Mathematics for IGCSE & O level - Proportion (Section 2)
1
When *y* is inversely proportional to the square root of *x*, and *y* = 4 when *x* = 16. What will be the value of x when y = 2?
Answer
(D)
64
2
If *y* is inversely proportional to the square root of *x*, then which statement is true?
Answer
(D)
*y* = k/√x
3
Which of the following statements is an example of a joint variation?
Answer
(B)
The area of a rectangle is the product of its length and width.
4
If *p* varies inversely with the square of *q*, then when *q* is doubled, *p* is:
Answer
(C)
quartered
5
Which of the following scenarios demonstrates an inverse relationship?
Answer
(B)
The speed of a car and the time taken to travel a fixed distance.
6
If *p* is inversely proportional to the square of *r* (*p* α 1/*r*2), and *p* = 4 when *r* = 3, find the constant of proportionality.
Answer
(A)
9
7
If *a* varies inversely as *b*, and *a* = 5 when *b* = 4, what is the value of *b* when *a* = 2?
Answer
(C)
16
8
If *y* is directly proportional to the square root of *x*, and *y* = 6 when *x* = 9, which equation correctly represents this relationship?
Answer
(C)
y = √x
9
The force of gravity between two objects varies inversely as the square of the distance between them. If the distance is doubled, by what factor does the force change?
Answer
(A)
1/4
10
If *a* varies inversely with the square of *b*, and *a* = 4 when *b* = 2, find the value of *a* when *b* = 4.
Answer
(B)
2
11
If y is inversely proportional to x, which of the following is always true?
Answer
B
D
12
If *y* is directly proportional to *x* and *y* = 4 when *x* = 2, which equation represents the relationship between *x* and *y*?
Answer
(B)
y = 2x
13
If *y* is inversely proportional to *x*, and *y* = 8 when *x* = 2, what is *y* when *x* = 4?
Answer
(B)
4
14
In the formula *y* = *kx*n, if *y* is inversely proportional to *x*3, what is the value of *n*?
Answer
(A)
-3
15
If *x* varies directly as *y* and *x* = 15 when *y* = 3, find *x* when *y* = 7.
Answer
(C)
40
16
If *y* varies jointly as *x* and the square of *z*, and *y* = 18 when *x* = 2 and *z* = 3, what is *y* when *x* = 4 and *z* = 2?
Answer
(B)
12
17
If *y* is inversely proportional to *x*, and *y* = 10 when *x* = 5, what is the constant of proportionality?
Answer
(D)
100
18
If y is directly proportional to x, and y is 6 when x is 4, what is the equation representing this relationship?
Answer
(B)
y = (3/2)x
19
The time taken for a journey, *t*, is inversely proportional to the speed, *s*. If *t* is 3 hours when *s* is 60 km/h, find *s* when *t* is 2 hours.
Answer
(B)
90 km/h
20
In the formula *y* = *kx*2, if *x* is halved, by what factor does *y* change?
Answer
(A)
1/4
21
If *y* varies inversely as *x*, what happens to *y* when *x* is multiplied by 0.5?
Answer
(C)
y is multiplied by 2
22
The amount of fuel used by a car is directly proportional to the distance traveled. If a car uses 5 liters of fuel to travel 50 km, how many liters of fuel will it use to travel 120 km?
Answer
(D)
15
23
If the time taken (*t*) to travel a distance is inversely proportional to the speed (*s*), which of the following statements is true?
Answer
A
C
D
24
In a scenario where *y* is inversely proportional to the square root of *x*, which of these is true?
Answer
(C)
As *x* increases, *y* decreases.
25
A car travels at a speed of *s* km/h and takes *t* hours to cover a certain distance. Which of the following statements are true if the distance is constant?
Answer
A
C
D
26
If *y* varies inversely as *x*, and *y* = 4 when *x* = 3, what is the formula connecting *x* and *y*?
Answer
(B)
y = \(\frac{12}{x}\)
27
The number of bricks needed to build a wall is inversely proportional to the number of workers. If it takes 8 workers 10 days to build a wall, how many days will it take 4 workers to build a wall?
Answer
(D)
20 days
28
If *A* varies directly as *B* and inversely as *C*, then which of the following is true?
Answer
(B)
*A* = kB/C
29
If *y* is directly proportional to *x* and *y* = 10 when *x* = 5, what is the value of *y* when *x* = 8?
Answer
(B)
13
30
If *z* is directly proportional to *x* and the square of *y*, and *z* = 24 when *x* = 2 and *y* = 3, what is *z* when *x* = 3 and *y* = 2?
Answer
(D)
24
31
What type of proportion is displayed when y is directly proportional to x?
Answer
(C)
Direct
32
If *y* is inversely proportional to *x*2, and *y* = 8 when *x* = 2, what is the value of *y* when *x* = 4?
Answer
(B)
2
33
Which of the following scenarios could represent the relationship between two variables that are inversely proportional?
Answer
(B)
The speed of a car and the time it takes to travel a fixed distance.
34
Which of the following equations demonstrate inverse proportionality?
Answer
A
C
D
35
If a car travels 100 miles in 2 hours, how far will it travel in 3 hours at the same speed?
Answer
(B)
150 miles
36
What does the phrase "y varies directly as x" mean mathematically?
Answer
(B)
y = kx
37
If y varies directly with x, what is the constant of proportionality if y=10 when x=2?
Answer
(B)
5
38
What are the key points from the key points section of the image?
Answer
A
C
D
39
If *y* varies directly as the square root of *x*, and *y* = 6 when *x* = 4, find *y* when *x* = 9.
Answer
(C)
9
40
What is the relationship between the distance traveled by a car at a constant speed and the time it takes?
Answer
(A)
Direct proportion
41
Which equation represents the statement: *y* varies inversely as the square of *x*?
Answer
(D)
y = k/x^2
42
In which of the following scenarios is inverse proportion demonstrated?
Answer
(B)
The number of workers and the time to complete a job.
43
The volume of a gas is inversely proportional to its pressure. If a gas occupies 10 liters at a pressure of 2 atmospheres, what volume will it occupy at a pressure of 5 atmospheres?
Answer
(B)
4 liters
44
If y is directly proportional to x, which of the following graphs would represent this relationship?
Answer
(B)
A straight line through the origin.
45
If *y* varies inversely as *x*, and *y* = 2 when *x* = 10, find *y* when *x* = 4.
Answer
(B)
5
46
Which of the following equations represents an inverse proportion?
Answer
(C)
xy = 5
47
What is the first step to find the formula for the proportion in the method?
Answer
(C)
Replace the = sign with a ∝ sign
48
The time taken to complete a journey varies inversely with the speed. If a journey takes 4 hours at 60 mph, how long would it take at 40 mph?
Answer
(C)
6 hours
49
The number of days to complete a project is inversely proportional to the number of workers. If 10 workers can complete a project in 14 days, how many days will it take 7 workers to complete the same project?
Answer
(B)
10
50
If *y* varies inversely as *x*, and *y* = 4 when *x* = 3, what is the value of *x* when *y* = 6?
