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