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Mathematics for IGCSE & O level - Equations (Section 7)

1
If you're solving a linear equation and get a statement like 3 = 5, what does this indicate?
Answer
(C)
There is no solution.
2
What must be true for the product of two or more real numbers to equal zero?
Answer
(A)
At least one of the numbers must be zero.
3
If you are given the formula for the volume of a cone, V = (1/3)πr²h. Which steps are used to find 'r'?
Answer
A
B
C
4
Which of the following are correct statements about the quadratic equation?
Answer
A
B
C
5
If you want to rearrange the formula P = 2(l + w) to solve for 'l' (length), what's the correct first step?
Answer
(B)
Divide both sides by 2.
6
What must be done to factor a quadratic equation?
Answer
A
C
D
7
The formula for the area of a circle is A = πr². If we want to make 'r' the subject, the first step is:
Answer
(A)
Divide both sides by π
8
What is the first step to solve the equation x² + 4x - 5 = 0 by factorization?
Answer
(B)
Find two numbers that multiply to -5 and add to 4.
9
The expression x² + 10x + 25 can be written as:
Answer
(A)
(x + 5)²
10
Which concepts are used when solving a quadratic equation?
Answer
A
B
C
11
Which of these equations represents a difference of squares?
Answer
(C)
x² - 9 = 0
12
If you want to rearrange a formula to solve for a specific variable, which of the following is the best practice?
Answer
(A)
Isolate the variable by applying inverse operations to both sides of the equation.
13
What is the first step when solving equations involving fractions?
Answer
(C)
Eliminating the denominators
14
Which of the following is a key step in solving a quadratic equation by factoring?
Answer
(C)
Finding two numbers whose sum is 'b' and product is 'c'.
15
What is the best approach for rearranging complex formulas or equations to make a specific variable the subject?
Answer
(A)
Carefully apply inverse operations
16
Which term is added to both sides of a quadratic equation when completing the square?
Answer
(A)
(b/2)²
17
If the discriminant (b²-4ac) of a quadratic equation is negative, what does it tell you about the roots?
Answer
(C)
The roots are complex (non-real).
18
If you are given the equation x + y = 7 and x - y = 1. What method should you use to solve?
Answer
(C)
Elimination
19
When completing the square, how do you find the value that should be added and subtracted to the expression x² + bx?
Answer
(A)
(b/2)²
20
If the discriminant is zero, can we make a conclusion about the solutions?
Answer
(A)
Yes, there is one repeated root.
21
What are the different approaches when given a system of equations?
Answer
A
B
22
What should you do first to solve a quadratic equation by factorization?
Answer
A
D
23
If you have a quadratic equation and factorize it and the two roots are the same, this means what?
Answer
(C)
The discriminant is zero
24
If two quantities, A and B, are equal, and two other quantities, C and D, are equal, what does it imply about A + C and B + D?
Answer
(B)
A + C = B + D
25
What is the first step to solve a quadratic equation using completing the square?
Answer
(A)
Isolate the x² and x terms on one side of the equation.
26
How can you rearrange a formula to solve for a particular variable?
Answer
A
B
27
If the roots of a quadratic equation are x = 2 and x = -3, which of the following equations could represent this quadratic?
Answer
A
D
28
In solving simultaneous equations using substitution, which statement is typically NOT true?
Answer
(D)
You substitute the values for both variables from the start
29
When solving a linear equation, what is the goal?
Answer
(B)
To isolate the variable on one side of the equation
30
Which formula is used to solve quadratic equations?
Answer
(C)
Quadratic formula
31
Which method of solving a quadratic equation involves converting one side of the equation into a perfect square trinomial?
Answer
(B)
Completing the Square
32
Which of the following best describes how to solve a system of equations using substitution?
Answer
A
B
C
33
What are the roots of the quadratic equation x² - 5x + 6 = 0?
Answer
(A)
x = 2, x = 3
34
What does 'P' mean in the formula P = 2l + 2w?
Answer
(A)
Perimeter
35
Which statement is correct regarding rearranging formulas?
Answer
(C)
Whatever operation is done on one side must be done on the other side.
36
In the quadratic equation ax² + bx + c = 0, what does the constant 'c' represent graphically?
Answer
(B)
The y-intercept
37
When using the quadratic formula, what does the value of 'a' correspond to in a quadratic equation?
Answer
(C)
The coefficient of x²
38
Which are methods to solve a quadratic equation?
Answer
B
C
D
39
Which of these are key steps when applying the quadratic formula?
Answer
A
B
C
40
If you want to solve a system of equations using substitution, what do you need initially?
Answer
(C)
One equation already solved for a variable.
41
To factor a quadratic equation x² + bx + c = 0, what must the two numbers you find add up to?
Answer
(B)
b
42
Which steps are needed when solving a quadratic equation by completing the square?
Answer
A
B
C
43
If you know the area of a rectangle, A, and the length, l, what is the correct equation to find the width, w?
Answer
(C)
w = A / l
44
What is a characteristic of equations solved by completing the square?
Answer
(D)
All of the above
45
If the area of a rectangle is given by the formula A = lw, and you are given A and w, which algebraic operation is required to find l?
Answer
(D)
Division
46
If the discriminant of a quadratic equation is positive, what does this mean about the roots?
Answer
(C)
The roots are real and distinct.
47
If you solve 3x + 4y = 10 and x = 2 using substitution, what is the value of y?
Answer
(A)
1
48
In solving by factorization, after finding factors, what is the next action to be taken?
Answer
A
B
49
What does solving an equation mean?
Answer
(A)
Finding the value of the unknown variable
50
When solving by factorization, what is the zero-product property?
Answer
(A)
If a product is zero, then each factor must be zero.