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