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Mathematics for IGCSE & O level - Equations (Section 5)

1
Which of the following is the correct expression for the area of a rectangle with length (x + 5) and width 3?
Answer
(B)
3x + 15
2
What is the first step in solving simultaneous equations using substitution?
Answer
(B)
Isolate one of the variables in one of the equations.
3
If a quadratic equation has no real roots, what is the nature of its roots?
Answer
(C)
Imaginary or complex
4
What is the simplified form of 2(x + 3) + 4x?
Answer
(C)
6x + 5
5
When would you choose to use the quadratic formula over factorization?
Answer
(C)
When factorization is not possible or difficult.
6
If the discriminant of a quadratic equation is zero, how many real solutions does it have?
Answer
(B)
One
7
Which of the following is used when a quadratic equation is not readily factorable?
Answer
A
B
8
What is the correct order of operations for solving an equation when 'changing the subject'?
Answer
(D)
Reverse PEMDAS, focusing on isolation.
9
Which is the proper first step when solving for x in the equation x/3 + 2 = 6?
Answer
(A)
Subtract 2 from both sides.
10
What is the correct order of operations to isolate a variable when changing the subject of a formula?
Answer
(B)
Multiplication/division, then addition/subtraction.
11
How is the quadratic formula used?
Answer
(B)
To find the roots of a quadratic equation.
12
Solve: 5(x + 2) = 35
Answer
(B)
7
13
When solving a quadratic equation of the form ax² + bx + c = 0, what do you need to identify?
Answer
A
B
C
14
What is the first step to change the subject in a formula like a = b/c?
Answer
(B)
Multiply by c
15
Which of the following is a key characteristic of a quadratic equation that can be solved by factorization?
Answer
(C)
Can be expressed as a product of linear factors.
16
If you were to 'complete the square' for x² + 8x + 7 = 0, what number would you add and subtract?
Answer
(B)
16
17
What's the characteristic of a quadratic equation that can be solved by factoring?
Answer
B
D
18
What is the primary benefit of using factorization to solve a quadratic equation?
Answer
(B)
It's a quick way to find the roots if possible.
19
What is the term for the result of a quadratic equation?
Answer
(A)
The roots
20
In a quadratic equation, where does the y-intercept always occur?
Answer
(A)
When x = 0
21
If 3(x - 2) = 12, what is the value of x?
Answer
(A)
6
22
Solve for x: 3x + 2 = 11
Answer
(B)
9
23
When do you use the difference of two squares factorization technique?
Answer
(A)
When there is a perfect square minus another perfect square
24
Identify the step(s) required to eliminate a variable when solving a system of equations.
Answer
A
B
C
25
What is the value of x in the equation: -3x + 6 = 0?
Answer
(B)
-2
26
What does 'b' represent in the general quadratic equation ax² + bx + c = 0?
Answer
(B)
The coefficient of x
27
What is the value of x in the equation: 3x + 4 = 16?
Answer
(A)
4
28
What is the purpose of 'completing the square'?
Answer
(B)
To make one side a perfect square trinomial.
29
Which equation represents a line with a slope of 2 and a y-intercept of -3?
Answer
(B)
y = 2x - 3
30
What method should be used to solve the equation 2x² + 8x + 8 = 0?
Answer
(D)
All the above.
31
If x-5 = 12, what is the value of x?
Answer
(A)
17
32
In the equation 2x - 6 = 0, which is the correct solution to solve for x?
Answer
(A)
x=3
33
What is the area of a rectangle with a length of 7 and a width of 3?
Answer
(A)
21
34
Solve for x: 7x - 3 = 18
Answer
(B)
15
35
In the equation 2/5x = 10, what is the correct operation to solve for x?
Answer
(A)
Divide by 2/5
36
What is the primary application of the quadratic formula?
Answer
(C)
Solving quadratic equations.
37
If the circumference of a circle is 2πr and its radius is 3, what is the circumference?
Answer
(B)
9π
38
What is the value of x in the following equation: x/4 - 3 = 1?
Answer
(B)
16
39
Which of the following are components that are needed to use the quadratic formula?
Answer
A
C
40
What is the correct operation to use to solve the equation: x/4 = 6 ?
Answer
(A)
Multiply by 4
41
What is the standard form of a quadratic equation?
Answer
(B)
ax² + bx + c = 0
42
In the context of simultaneous equations, what does 'substitution' primarily involve?
Answer
(A)
Replacing one variable with its equivalent expression from another equation.
43
Which steps are used in the factorization of quadratic equations?
Answer
A
B
C
44
If you have (x + 2)(x - 3) = 0, what are the solutions for x?
Answer
(B)
x = -2, x = 3
45
Which equation represents a perfect square trinomial?
Answer
(A)
x² + 4x + 4 = 0
46
When solving the equation x² - 49 = 0 by factorization, the solutions are:
Answer
(C)
x = 7 and x = -7
47
What is the first step when solving quadratic equations of the form x² + bx + c = 0 by factorization?
Answer
(A)
Rearrange the equation to have all terms on one side.
48
In the equation 3x - 6y = 4 and x = 2, using substitution, what is the value of y?
Answer
(A)
-1/3
49
If you have (x + 4)(x - 1) = 0, what are the solutions for x?
Answer
(C)
x = -4, x = 1
50
Which operations will result to find the area of the path if you have a rectangular pen inside a rectangular path, using the given information?
Answer
A
B
C