Mathematics for IGCSE & O level - Proportion (Section 3)
1
If *y* ∝ √*x*, and *y* = 6 when *x* = 9, find *y* when *x* = 16.
Answer
(B)
8
2
When y varies inversely with x, what happens to y if x is multiplied by 3?
Answer
(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?
Answer
(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?
Answer
(B)
3 hours
5
Given that *y* ∝ 1/*x*2. If *x* increases by a factor of 2, by what factor does *y* change?
Answer
(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?
Answer
(B)
40 days
7
What is the inverse proportion formula?
Answer
(B)
y = k/x
8
If y is inversely proportional to x, and y=2 when x=8, what is the constant of proportionality?
Answer
(D)
20
9
If 'y' varies inversely as 'x', what happens to 'y' if 'x' is doubled?
Answer
(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.
Answer
(C)
16
11
Which of the following situations demonstrates inverse proportion?
Answer
(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.
Answer
(B)
15
13
If y is inversely proportional to x^2 and x is doubled, by what factor does y change?
Answer
(D)
1/4
14
If y= 1/x and x= 10, what is y?
Answer
(C)
1/10
15
If *y* varies directly with *x*, what is the relationship between the graph of *y* against *x*?
Answer
(B)
A straight line through the origin
16
What does "y ∝ x" mean?
Answer
(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.
Answer
(A)
1
18
If *y* varies inversely as the square of *x*, which of the following statements is correct?
Answer
(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.
Answer
(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)?
Answer
(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 =?
Answer
(B)
2
22
What does the symbol "∝" mean in proportion?
Answer
(C)
is proportional to
23
Which of the following situations *best* illustrates inverse proportion?
Answer
(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:
Answer
A
B
25
If *y* varies inversely as *x*, which of the following statements is correct?
Answer
(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.
Answer
(C)
6
27
If y varies directly with x, and y=10 when x=5, what is y when x=15?
Answer
(D)
30
28
Which of the following represents a direct proportion between two variables?
Answer
C
D
29
If y is inversely proportional to x, what happens to y if x is halved?
Answer
(B)
y is doubled
30
What does the phrase "y varies directly as x^2" mean?
Answer
(C)
y = kx^2
31
Which of the following statements best describes inverse proportion?
Answer
(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)?
Answer
(B)
The time halves
33
In the formula y = k/x, if k is a constant, what happens to y if x is tripled?
Answer
(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?
