Mathematics for IGCSE & O level - Equations (Section 6)
1
If you want to solve the equation 5x = 20, what operation will you use?
Answer
(D)
Divide both sides by 5.
2
Which of the following is equivalent to completing the square for the expression x² + 6x + 5?
Answer
(A)
(x+3)² - 4
3
If the equation is 2x - 3y = 7, and x = 4, what is the value of y?
Answer
(B)
1/3
4
When solving simultaneous equations, what strategies can you use to manipulate the equations? (Select all that apply)
Answer
A
B
C
D
5
Which is the general form for the area of a triangle?
Answer
(C)
A = 1/2bh
6
Which of the following is the correct formula to find the roots of the quadratic equation ax² + bx + c = 0?
Answer
(A)
x = (-b ± √(b² - 4ac)) / 2a
7
Which techniques can be employed for finding the dimensions of a rectangular pen, when knowing the area and perimeter?
Answer
A
B
C
D
8
When using substitution to solve simultaneous equations, what should you always substitute?
Answer
(A)
The expression for the subject into the other equation.
9
When would you use substitution to solve a system of equations?
Answer
A
B
10
What would be the correct starting point if you want to find the dimensions of a rectangular pen with an area of 27 m² and a perimeter that should be smaller than 25 m?
Answer
(B)
Set up the equations A = l x w and P = 2(l + w)
11
What formula can be used to find the area of a triangle?
Answer
(C)
Area = 1/2 * base * height
12
What is the solution for x in the equation 2x - 4 = 0?
Answer
(B)
x = 2
13
If a quadratic equation cannot be factored easily, which method is generally recommended?
Answer
A
B
14
If you're solving for the height 'h' in the area of a triangle, A = (1/2)bh, what is the correct formula for h?
Answer
(A)
h = 2A/b
15
When are the methods such as factoring and quadratic equations more suitable?
Answer
A
D
16
What is the first step in solving the equation 2x + 5 = 11?
Answer
(C)
Subtract 5 from both sides
17
In the formula d = rt, what algebraic operation should be used to isolate 't' (time)?
Answer
(D)
Division
18
What are the key steps when factorizing x² - 9?
Answer
A
C
D
19
What does the term 'discriminant' refer to in a quadratic equation?
Answer
(C)
The expression under the square root in the quadratic formula.
20
Which are the key steps to follow when changing the subject of the formulas?
Answer
A
B
C
21
What is the goal when using the elimination method to solve simultaneous equations?
Answer
(B)
To eliminate one variable by adding or subtracting the equations
22
What method is used to solve simultaneous equations by eliminating one of the variables?
Answer
(A)
Substitution
23
Which of the following is the correct approach when solving a simple equation like 3x = 12?
Answer
(D)
Divide both sides by 3
24
What method is typically used to solve equations involving fractions?
Answer
(B)
Multiplying both sides by the least common denominator
25
In the context of solving quadratic equations, when does 'x² + bx + c = 0' have two solutions?
Answer
(C)
When the discriminant is positive.
26
Which of the following are correct procedures when solving equations involving brackets? (Select all that apply)
Answer
A
B
C
D
27
In the formula for the volume of a cylinder, V = πr²h, what does 'r' represent?
Answer
(B)
Radius
28
What is a typical first step in solving a system of equations using substitution?
Answer
(B)
Isolating a variable in one of the equations.
29
What is a common error when multiplying through by a number or letter to solve equations involving fractions?
Answer
(B)
Forgetting to multiply every term
30
When solving quadratic equations by factorization, what mathematical principle is primarily used?
Answer
(D)
Zero Product Property
31
If you are asked to 'Solve for x: 3x - 7 = 8', what is the value of x?
Answer
(C)
15/3
32
If the equation is x² - 16 = 0, what are the roots?
Answer
(C)
4 and -4
33
What does it mean if the discriminant (b² - 4ac) of a quadratic equation is equal to zero?
Answer
(B)
There is one real root (a repeated root).
34
Which methods could be used to solve x² - 5x + 6 = 0?
Answer
A
B
C
35
In the equation x² + 5x + 6 = 0, what are the values of a, b, and c?
Answer
(A)
a = 1, b = 5, c = 6
36
Which method would be used if asked to 'Solve the following system of equations: y = 2x + 1 and x + y = 5'?
Answer
(C)
Substitution
37
When using the quadratic formula, what does the term 'b' represent in the equation ax² + bx + c = 0?
Answer
(C)
The coefficient of x
38
If an equation is in the form ax² + bx + c = 0 and you solve it using the quadratic formula, which of the following represents the solution?
Answer
(A)
x = (-b ± √(b² - 4ac)) / 2a
39
What steps are necessary to solve for 'x' if you have a = x/b - c?
Answer
A
B
40
What is the key to solving simultaneous equations?
Answer
(B)
Having the same variables in each equation
41
Which methods are used to solve simultaneous equations?
Answer
A
B
C
42
Which of the following is the correct rearrangement of the equation a = x + b - c to make x the subject?
Answer
(B)
x = a - b + c
43
What must be done to the equation x² + 8x + 7 = 0 before completing the square?
Answer
A
C
44
How do you find the length of a rectangle given the area and width?
Answer
(C)
Length = Area / Width
45
How does completing the square help you solve a quadratic equation?
Answer
(B)
It makes one side of the equation a perfect square.
46
What should you do with the result when the two factors of a quadratic expression equal to zero?
Answer
(C)
Set each factor equal to zero.
47
In the equation 2x + 3 = 7, what operation should be performed first to isolate the term with 'x'?
Answer
(B)
Subtract 3 from both sides
48
When using completing the square, which steps lead to finding the new equation?
Answer
B
C
D
49
Which steps must be completed when solving a formula for a specific variable?
Answer
A
B
C
50
What is the next step after identifying the values of a, b, and c, and substituting them into the quadratic formula?
