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