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