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