Mathematics for IGCSE & O level - Proportion (Section 1)
1
Which of the following represents the correct equation if *y* is directly proportional to *x*?
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A
B
D
2
The area of a triangle varies jointly with its base (*b*) and height (*h*). If the area is 10 when b=4 and h=5, what is the area when b=6 and h=3?
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(B)
18
3
Given that *y* varies inversely as the square root of *x*, if *x* increases by a factor of 4, how does *y* change?
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(B)
y decreases by a factor of 2
4
Which scenario best represents a direct proportion relationship?
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(C)
The number of items purchased and the total cost.
5
If *z* varies jointly as *x* and *y*, and *z* = 12 when *x* = 2 and *y* = 3, find *z* when *x* = 4 and *y* = 5.
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(D)
40
6
If the area of a square is directly proportional to the square of the side length, and a square with side length 3 has an area of 9, what is the area of a square with side length 5?
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(C)
25
7
The amount of money you have, *m*, is directly proportional to the number of ice creams you have, *i*. Which of the following is/are true?
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A
B
C
8
If *a* is directly proportional to the square of *b*, which of these equations describes the relationship?
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(C)
a = kb^2
9
If *y* is inversely proportional to *x* and *y* = 4 when *x* = 3, find *y* when *x* = 6.
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(B)
3
10
If *a* is directly proportional to *b* and *a* is 10 when *b* is 2, what is the value of *a* when *b* = 5?
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(D)
50
11
If *y* is inversely proportional to *x*3, and *y* = 2 when *x* = 2, then what is the constant of proportionality?
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(C)
16
12
The volume of a gas, *V*, is inversely proportional to its pressure, *P*. If *V* = 10 cubic units when *P* = 2 atm, what is *V* when *P* = 5 atm?
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(B)
5
13
Which scenario describes direct proportion?
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(C)
The number of products sold and the total revenue earned.
14
In the context of proportion, which statement best describes an indirect proportion?
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(D)
As one quantity increases, the other quantity decreases.
15
If *y* is inversely proportional to *x*, which statement is true?
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(C)
xy = k for some constant k.
16
The braking distance, *d*, of a car is directly proportional to the square of its speed, *s*. If the braking distance is 6 meters when the speed is 10 m/s, what is the braking distance when the speed is increased by 200%?
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(D)
54 m
17
Which of the following statements best illustrates the concept of inverse variation?
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(D)
The larger the number of workers, the less time it takes to complete a task.
18
The amount of simple interest earned, *I*, is directly proportional to the principal, *P*, the rate, *R*, and the time, *T*. Which of the following equations represents this relationship, where k is a constant?
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(B)
I = kPRT
19
If the volume (V) of a sphere is proportional to the cube of its radius (r), which of these equations is correct?
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(C)
V = kr^3
20
If *y* varies jointly as *x* and the square root of *z*, and *y* = 12 when *x* = 2 and *z* = 9, find *y* when *x* = 4 and *z* = 4.
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(D)
24
21
The time (*t*) to cook a roast is directly proportional to its weight (*w*). If a 2-kg roast takes 1 hour to cook, how long will it take to cook a 3-kg roast?
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(B)
1.5 hours
22
If *y* varies inversely as *x*2, which of the following is the correct equation?
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(C)
y = k/x2
23
The time it takes to complete a job is inversely proportional to the number of people working. If 3 people take 12 hours to complete a job, how long would it take 4 people?
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(C)
16 hours
24
The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). Which equation describes this relationship?
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(B)
R = kL/A
25
If *z* varies jointly with *x* and the square of *y*, then which of the following equations is true?
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(C)
z = kxy^2
26
Given that *y* varies inversely as *x*2, and *y* = 4 when *x* = 1.5, what is the value of *y* when *x* = 3?
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(A)
1
27
If *y* varies inversely as *x*, and *y* is 5 when *x* = 2, then what is the value of *y* when *x* = 10?
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(B)
2
28
If *a* is directly proportional to the square root of *b*, and *a* = 6 when *b* = 9, then find *a* when *b* = 4.
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(D)
8
29
The time, *t*, taken for a journey at a fixed speed is inversely proportional to the number of people, *n*, travelling. If *t* = 10 hours when *n* = 5, what is the formula?
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(C)
t = 50/n
30
The number of pages in a book, *p*, is inversely proportional to the number of words on each page, *w*. Which equation correctly describes this relationship?
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(B)
pw = k
31
A rectangular garden has a length of *L* meters and a width of *W* meters. If the area of the garden is fixed, which of the following is true?
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B
C
32
If *y* is inversely proportional to the square root of *x*, and *y* = 6 when *x* = 4, find *y* when *x* = 9.
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(D)
9
33
If *a* is inversely proportional to *b*, and *a* is doubled, what happens to *b*?
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(A)
*b* is halved
34
If *y* is directly proportional to *x*, and *y* = 6 when *x* = 2, what is the constant of proportionality?
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(B)
3
35
If *x* varies inversely as the square of *y*, and *x* = 4 when *y* = 3, what is the formula connecting *x* and *y*?
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(B)
x = 12/y^2
36
The pressure exerted by a gas on the walls of a container is inversely proportional to the volume of the container. If the volume of the container is halved, what happens to the pressure?
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(B)
The pressure doubles.
37
If *a* varies inversely with *b*, and *a* = 3 when *b* = 4, find *a* when *b* = 6.
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(B)
2
38
If y varies inversely as x, what happens to y if x is tripled?
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(C)
y is divided by 3
39
The force of gravity between two objects is inversely proportional to the square of the distance between them. If the distance between two objects is increased by a factor of 3, the gravitational force between them will be:
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(A)
1/9 of the original force
40
If *x* is directly proportional to *y*, and *x* = 10 when *y* = 2, find the value of *x* when *y* = 7.
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(C)
40
41
If *a* varies jointly as *b* and *c*, which equation represents the relationship, where *k* is the constant of proportionality?
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(B)
*a* = k*b*c
42
The variable *a* is directly proportional to *b*, and *a* = 6 when *b* = 2. Which of the following equations is correct?
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(B)
a = 3b
43
The number of apples you can buy with a fixed amount of money varies inversely with the price of each apple. If you can buy 10 apples when each apple costs $1, how many apples can you buy if each apple costs $2?
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(C)
10
44
If *a* is inversely proportional to the cube of *b*, and *a* = 2 when *b* = 2, find *a* when *b* = 4.
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(B)
1/4
45
If *y* varies jointly as *x* and *z*, and *y* = 20 when *x* = 2 and *z* = 5, find *y* when *x* = 3 and *z* = 4.
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(C)
30
46
If *a* is inversely proportional to *b* and *a* = 2 when *b* = 6, what is *a* when *b* = 3?
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(D)
6
47
If *y* is directly proportional to *x* and *z*, which equation expresses the relationship, where k is a constant?
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(B)
y = kxz
48
If *y* is jointly proportional to *x* and *z* and *y* = 30 when *x* = 2 and *z* = 3, find *y* when *x* = 4 and *z* = 5.
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(C)
100
49
Which of the following best describes the relationship between the number of hours worked and the amount of money earned if you earn a fixed hourly wage?
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(A)
Direct proportion
50
Which of the following are true statements about direct proportion? (Where *k* is the constant of proportionality)
