Mathematics for IGCSE & O level - Proportion (Section 3)
1
If *y* ∝ √*x*, and *y* = 6 when *x* = 9, find *y* when *x* = 16.
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(B)
8
2
When y varies inversely with x, what happens to y if x is multiplied by 3?
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(B)
y is divided by 3
3
Which statement about the relationship between x and y is true if y = k/x, where k is a constant?
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(B)
y is inversely proportional to x.
4
The time, *t*, taken for a journey is inversely proportional to the speed, *s*. If a journey takes 4 hours at a speed of 60 km/h, how long will the journey take at a speed of 80 km/h?
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(B)
3 hours
5
Given that *y* ∝ 1/*x*2. If *x* increases by a factor of 2, by what factor does *y* change?
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(D)
1/4
6
A farmer has enough feed to last his cows for 60 days. If he increases the number of cows by 50%, how long will the feed last?
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(B)
40 days
7
What is the inverse proportion formula?
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(B)
y = k/x
8
If y is inversely proportional to x, and y=2 when x=8, what is the constant of proportionality?
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(D)
20
9
If 'y' varies inversely as 'x', what happens to 'y' if 'x' is doubled?
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(B)
'y' halves
10
If *y* is directly proportional to the square root of *x*, and *y* = 8 when *x* = 4, find the value of *y* when *x* = 16.
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(C)
16
11
Which of the following situations demonstrates inverse proportion?
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(B)
The number of workers and the time it takes to build a wall.
12
If y varies directly with x, and y = 6 when x = 2, find y when x = 5.
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(B)
15
13
If y is inversely proportional to x^2 and x is doubled, by what factor does y change?
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(D)
1/4
14
If y= 1/x and x= 10, what is y?
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(C)
1/10
15
If *y* varies directly with *x*, what is the relationship between the graph of *y* against *x*?
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(B)
A straight line through the origin
16
What does "y ∝ x" mean?
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(B)
y varies directly as x
17
If 'z' varies inversely as the square of 'w', and z=4 when w=2, find z when w=4.
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(A)
1
18
If *y* varies inversely as the square of *x*, which of the following statements is correct?
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(B)
As x increases, y decreases.
19
If y is inversely proportional to the square root of x, and y=6 when x=9, find y when x=4.
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(C)
9
20
A car travels a certain distance at a constant speed. If the time taken is doubled, what happens to the speed (assuming distance remains constant)?
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(B)
The speed halves.
21
If 'y' varies inversely with the square root of 'x', and x = 4 when y = 3, then when x = 9, y =?
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(B)
2
22
What does the symbol "∝" mean in proportion?
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(C)
is proportional to
23
Which of the following situations *best* illustrates inverse proportion?
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(B)
The number of workers painting a house and the time taken to paint the house
24
The braking distance, *d*, of a car is directly proportional to the square of its speed, *v*. If the braking distance is 6m when the speed is *v* meters per second, select the correct statements:
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A
B
25
If *y* varies inversely as *x*, which of the following statements is correct?
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(B)
As *x* increases, *y* decreases.
26
If 'y' varies inversely as the square root of 'x' and y = 4 when x = 9, find y when x = 4.
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(C)
6
27
If y varies directly with x, and y=10 when x=5, what is y when x=15?
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(D)
30
28
Which of the following represents a direct proportion between two variables?
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C
D
29
If y is inversely proportional to x, what happens to y if x is halved?
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(B)
y is doubled
30
What does the phrase "y varies directly as x^2" mean?
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(C)
y = kx^2
31
Which of the following statements best describes inverse proportion?
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(A)
As one quantity increases, the other decreases.
32
If the number of workers on a project is doubled, what happens to the time required to complete the project (assuming the amount of work remains constant)?
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(B)
The time halves
33
In the formula y = k/x, if k is a constant, what happens to y if x is tripled?
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(B)
y is divided by 3.
34
The distance a car travels is directly proportional to the time it travels. If a car travels 100km in 2 hours, how far will it travel in 5 hours?
