zero the output will result in a 1 and thus turn on the warning light.
→ In effect, the warning light will remain ON until all conditions for safe operation are met.
ii.
i. NAND gate purpose:
→ Ensures that if any or all of the inputs are zero the output will result in a 1 and thus turn on the warning light.
→ In effect, the warning light will remain ON until all conditions for safe operation are met.
ii.
Why is it detrimental for a predator to be totally efficient at catching its prey? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
→ When predators are efficient at hunting and catch too many prey, it leads to a rapid decline in the prey’s population.
→ This can lead to a reduction in available food for the predators, causing their population to decline or their need to migrate somewhere else.
→ When predators are efficient at hunting and catch too many prey, it leads to a rapid decline in the prey’s population.
→ This can lead to a reduction in available food for the predators, causing their population to decline or their need to migrate somewhere else.
The diagram shows a child with a mass of 45 kg hanging 2 metres from the left end of a structure, and an adult with a mass of 85 kg hanging 1 metre from the right end.
Red and white blood cells are critical components of human blood with very different functions.
--- 7 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
a. Red blood cells:
→ Red blood cells (RBCs) make up 40-50% of total blood volume and transport oxygen and carbon dioxide throughout the body.
→ They are able to achieve this by haemoglobin, a globular protein consisting of 4 polypeptide chains and iron. Haemoglobin’s structure allows each of its proteins to carry 4 molecules of oxygen and 4 molecules of carbon dioxide.
→ RBCs are specialised cells and have no nucleus which allows them to carry more haemoglobin, and therefore more oxygen, around the body.
b. White blood cells and platelets:
→ Platelets are small membrane bound cell fragments derived from bone marrow. They are involved in initiating blood clotting.
→ White blood cells (leucocytes) are involved in internal defence.
→ This can include antibody production (B cells), mediating allergic responses (eosinophils) and fighting inflammation (basophils).
a. Red blood cells:
→ Red blood cells (RBCs) make up 40-50% of total blood volume and transport oxygen and carbon dioxide throughout the body.
→ They are able to achieve this by haemoglobin, a globular protein consisting of 4 polypeptide chains and iron. Haemoglobin’s structure allows each of its proteins to carry 4 molecules of oxygen and 4 molecules of carbon dioxide.
→ RBCs are specialised cells and have no nucleus which allows them to carry more haemoglobin, and therefore more oxygen, around the body.
b. White blood cells and platelets:
→ Platelets are small membrane bound cell fragments derived from bone marrow. They are involved in initiating blood clotting.
→ White blood cells (leucocytes) are involved in internal defence.
→ This can include antibody production (B cells), mediating allergic responses (eosinophils) and fighting inflammation (basophils).
According to Collision Theory, to increase the rate of a reaction, which of the following must occur?
→ Options A and C will increase the rate of a reaction but neither “must” occur for the rate of a reaction to increase.
→ The frequency of successful collisions defines the rate of reaction.
Explain how decreasing temperature in an exothermic reaction influences the rate of a chemical reaction. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
→ In an exothermic reaction, heat is released as the reaction progresses from the reactants to the products.
→ Decreasing the temperature in an exothermic reaction leads to a decrease in the reaction rate.
→ A decrease in temperature lowers the kinetic energy of particles which leads to less successful collisions that exceed activation energy
→ In an exothermic reaction, heat is released as the reaction progresses from the reactants to the products.
→ Decreasing the temperature in an exothermic reaction leads to a decrease in the reaction rate.
→ A decrease in temperature lowers the kinetic energy of particles which leads to less successful collisions that exceed activation energy
--- 2 WORK AREA LINES (style=lined) ---
--- 8 WORK AREA LINES (style=lined) ---
i. Differentiation:
→ The difference in shape and size between different cells in a multicellular organism due to their specialised function.
ii. Multicellular organisms require specialised cells:
→ Multicellular organisms are large organisms which require many complex internal processes to function.
→ To be more effective, multicellular organisms have specialised cells. Specialised cells have a certain shape, size and number and type of organelles.
→ Cell specialisation allows cells to perform one specific role to benefit the whole organism rather than every individual cell performing every function.
→ This makes multicellular organisms able to carry out many complex functions while still remaining energy efficient.
i. Differentiation:
→ The difference in shape and size between different cells in a multicellular organism due to their specialised function.
ii. Multicellular organisms require specialised cells:
→ Multicellular organisms are large organisms which require many complex internal processes to function.
→ To be more effective, multicellular organisms have specialised cells. Specialised cells have a certain shape, size and number and type of organelles.
→ Cell specialisation allows cells to perform one specific role to benefit the whole organism rather than every individual cell performing every function.
→ This makes multicellular organisms able to carry out many complex functions while still remaining energy efficient.
Explain how increasing temperature in an endothermic reaction influences the rate of a chemical reaction. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
→ In an endothermic reaction heat is absorbed as the reaction progresses from reactants to products.
→ An increase in temperature raises the kinetic energy of particles and leads to more successful particle collisions that exceed activation energy
What are the valencies of the following simple ions
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i. Valency: Barium
ii. Valency: Phosphide
iii. Valency: Silver
i. Valency: Barium
ii. Valency: Phosphide
iii. Valency: Silver
Draw Lewis electron dot structures for the following ionic molecular compounds
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
Draw Lewis electron dot structures for
--- 3 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
i.
ii.
i.
ii.
When proteins are broken down in chemical digestion, they become
→ Proteins are broken down so as their beneficial components can be absorbed in the small intestine.
→ Amino acid chains (called polypeptide chains) make up all proteins, and are hence the smallest unit of a protein possible in chemical digestion.
A soccer ball leaves the ground with a velocity of 10 ms
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i.
ii.
i.
ii.
A ball is thrown vertically upwards from ground level, it gains 50 metres vertically and then falls back to the ground.
--- 4 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i.
ii.
i.
ii.
Complete the table below by outlining one physical indication of each chemical change described below. (3 marks)
--- 0 WORK AREA LINES (style=lined) ---
Outline both a physical and chemical property of the elements contained in the highlighted periodic table groups below. (4 marks)
--- 6 WORK AREA LINES (style=lined) ---
Group
→ Physical properties: Group 1 metals are soft and shiny.
→ Chemical properties: They are highly reactive and have low melting/boiling points.
Group
→ Physical properties: Group 8 elements are colourless gases with no odour or taste.
→ Chemical properties: They are virtually unreactive and all have cryogenic boiling points.
Group
→ Physical properties: Group 1 metals are soft and shiny.
→ Chemical properties: They are highly reactive and have low melting/boiling points.
Group
→ Physical properties: Group 8 elements are colourless gases with no odour or taste.
→ Chemical properties: They are virtually unreactive and all have cryogenic boiling points.