PR.6C, SEC 3, invrs sqr & cube prpn↗️ (50)

Question 1 of 50

1. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 12$ when $x = 2$ .

What is the value of $y$ when $x = 6$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.

]
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 2 of 50

2. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1$ when $x = 10$ .

What is the value of $x$ when $y = 4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 3 of 50

3. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 2$ when $x = 8$ .

What is the value of $x$ when $y = 16$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 4 of 50

4. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1.8$ when $x = 10$ .

What is the value of $x$ when $y = 20$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 5 of 50

5. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.2$ when $x = 5$ .

What is the value of $y$ when $x = 10$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 6 of 50

6. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 3$ when $x = 2$ .

What is the value of $x$ when $y = 0.375$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 7 of 50

7. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.96$ when $x = 6$ .

What is the value of $y$ when $x = 4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 8 of 50

8. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 2$ when $x = 4$ .

What is the value of $y$ when $x = 8$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 9 of 50

9. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.512$ when $x = 2.5$ .

What is the value of $y$ when $x = 5$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 10 of 50

10. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 3.2$ when $x = 4$ .

What is the value of $x$ when $y = 2.048$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 11 of 50

11. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 24$ when $x = 3$ .

What is the value of $x$ when $y = 3$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 12 of 50

12. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.8$ when $x = 10$ .

What is the value of $x$ when $y = 6.4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
Correct

Incorrect

Hint

x = {5}

⌨️ Enter your answer in the field provided.
Question 13 of 50

13. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 7.5$ when $x = 2.5$ .

What is the value of $x$ when $y = 1.875$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.

===
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 14 of 50

14. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1$ when $x = 5$ .

What is the value of $y$ when $x = 10$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 15 of 50

15. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 6.4$ when $x = 4$ .

What is the value of $y$ when $x = 2$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 16 of 50

16. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 45$ when $x = 3$ .

What is the value of $y$ when $x = 15$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 17 of 50

17. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1$ when $x = 8$ .

What is the value of $x$ when $y = 8$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 18 of 50

18. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1$ when $x = 3$ .

What is the value of $x$ when $y = 0.125$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 19 of 50

19. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.2$ when $x = 10$ .

What is the value of $x$ when $y = 1.25$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 20 of 50

20. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 2$ when $x = 3$ .

What is the value of $y$ when $x = 9$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 21 of 50

21. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.3072$ when $x = 7.5$ .

What is the value of $y$ when $x = 5$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 22 of 50

22. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.81$ when $x = 9$ .

What is the value of $y$ when $x = 3$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 23 of 50

23. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.4$ when $x = 10$ .

What is the value of $x$ when $y = 3.2$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 24 of 50

24. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.5$ when $x = 6$ .

What is the value of $x$ when $y = 0.864$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 25 of 50

25. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1.28$ when $x = 4$ .

What is the value of $x$ when $y = 0.32$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 26 of 50

26. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1.024$ when $x = 2.5$ .

What is the value of $y$ when $x = 4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 27 of 50

27. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 6$ when $x = 2$ .

What is the value of $y$ when $x = 12$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 28 of 50

28. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 18$ when $x = 3$ .

What is the value of $y$ when $x = 9$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 29 of 50

29. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 14.4$ when $x = 2$ .

What is the value of $x$ when $y = 3.6$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 30 of 50

30. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.5$ when $x = 4$ .

What is the value of $x$ when $y = 4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 31 of 50

31. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1$ when $x = 9$ .

What is the value of $x$ when $y = 27$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 32 of 50

32. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.3072$ when $x = 7.5$ .

What is the value of $y$ when $x = 5$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 33 of 50

33. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 25$ when $x = 5$ .

What is the value of $y$ when $x = 8$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 34 of 50

34. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.125$ when $x = 12$ .

What is the value of $y$ when $x = 3$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 35 of 50

35. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1.728$ when $x = 4.5$ .

What is the value of $y$ when $x = 6$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 36 of 50

36. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 2$ when $x = 6$ .

What is the value of $x$ when $y = 8$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 37 of 50

37. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 4.5$ when $x = 3$ .

What is the value of $x$ when $y = 2.25$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 38 of 50

38. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.432$ when $x = 5$ .

What is the value of $x$ when $y = 0.128$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 39 of 50

39. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1.6$ when $x = 5$ .

What is the value of $y$ when $x = 8$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 40 of 50

40. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 27$ when $x = 3$ .

What is the value of $y$ when $x = 6$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 41 of 50

41. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 54$ when $x = 3$ .

What is the value of $y$ when $x = 6$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 42 of 50

42. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 2$ when $x = 9$ .

What is the value of $x$ when $y = 4.5$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 43 of 50

43. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 9.6$ when $x = 4$ .

What is the value of $x$ when $y = 2.4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 44 of 50

44. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 8$ when $x = 2$ .

What is the value of $x$ when $y = 0.512$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 45 of 50

45. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.5$ when $x = 10$ .

What is the value of $y$ when $x = 4$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 46 of 50

46. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 32$ when $x = 2$ .

What is the value of $y$ when $x = 16$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 47 of 50

47. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.4$ when $x = 5$ .

What is the value of $y$ when $x = 10$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 48 of 50

48. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 7.2$ when $x = 6$ .

What is the value of $x$ when $y = 16.2$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- x =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 49 of 50

49. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 2$ when $x = 2$ .

What is the value of $y$ when $x = 5$ ?

You may find the following equation useful:

$y = \frac{k}{x^{2}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.
Question 50 of 50

50. Question
Topic: Inverse Square & Cube Relationships.

Please have pen and paper handy to show workings out. 📝

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 1.5$ when $x = 6$ .

What is the value of $y$ when $x = 3$ ?

You may find the following equation useful:

$y = \frac{k}{x^{3}}$

Round to 2 decimal places where appropriate.
- y =
  
  ⌨️ Enter your answer in the field provided.
Correct

Incorrect

Hint

💡 Quick inverse-square and inverse-cube tips.

These models use y = k divided by a power of x.

Build a number machine left to right with x at the input and y at the output.

Inverse-square forward chain is square x then take the reciprocal then multiply by k.

Inverse-cube forward chain is cube x then take the reciprocal then multiply by k.

Reciprocal means 1 divided by the number.

The constant k is fixed for the whole question.

Use k = y × x² for inverse-square or k = y × x³ for inverse-cube.

To find y for a new x run the machine in order and round only at the end.

To recover x from a known y go backwards by dividing by k then taking the reciprocal then the square root or cube root as needed.

Do powers before reciprocals and reciprocals before multiplying to keep the order of operations correct.

Check your k by reproducing the given pair through the machine to confirm the output matches.

Use the ANS button so long decimals carry through accurately without retyping.

PR.6C, SEC 3, invrs sqr & cube prpn↗️ (50)

PR.6C, SEC 3, invrs sqr & cube prpn↗️ (50)

Quiz Summary

Information

Results

Results

Categories

1. Question

Topic: Inverse Square & Cube Relationships.

📉 y is inversely proportional to the square of x.

We know: y=12 when x=2.

What is the value of y when x=6?

You may find the following equation useful:

y=kx2

Round to 2 decimal places where appropriate.

y =

⌨️ Enter your answer in the field provided.

Hint

2. Question

Topic: Inverse Square & Cube Relationships.

📐 y is inversely proportional to the square of x.

We know: y=1 when x=10.

What is the value of x when y=4?

You may find the following equation useful:

y=kx2

Round to 2 decimal places where appropriate.

x =

⌨️ Enter your answer in the field provided.

Hint

3. Question

Topic: Inverse Square & Cube Relationships.

📐 y is inversely proportional to the cube of x.

We know: y=2 when x=8.

What is the value of x when y=16?

You may find the following equation useful:

y=kx3

Round to 2 decimal places where appropriate.

x =

⌨️ Enter your answer in the field provided.

Hint

4. Question

Topic: Inverse Square & Cube Relationships.

📐 y is inversely proportional to the square of x.

We know: y=1.8 when x=10.

What is the value of x when y=20?

You may find the following equation useful:

y=kx2

Round to 2 decimal places where appropriate.

x =

⌨️ Enter your answer in the field provided.

Hint

5. Question

Topic: Inverse Square & Cube Relationships.

📉 y is inversely proportional to the square of x.

We know: y=0.2 when x=5.

What is the value of y when x=10?

You may find the following equation useful:

y=kx2

Round to 2 decimal places where appropriate.

y =

⌨️ Enter your answer in the field provided.

Hint

6. Question

Topic: Inverse Square & Cube Relationships.

📐 y is inversely proportional to the cube of x.

We know: y=3 when x=2.

What is the value of x when y=0.375?

You may find the following equation useful:

y=kx3

Round to 2 decimal places where appropriate.

x =

⌨️ Enter your answer in the field provided.

Hint

7. Question

Topic: Inverse Square & Cube Relationships.

📉 y is inversely proportional to the square of x.

We know: y=0.96 when x=6.

What is the value of y when x=4?

You may find the following equation useful:

y=kx2

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 12$ when $x = 2$ .

What is the value of $y$ when $x = 6$ ?

$y = \frac{k}{x^{2}}$

`y =`

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1$ when $x = 10$ .

What is the value of $x$ when $y = 4$ ?

$y = \frac{k}{x^{2}}$

`x =`

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 2$ when $x = 8$ .

What is the value of $x$ when $y = 16$ ?

$y = \frac{k}{x^{3}}$

`x =`

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 1.8$ when $x = 10$ .

What is the value of $x$ when $y = 20$ ?

$y = \frac{k}{x^{2}}$

`x =`

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.2$ when $x = 5$ .

What is the value of $y$ when $x = 10$ ?

$y = \frac{k}{x^{2}}$

`y =`

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 3$ when $x = 2$ .

What is the value of $x$ when $y = 0.375$ ?

$y = \frac{k}{x^{3}}$

`x =`

📉 $y$ is inversely proportional to the square of $x$ .

We know: $y = 0.96$ when $x = 6$ .

What is the value of $y$ when $x = 4$ ?

$y = \frac{k}{x^{2}}$

`y =`

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 2$ when $x = 4$ .

What is the value of $y$ when $x = 8$ ?

$y = \frac{k}{x^{3}}$

`y =`

📉 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.512$ when $x = 2.5$ .

What is the value of $y$ when $x = 5$ ?

$y = \frac{k}{x^{3}}$

`y =`

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 3.2$ when $x = 4$ .

What is the value of $x$ when $y = 2.048$ ?

$y = \frac{k}{x^{2}}$

`x =`

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 24$ when $x = 3$ .

What is the value of $x$ when $y = 3$ ?

$y = \frac{k}{x^{3}}$

`x =`

📐 $y$ is inversely proportional to the cube of $x$ .

We know: $y = 0.8$ when $x = 10$ .

What is the value of $x$ when $y = 6.4$ ?

$y = \frac{k}{x^{3}}$

`x =` `{5}`

📐 $y$ is inversely proportional to the square of $x$ .

We know: $y = 7.5$ when $x = 2.5$ .

What is the value of $x$ when $y = 1.875$ ?

$y = \frac{k}{x^{2}}$

`x =`