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