A cyclist rides a bicycle at a constant speed around a circular track.
Which of the graphs best illustrates the distance of the cyclist from the centre of the track as time varies?
Algebra, STD1 A3 2023 HSC 4 MC
The diagram shows water in a pool which is in the shape of a triangular prism. The pool is being emptied of water at a constant rate.
Which graph best illustrates the change in depth of water with time?
Algebra, STD1 A3 2022 HSC 10 MC
The diagram shows a container, closed at the base. It is to be filled with water at a constant rate.
Which graph best shows the depth of water in the container as time varies?
Algebra, STD1 A3 2021 HSC 25
The diagram shows a container which consists of a small cylinder on top of a larger
cylinder.
The container is filled with water at a constant rate to the top of the smaller cylinder. It takes 5 minutes to fill the larger cylinder.
Draw a possible graph of the water level in the container against time. (2 marks)
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♦ Mean mark 38%.
Algebra, STD1 A3 2020 HSC 19
Each year the number of fish in a pond is three times that of the year before.
- The table shows the number of fish in the pond for four years.
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Year}\rule[-1ex]{0pt}{0pt} & \ \ \ 2020\ \ \ & \ \ \ 2021\ \ \ & \ \ \ 2022\ \ \ & \ \ \ 2023\ \ \ \\
\hline
\rule{0pt}{2.5ex}\textit{Number of fish}\rule[-1ex]{0pt}{0pt} & 100 & & & 2700\\
\hline
\end{array}Complete the table above showing the number of fish in 2021 and 2022. (2 marks)
- Plot the points from the table in part (a) on the grid. (2 marks)
- Which model is more suitable for this dataset: linear or exponential? Briefly explain your answer. (2 marks)
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a.
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Year}\rule[-1ex]{0pt}{0pt} & \ \ \ 2020\ \ \ & \ \ \ 2021\ \ \ & \ \ \ 2022\ \ \ & \ \ \ 2023\ \ \ \\
\hline
\rule{0pt}{2.5ex}\textit{Number of fish}\rule[-1ex]{0pt}{0pt} & 100 & 300 & 900 & 2700\\
\hline
\end{array}
b.
c. The more suitable model is exponential.
A linear dataset would graph a straight line which is not the case here.
An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.
Show Worked Solution
a.
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Year}\rule[-1ex]{0pt}{0pt} & \ \ \ 2020\ \ \ & \ \ \ 2021\ \ \ & \ \ \ 2022\ \ \ & \ \ \ 2023\ \ \ \\
\hline
\rule{0pt}{2.5ex}\textit{Number of fish}\rule[-1ex]{0pt}{0pt} & 100 & 300 & 900 & 2700\\
\hline
\end{array}
b.
c. The more suitable model is exponential.
A linear dataset would graph a straight line which is not the case here.
An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.
♦ Mean mark (c) 31%.
Algebra, STD1 A3 2020 HSC 14
Adam travels on a straight road away from his home. His journey is shown in the distance – time graph.
- Describe the journey in the first 4 minutes by referring to change in speed and distance travelled. (2 marks)
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- After the 4 minutes shown on the graph. Adam rests for 2 minutes and then return home by travelling on the same road at a constant speed. Adam is away from home for a total of 10 minutes.
On the above, complete the distance-time using the information provided. (2 marks)
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-
`text{Speed: Adam increases speed until approximately}\ \ t=2,`
`text{and then decreases speed until he stops when}\ \ t=4.`
`text{Distance travelled: Adam’s distance from home increases}`
`text{at an increasing rate until}\ \ t=2, \ text{and then continues}`
`text{to increase but at a decreasing rate until}\ \ t=4, \ text(when the)`
`text(distance from home remains the same.)`
-
Show Worked Solution
a. `text{Speed: Adam increases speed until approximately}\ \ t=2,`
♦ Mean mark part (a) 35%.
`text{and then decreases speed until he stops when}\ \ t=4.`
`text{Distance travelled: Adam’s distance from home increases}`
`text{at an increasing rate until}\ \ t=2, \ text{and then continues}`
`text{to increase but at a decreasing rate until}\ \ t=4, \ text(when the)`
`text(distance from home remains the same.)`
Mean mark part (b) 51%.
b. `text(S)text(ince Adam travels home at a constant speed, the graph is)`
`text{is a straight line and ends at (10, 0).}`
Algebra, STD1 A3 2019 HSC 23
Five rabbits were introduced onto a farm at the start of 2018. At the start of 2019 there were 10 rabbits on the farm. It is predicted that the number of rabbits on the farm will continue to double each year.
- Complete the following table. (1 mark)
- Complete the scale on the vertical axis and then plot the data from part (a) on the grid. (2 marks)
- Would a linear model or an exponential model better fit this graph? Explain the reason for your answer. (1 mark)
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-
-
- `text(Exponential model – the graph isn’t a straight line.)`
`text(The number of rabbits grow at an increasing rate.)`
Show Worked Solution
| a. | |
| b. | |
♦ Mean mark part (c) 25%.
c. `text(Exponential model – the graph isn’t a straight line.)`
`text(The number of rabbits grow at an increasing rate.)`
Algebra, STD1 A3 2019 HSC 9 MC
The container shown is initially full of water.
Water leaks out of the bottom of the container at a constant rate.
Which graph best shows the depth of water in the container as time varies?
| A. |  |
B. |  |
| C. |  |
D. |  |
Algebra, STD2 A4 EQ-Bank 8 MC
Water was poured into a container at a constant rate. The graph shows the depth of water in the container as it was being filled.
Which of the following containers could have been used to produce this result?
| A. |  |
B. |  |
| C. |  |
D. |  |
Show Worked Solution
`text(S)text(ince the graph is a straight line, the cup fills up at)`
`text(a constant rate.)`
`=> B`