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