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