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