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