Algebra, NAPX-G4-CA25 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

706

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 80.

Use this to calculate the value of k\large k.

Worked Solution

(80, 40) represents one point on the graph.

Substituting into the given formula:
40 = 802k\dfrac{80^2}{\large k}
∴k\therefore \large k = 80240\dfrac{80^2}{40}
= 160

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v0.svg 470 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 80. Use this to calculate the value of $\large k$.
workedSolution
(80, 40) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 40 | \= $\dfrac{80^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{80^2}{40}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
160
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0160

Variant 1

DifficultyLevel

700

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 30 km² area of bushland is estimated to have a feral cat population of 60.

Use this to calculate the value of k\large k.

Worked Solution

(60, 30) represents one point on the graph.

Substituting into the given formula:
30 = 602k\dfrac{60^2}{\large k}
∴k\therefore \large k = 60230\dfrac{60^2}{30}
= 120

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v1.svg 450 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 30 km² area of bushland is estimated to have a feral cat population of 60. Use this to calculate the value of $\large k$.
workedSolution
(60, 30) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 30 | \= $\dfrac{60^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{60^2}{30}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
120
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0120

Variant 2

DifficultyLevel

700

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 60.

Use this to calculate the value of k\large k.

Worked Solution

(60, 40) represents one point on the graph.

Substituting into the given formula:
40 = 602k\dfrac{60^2}{\large k}
∴k\therefore \large k = 60240\dfrac{60^2}{40}
= 90

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v2.svg 420 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 60. Use this to calculate the value of $\large k$.
workedSolution
(60, 40) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 40 | \= $\dfrac{60^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{60^2}{40}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
90
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer090

Variant 3

DifficultyLevel

700

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 20 km² area of bushland is estimated to have a feral cat population of 40.

Use this to calculate the value of k\large k.

Worked Solution

(40, 20) represents one point on the graph.

Substituting into the given formula:
20 = 402k\dfrac{40^2}{\large k}
∴k\therefore \large k = 40220\dfrac{40^2}{20}
= 80

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v3.svg 400 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 20 km² area of bushland is estimated to have a feral cat population of 40. Use this to calculate the value of $\large k$.
workedSolution
(40, 20) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 20 | \= $\dfrac{40^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{40^2}{20}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
80
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer080

Variant 4

DifficultyLevel

698

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 100.

Use this to calculate the value of k\large k.

Worked Solution

(100, 40) represents one point on the graph.

Substituting into the given formula:
40 = 1002k\dfrac{100^2}{\large k}
∴k\therefore \large k = 100240\dfrac{100^2}{40}
= 250

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v4.svg 500 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 100. Use this to calculate the value of $\large k$.
workedSolution
(100, 40) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 40 | \= $\dfrac{100^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{100^2}{40}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
250
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0250

Variant 5

DifficultyLevel

694

Question

The rule for the graph is

A=c2kA= \dfrac{\large c^2}{\large k}


AA is the area of bushland in square kilometres.

c\large c is the estimated population of feral cats.

The graph shows that a 20 km² area of bushland is estimated to have a feral cat population of 60.

Use this to calculate the value of k\large k.

Worked Solution

(60, 20) represents one point on the graph.

Substituting into the given formula:
20 = 602k\dfrac{60^2}{\large k}
∴k\therefore \large k = 60220\dfrac{60^2}{20}
= 180

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-G4-CA25-SA_v5.svg 500 indent vpad The rule for the graph is >>$A= \dfrac{\large c^2}{\large k}$
$A$ is the area of bushland in square kilometres. $\large c$ is the estimated population of feral cats. The graph shows that a 20 km² area of bushland is estimated to have a feral cat population of 60. Use this to calculate the value of $\large k$.
workedSolution
(60, 20) represents one point on the graph. Substituting into the given formula:
| | | | ------------: | ---------- | | 20 | \= $\dfrac{60^2}{\large k}$ | | | | | $\therefore \large k$ | \= $\dfrac{60^2}{20}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
180
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0180

Tags

  • ms_ca