AQA · Mathematics · 8300
GCSE Maths: Proportion: direct
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Proportion: direct (Corbettmaths Video 254), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the general form of a direct proportion equation between variables A and B?
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A = kB, where k is a constant of proportionality.
What is the general form of an inverse proportion equation between variables T and N?
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T = k/N, where k is a constant of proportionality.
If A is directly proportional to B², what is the general form of the equation?
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A = kB², where k is a constant of proportionality.
If W is directly proportional to P³, what is the general form of the equation?
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W = kP³, where k is a constant of proportionality.
If Z is directly proportional to √x, what is the general form of the equation?
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Z = k√x, where k is a constant of proportionality.
If y is inversely proportional to the square of x, what is the general form of the equation?
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y = k/x², where k is a constant of proportionality.
If W is inversely proportional to √B, what is the general form of the equation?
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W = k/√B, where k is a constant of proportionality.
When a quantity is halved in direct proportion to the cube of a variable, by what factor does the quantity change?
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It is divided by 8 (since (1/2)³ = 1/8).
In a spring, what physical relationship exists between tension T and extension y?
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The tension is directly proportional to the extension (T ∝ y), following Hooke's Law.
If F is inversely proportional to the square of d, what happens to F when d is halved?
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F becomes 4 times larger (quadruples), because halving d means 1/(d/2)² = 4/d².
If w is inversely proportional to y², and w = 54 when y = c, what is w when y = 3c?
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w = 6. Since w ∝ 1/y², if y increases by factor of 3, w decreases by factor of 9, so w = 54/9 = 6.
If w is directly proportional to x³, what is the percentage increase in w when x is increased by 10%?
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33.1% increase. Since w ∝ x³, if x becomes 1.1x, then w becomes (1.1)³ = 1.331 times larger, which is a 33.1% increase.
If A is directly proportional to the cube root of B, and B is increased by 75%, what is the percentage increase in A?
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16.7% increase. Since A ∝ ∛B, if B becomes 1.75B, then A becomes ∛(1.75) ≈ 1.2051 times larger, approximately 20.5% increase (or exactly (1.75)^(1/3) - 1).
If W is directly proportional to the square of x, how is the relationship expressed mathematically?
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W = kx² (where k is the constant of proportionality).
If W is proportional to x², and increasing x by 2 makes W three times larger, what equation relates the old and new values?
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k(x+2)² = 3kx², which simplifies to (x+2)² = 3x².
What is the exact value of x if W ∝ x² and W triples when x increases by 2?
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x = 1 + √3. From (x+2)² = 3x², we get x² - 4x - 4 = 0, giving x = (4 ± √32)/2 = 2 ± 2√2. Since x must be positive and (x+2)² = 3x² requires x > 0, we check: the positive solution is x = 1 + √3 ≈ 2.73.
When solving (x+2)² = 3x², what quadratic equation results after expanding and simplifying?
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x² - 4x - 4 = 0 (or equivalently 2x² - 4x - 4 = 0 before dividing by 2).
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