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If y varies directly with x and y = 6 when x = 2, what is y when x = 5?
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Correct answer: 15
y = k x with k = 3, so y = 15.
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If y is inversely proportional to x and y = 4 when x = 3, what is y when x = 6?
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Correct answer: 2
xy = 12 is constant, so y = 12 / 6 = 2.
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In y = k x, k is called:
- 1 Constant of variation
- 2 Slope only
- 3 Exponent
- 4 Variable
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Correct answer: Constant of variation
k is the constant of variation.
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If a is proportional to b² and a = 8 when b = 2, what is a when b = 3?
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Correct answer: 18
a = k b² with k = 2, so a = 2 x 9 = 18.
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Speed and time for a fixed distance are in:
- 1 Direct variation
- 2 Joint variation
- 3 Inverse variation
- 4 No variation
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Correct answer: Inverse variation
Doubling the speed halves the time.
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If y is proportional to x and y = 10 when x = 2, then k is:
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Correct answer: 5
k = y / x = 5.
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If xy = 20 and x = 5, then y is:
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Correct answer: 4
y = 20 / 5 = 4.
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If the speed is doubled and the distance is fixed, the time:
- 1 Is unchanged
- 2 Is four times
- 3 Is doubled
- 4 Is halved
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Correct answer: Is halved
Time is inversely proportional to speed.
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The area of a circle varies directly with the square of its:
- 1 Diameter only
- 2 Circumference only
- 3 Colour
- 4 Radius
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Correct answer: Radius
A = pi r².
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