Mathematics for IGCSE & O level - Equations (Section 8)
1
What does the 'b² - 4ac' part of the quadratic formula represent?
Answer
(B)
The discriminant
2
When solving a system of equations by substitution, what can happen after substituting?
Answer
A
B
C
3
What is the relationship between the roots and the factors of a quadratic expression?
Answer
(C)
The roots are the solutions when each factor equals zero.
4
What are you doing when you are solving a quadratic equation?
Answer
(B)
Finding the x-intercepts of the parabola.
5
In the formula F = (9/5)C + 32, if C = 20, what is the value of F?
Answer
(A)
68
6
Which of the following is a valid method for finding the roots of a quadratic equation?
Answer
(B)
Using the quadratic formula.
7
Which method(s) are used to solve linear equations?
Answer
A
B
8
What form does the quadratic equation take after completing the square?
Answer
(A)
a(x + p)² + q = 0
9
What do you do to solve a simple linear equation like x + 5 = 10?
Answer
(B)
Subtract 5 from both sides
10
What are the steps to solving a linear simultaneous equation by elimination?
Answer
A
B
C
D
11
When solving simultaneous equations graphically, what does the point of intersection of the lines represent?
Answer
(A)
The solution to the equations
12
When solving a system of equations by elimination, what is the goal?
Answer
(B)
To eliminate one of the variables.
13
If a quadratic equation in standard form has a negative discriminant, how many real solutions does it have?
Answer
(A)
Zero
14
Which are necessary steps for factorizing a quadratic equation of the form x² + bx + c = 0?
Answer
A
B
C
15
What is the formula for the area of a rectangle?
Answer
(B)
A = lw
16
If you're solving the system of equations: y = 3x - 2 and 2x + y = 8, which method would be most suitable?
Answer
(C)
Substitution
17
In the context of solving simultaneous equations, what does it mean to 'eliminate' a variable?
Answer
(A)
To make the coefficient of a variable zero
18
In the equation y = mx + c, what does 'm' represent?
Answer
(B)
The slope
19
Which of the following is a key step in solving a system of equations using the elimination method?
Answer
(A)
Multiplying one or both equations by a constant to make the coefficients of one variable opposites.
20
What are the key steps when completing the square to solve a quadratic equation?
Answer
A
B
C
21
When solving equations involving brackets, what is generally done first?
Answer
(C)
Expand the bracket
22
What is the correct factorization of x² - 25?
Answer
(C)
(x+5)(x-5)
23
In the equation x² - 6x + 9 = 0, after completing the square, what does it become?
Answer
(A)
(x - 3)² = 0
24
If the area of a circle is 28.26 cm², and you know the formula is A = πr², what are the first steps to rearrange to find the radius?
Answer
(B)
Divide by π, then square root.
25
What is a characteristic of the solutions for equations solved by factoring?
Answer
A
C
26
What type of method is used to solve quadratic equations of the form ax² + bx + c = 0, where a ≠ 0?
Answer
(D)
All of the above
27
What must be done to both sides of an equation when changing the subject of a formula?
Answer
(A)
The same operation must be done.
28
When we have the equation, 3x + 5 = 2x + 10, to find 'x', what is the first step to do?
Answer
C
D
29
When completing the square on an equation, what should the coefficient of the x² term be?
Answer
(B)
1
30
Which of these formulas are used to change the subject?
Answer
A
B
C
D
31
To change the subject of a formula like V = πr²h to r, what are the key steps?
Answer
A
B
32
If you need to solve a quadratic equation, which of these method(s) would you use?
Answer
A
B
C
33
In order to solve for 'x' in the equation y = mx + c, what step should be taken first?
Answer
(B)
Subtract 'c' from both sides
34
What is the purpose of completing the square?
Answer
(C)
To rewrite a quadratic expression in a different form.
35
What are the factors of the quadratic expression x² + 7x + 12?
Answer
(A)
(x + 3)(x + 4)
36
If a quadratic equation has a discriminant equal to zero, what does this mean about its roots?
Answer
(C)
One real root (repeated)
37
In the formula for the circumference of a circle, C = 2πr, what does 'C' represent?
Answer
(D)
Circumference
38
In the equation x² - 8x + 12 = 0, what are the factors of the quadratic expression?
Answer
(A)
(x - 6)(x - 2)
39
When rearranging formulas, which methods are useful to apply for a successful result?
Answer
A
B
C
D
40
What is the solution to the equation (x - 3)(x + 2) = 0?
Answer
(C)
x = 3, x = -2
41
The formula for the curved surface area of a cylinder is S = 2πrh. Rearrange this formula to solve for r.
Answer
(A)
r = S / 2πh
42
If we want to make 'h' the subject of the formula V = (1/3)πr²h, what operation should be performed first?
Answer
(A)
Multiply both sides by 3
43
If you have an equation in the form ax² + bx + c = 0, which part of the equation determines whether you'll have two solutions, one solution, or no real solutions?
