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