Easy1 markMultiple Choice
AQA GCSE · Question 18 · Ratio Proportion and Rates of Change
X is inversely proportional to Y. Circle the correct statement.
X is inversely proportional to Y. Circle the correct statement.
Answer options:
A.
X is directly proportional to Y
B.
X is directly proportional to 1/Y
C.
X is directly proportional to 2Y
D.
X is directly proportional to √Y
How to approach this question
1. Recall the definition of inverse proportionality. "X is inversely proportional to Y" means that as Y increases, X decreases by the same factor.
2. Mathematically, this is written as X ∝ 1/Y or X = k/Y, where k is the constant of proportionality.
3. The statement X ∝ 1/Y can be read as "X is directly proportional to 1/Y".
4. Compare this with the given options. Option B matches this definition.
Full Answer
B.X is directly proportional to 1/Y✓ Correct
X is directly proportional to 1/Y
The statement "X is inversely proportional to Y" means that X and Y are linked by the equation:
X = k / Y
where k is a constant of proportionality.
This can also be written as:
X = k * (1/Y)
When an equation is in the form A = k * B, it means "A is directly proportional to B".
In our case, A is X and B is (1/Y).
So, we can say that "X is directly proportional to 1/Y".
Let's look at the options:
- A: X is directly proportional to Y (X = kY) - Incorrect.
- B: X is directly proportional to 1/Y (X = k/Y) - Correct.
- C: X is directly proportional to 2Y (X = k(2Y)) - Incorrect.
- D: X is directly proportional to √Y (X = k√Y) - Incorrect.
Common mistakes
✗ Confusing inverse and direct proportion.
✗ Not understanding that "inversely proportional to Y" is the same as "directly proportional to 1/Y".
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