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