Mathematics for IGCSE & O level - Proportion (Section 1)
1
Which of the following represents the correct equation if *y* is directly proportional to *x*?
Хариулт
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?
Хариулт
(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?
Хариулт
(B)
y decreases by a factor of 2
4
Which scenario best represents a direct proportion relationship?
Хариулт
(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.
Хариулт
(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?
Хариулт
(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?
Хариулт
A
B
C
8
If *a* is directly proportional to the square of *b*, which of these equations describes the relationship?
Хариулт
(C)
a = kb^2
9
If *y* is inversely proportional to *x* and *y* = 4 when *x* = 3, find *y* when *x* = 6.
Хариулт
(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?
Хариулт
(D)
50
11
If *y* is inversely proportional to *x*3, and *y* = 2 when *x* = 2, then what is the constant of proportionality?
Хариулт
(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?
Хариулт
(B)
5
13
Which scenario describes direct proportion?
Хариулт
(C)
The number of products sold and the total revenue earned.
14
In the context of proportion, which statement best describes an indirect proportion?
Хариулт
(D)
As one quantity increases, the other quantity decreases.
15
If *y* is inversely proportional to *x*, which statement is true?
Хариулт
(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%?
Хариулт
(D)
54 m
17
Which of the following statements best illustrates the concept of inverse variation?
Хариулт
(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?
Хариулт
(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?
Хариулт
(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.
Хариулт
(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?
Хариулт
(B)
1.5 hours
22
If *y* varies inversely as *x*2, which of the following is the correct equation?
Хариулт
(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?
Хариулт
(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?
Хариулт
(B)
R = kL/A
25
If *z* varies jointly with *x* and the square of *y*, then which of the following equations is true?
Хариулт
(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?
Хариулт
(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?
Хариулт
(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.
Хариулт
(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?
Хариулт
(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?
Хариулт
(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?
Хариулт
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.
Хариулт
(D)
9
33
If *a* is inversely proportional to *b*, and *a* is doubled, what happens to *b*?
Хариулт
(A)
*b* is halved
34
If *y* is directly proportional to *x*, and *y* = 6 when *x* = 2, what is the constant of proportionality?
Хариулт
(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*?
Хариулт
(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?
Хариулт
(B)
The pressure doubles.
37
If *a* varies inversely with *b*, and *a* = 3 when *b* = 4, find *a* when *b* = 6.
Хариулт
(B)
2
38
If y varies inversely as x, what happens to y if x is tripled?
Хариулт
(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:
Хариулт
(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.
Хариулт
(C)
40
41
If *a* varies jointly as *b* and *c*, which equation represents the relationship, where *k* is the constant of proportionality?
Хариулт
(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?
Хариулт
(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?
Хариулт
(C)
10
44
If *a* is inversely proportional to the cube of *b*, and *a* = 2 when *b* = 2, find *a* when *b* = 4.
Хариулт
(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.
Хариулт
(C)
30
46
If *a* is inversely proportional to *b* and *a* = 2 when *b* = 6, what is *a* when *b* = 3?
Хариулт
(D)
6
47
If *y* is directly proportional to *x* and *z*, which equation expresses the relationship, where k is a constant?
Хариулт
(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.
Хариулт
(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?
Хариулт
(A)
Direct proportion
50
Which of the following are true statements about direct proportion? (Where *k* is the constant of proportionality)
