Easy1 markMultiple Choice
Ratio Proportion and Rates of Changeproportioninverse proportionalgebra

AQA GCSE · Question 18 · Ratio Proportion and Rates of Change

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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