Mathematics for IGCSE & O level - Equations (Section 3)
1
In the context of completing the square, what is the purpose of adding a number to the left-hand side of the equation?
Answer
(B)
To make the left-hand side a complete square.
2
In the context of the quadratic formula, why is the ± symbol important?
Answer
(C)
It gives you two separate solutions for the equation.
3
What should be done after factoring a quadratic equation such as x² - 5x + 6 = 0?
Answer
(C)
Set each factor equal to zero and solve for x.
4
If 2(x + 4) = 18, what is the value of x?
Answer
(B)
5
5
Which of the following is equivalent to the formula, C=K+dR?
Answer
A
C
6
If the perimeter of a square is 28, what is the length of one side?
Answer
(A)
7
7
In the equation 2/3x + 4 = 10, what should be the first step to solve for x?
Answer
(B)
Subtract 4 from both sides
8
Solve for y: 2y + 3 = y + 7.
Answer
(B)
4
9
Which of the following methods are often used to solve quadratic equations?
Answer
A
B
C
10
What is the role of the 'c' term in the standard form of a quadratic equation, ax² + bx + c = 0?
Answer
(C)
It defines the y-intercept of the parabola.
11
If a=100 and b = 10, what is the value of a/b?
Answer
(B)
10
12
The formula for the area of a square is side * side. If the side is 7, what is the area?
Answer
(C)
49
13
Which step is typically performed after factoring a quadratic expression?
Answer
(A)
Set each factor to zero.
14
If a quadratic equation can be readily factored, what is the easiest method to solve it?
Answer
(C)
Factorization
15
If y - 7 = 20, what is the value of y?
Answer
(A)
27
16
What type of equations can often be solved using the difference of squares method?
Answer
(A)
Equations with a perfect square minus another perfect square.
17
When is the substitution method most effective for solving a system of equations?
Answer
(B)
When one equation is easily solved for one variable.
18
Solve: 2(x - 1) + 3 = 9
Answer
(A)
4
19
How do you find the x-intercept of a linear equation in the form of y=mx+c?
Answer
(A)
Set y = 0 and solve for x
20
What should be the next step after expanding the brackets in an equation such as 3(x + 2) = 15?
Answer
(D)
Subtract 6 from both sides
21
Which part of the quadratic formula is the discriminant?
Answer
(B)
b² - 4ac
22
What does a negative value for the discriminant indicate in a quadratic equation?
Answer
B
D
23
In the context of solving a quadratic equation, what information does the discriminant provide?
Answer
(B)
The number and type of solutions.
24
In the formula T = 7a + 3c, which variable represents the total cost of entry to the cinema?
Answer
(C)
T
25
When solving a system of equations graphically, what does the solution represent?
Answer
B
D
26
Solve for x: x/5 + 2 = 7
Answer
(B)
10
27
In a system of equations, if the coefficients of a variable are the same but with opposite signs, what is the most efficient method to eliminate that variable?
Answer
(C)
Add the equations.
28
What does setting a quadratic equation equal to zero enable you to do?
Answer
(C)
Find the roots/x-intercepts.
29
Solve the equation: 4x - 7 = 9.
Answer
(A)
4
30
To find the value of x in the equation, what is the correct operation to be used x/5 = 30?
Answer
(D)
Multiply 5
31
When can the quadratic formula be applied?
Answer
(B)
To any quadratic equation.
32
When changing the subject of a formula, how are inverse operations applied?
Answer
(A)
The opposite operations are applied to both sides.
33
What is the solution to the equation: 4x + 5 = 2x + 11?
Answer
(A)
3
34
In the process of completing the square, after calculating (b/2)², what is the next step?
Answer
A
D
35
What is the y-intercept of the line y = 3x + 2?
Answer
(B)
2
36
What type of operations are used to rearrange a formula to change the subject?
Answer
(B)
Inverse operations.
37
What does a positive value of 'a' indicate in the general quadratic equation (ax² + bx + c = 0) ?
Answer
(A)
The parabola opens upwards.
38
In the context of changing the subject of a formula, which steps are involved?
Answer
A
B
C
39
In the formula P = 2l + 2w, what does 'P' represent?
Answer
(B)
Perimeter
40
The first angle of a triangle is x, and the second is twice the first. The third angle is 30 degrees. Write an equation to find x (the sum of angles in a triangle is 180 degrees).
Answer
(A)
x + 2x + 30 = 180
41
Which of the following is equivalent to the formula, A = 1/2 * b * h?
Answer
(A)
h=2A/b
42
Which of the following represents the formula for the area of a triangle?
Answer
(B)
A = 1/2bh
43
What does it mean to "make the letter the subject" of a formula?
Answer
(B)
To isolate that letter on one side of the equation.
44
Which technique would most easily solve an equation such as x² - 100 = 0?
Answer
(C)
Factorization of the difference of squares
45
In the quadratic formula, what is the role of the '±' symbol?
Answer
(B)
To find the solutions, there are two, possibly different, solutions.
46
In the quadratic equation ax² + bx + c = 0, what does the sign of 'a' determine?
Answer
(B)
Whether the parabola opens upwards or downwards.
47
What is the role of the 'a' in the standard quadratic equation?
Answer
(C)
Coefficient of the x² term.
48
Solve: 20x - 3(x - 4) = 30 - x
Answer
(A)
3/2
49
Which of the following represents a correct application of the distributive property in the context of solving an equation?
