The time for a car to travel a certain distance varies inversely with its speed.
Which of the following graphs shows this relationship?
Rates of Change, SMB-009
The number of trees that can be planted along the fence line of a paddock varies inversely with the distance between each tree.
There will be 108 trees if the distance between them is 5 metres.
- How many trees can be planted if the distance between them is 6 metres? (2 marks)
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- What is the distance between the trees if 120 trees are planted? (1 mark)
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Rates of Change, SMB-007
It is known that a quantity `P` kgs is proportional to the reciprocal of another quantity `Q` kgs such that `P prop 1/Q`.
If `P=12` when `Q=20`, calculate the estimated quantity of `Q` when `P=45` kgs, to the nearest gram. (3 marks)
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Rates of Change, SMB-003
The current of an electrical circuit, measured in amps (A), varies inversely with its resistance, measured in ohms (R).
When the resistance of a circuit is 28 ohms, the current is 3 amps.
What is the current when the resistance is 8 ohms? (2 marks)
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Rates of Change, SMB-001
It is known that a quantity `y` is inversely proportional to another quantity `x`.
If `y=3` when `x=1.8`, calculate the constant of variation `k`. (2 marks)
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Functions, 2ADV F1 2022 HSC 12
A student believes that the time it takes for an ice cube to melt (`M` minutes) varies inversely with the room temperature `(T^@ text{C})`. The student observes that at a room temperature of `15^@text{C}` it takes 12 minutes for an ice cube to melt.
- Find the equation relating `M` and `T`. (2 marks)
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- By first completing this table of values, graph the relationship between temperature and time from `T=5^@C` to `T=30^@ text{C}`. (2 marks)
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & & & \\
\hline \end{array}
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Show Answers Only
a. `M=180/T`
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
Show Worked Solution
| a. | `M` | `prop 1/T` |
| `M` | `=k/T` | |
| `12` | `=k/15` | |
| `k` | `=15 xx 12` | |
| `=180` |
`:.M=180/T`
♦ Mean mark (a) 49%.
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
Algebra, STD2 A4 2019 HSC 33
The time taken for a car to travel between two towns at a constant speed varies inversely with its speed.
It takes 1.5 hours for the car to travel between the two towns at a constant speed of 80 km/h.
- Calculate the distance between the two towns. (1 mark)
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- By first plotting four points, draw the curve that shows the time taken to travel between the two towns at different constant speeds. (3 marks)
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Show Answers Only
- `120\ text(km)`
-
Show Worked Solution
| a. | `D` | `= S xx T` |
| `= 80 xx 1.5` | ||
| `= 120\ text(km)` |
b.
\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ s\ \ \rule[-1ex]{0pt}{0pt} & 20 & 40 & 60 & 80 \\
\hline
\rule{0pt}{2.5ex} t \rule[-1ex]{0pt}{0pt} & 6 & 3 & 2 & 1.5 \\
\hline
\end{array}
Algebra, STD2 A4 2007 HSC 15 MC
If pressure (`p`) varies inversely with volume (`V`), which formula correctly expresses `p` in terms of `V` and `k`, where `k` is a constant?
- `p = k/V`
- `p = V/k`
- `p = kV`
- `p = k + V`
Algebra, STD2 A4 2011 HSC 28a
The air pressure, `P`, in a bubble varies inversely with the volume, `V`, of the bubble.
- Write an equation relating `P`, `V` and `a`, where `a` is a constant. (1 mark)
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- It is known that `P = 3` when `V = 2`.
By finding the value of the constant, `a`, find the value of `P` when `V = 4`. (2 marks)
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- Sketch a graph to show how `P` varies for different values of `V`.
Use the horizontal axis to represent volume and the vertical axis to represent air pressure. (2 marks)
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Show Answers Only
- `P = a/V`
- `P = 1 1/2`
-
Show Worked Solution
♦ Mean mark (i) 39%
COMMENT: Expressing the proportional relationship `P prop 1/V` as the equation `P=k/V` is a core skill here.
COMMENT: Expressing the proportional relationship `P prop 1/V` as the equation `P=k/V` is a core skill here.
| i. | `P` | `prop 1/V` |
| `= a/V` |
| ii. | `text(When)\ P=3,\ V = 2` |
| `3` | `= a/2` |
| `a` | `=6` |
`text(Need to find)\ P\ text(when)\ V = 4`
♦ Mean mark (ii) 47%
| `P` | `=6/4` |
| `= 1 1/2` |
♦♦ Mean mark (iii) 26%
COMMENT: An inverse relationship is reflected by a hyperbola on the graph.
COMMENT: An inverse relationship is reflected by a hyperbola on the graph.
| iii. | |
Algebra, STD2 A1 2009 HSC 16 MC
The time for a car to travel a certain distance varies inversely with its speed.
Which of the following graphs shows this relationship?
Algebra, STD2 A4 2010 HSC 13 MC
The number of hours that it takes for a block of ice to melt varies inversely with the temperature. At 30°C it takes 8 hours for a block of ice to melt.
How long will it take the same size block of ice to melt at 12°C?
- 3.2 hours
- 20 hours
- 26 hours
- 45 hours