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