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