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?
Хариулт
(D)
64
2
If *y* is inversely proportional to the square root of *x*, then which statement is true?
Хариулт
(D)
*y* = k/√x
3
Which of the following statements is an example of a joint variation?
Хариулт
(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:
Хариулт
(C)
quartered
5
Which of the following scenarios demonstrates an inverse relationship?
Хариулт
(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.
Хариулт
(A)
9
7
If *a* varies inversely as *b*, and *a* = 5 when *b* = 4, what is the value of *b* when *a* = 2?
Хариулт
(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?
Хариулт
(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?
Хариулт
(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.
Хариулт
(B)
2
11
If y is inversely proportional to x, which of the following is always true?
Хариулт
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*?
Хариулт
(B)
y = 2x
13
If *y* is inversely proportional to *x*, and *y* = 8 when *x* = 2, what is *y* when *x* = 4?
Хариулт
(B)
4
14
In the formula *y* = *kx*n, if *y* is inversely proportional to *x*3, what is the value of *n*?
Хариулт
(A)
-3
15
If *x* varies directly as *y* and *x* = 15 when *y* = 3, find *x* when *y* = 7.
Хариулт
(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?
Хариулт
(B)
12
17
If *y* is inversely proportional to *x*, and *y* = 10 when *x* = 5, what is the constant of proportionality?
Хариулт
(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?
Хариулт
(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.
Хариулт
(B)
90 km/h
20
In the formula *y* = *kx*2, if *x* is halved, by what factor does *y* change?
Хариулт
(A)
1/4
21
If *y* varies inversely as *x*, what happens to *y* when *x* is multiplied by 0.5?
Хариулт
(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?
Хариулт
(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?
Хариулт
A
C
D
24
In a scenario where *y* is inversely proportional to the square root of *x*, which of these is true?
Хариулт
(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?
Хариулт
A
C
D
26
If *y* varies inversely as *x*, and *y* = 4 when *x* = 3, what is the formula connecting *x* and *y*?
Хариулт
(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?
Хариулт
(D)
20 days
28
If *A* varies directly as *B* and inversely as *C*, then which of the following is true?
Хариулт
(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?
Хариулт
(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?
Хариулт
(D)
24
31
What type of proportion is displayed when y is directly proportional to x?
Хариулт
(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?
Хариулт
(B)
2
33
Which of the following scenarios could represent the relationship between two variables that are inversely proportional?
Хариулт
(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?
Хариулт
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?
Хариулт
(B)
150 miles
36
What does the phrase "y varies directly as x" mean mathematically?
Хариулт
(B)
y = kx
37
If y varies directly with x, what is the constant of proportionality if y=10 when x=2?
Хариулт
(B)
5
38
What are the key points from the key points section of the image?
Хариулт
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.
Хариулт
(C)
9
40
What is the relationship between the distance traveled by a car at a constant speed and the time it takes?
Хариулт
(A)
Direct proportion
41
Which equation represents the statement: *y* varies inversely as the square of *x*?
Хариулт
(D)
y = k/x^2
42
In which of the following scenarios is inverse proportion demonstrated?
Хариулт
(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?
Хариулт
(B)
4 liters
44
If y is directly proportional to x, which of the following graphs would represent this relationship?
Хариулт
(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.
Хариулт
(B)
5
46
Which of the following equations represents an inverse proportion?
Хариулт
(C)
xy = 5
47
What is the first step to find the formula for the proportion in the method?
Хариулт
(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?
Хариулт
(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?
Хариулт
(B)
10
50
If *y* varies inversely as *x*, and *y* = 4 when *x* = 3, what is the value of *x* when *y* = 6?
