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Mathematics for IGCSE & O level - Equations (Section 2)

1
In factorization, what is the next step when you have an equation like x² - 9 = 0?
Answer
(B)
Factor by the method 'difference of two squares'.
2
In the formula for the area of a circle, A = πr², what does 'r' represent?
Answer
(B)
Radius
3
What value of x makes the following true: 2x + 1 = x - 3?
Answer
(B)
-4
4
What type of expression can be solved by completing the square?
Answer
(C)
Quadratic equations.
5
Given the equation C = d + KR. Solve for R.
Answer
(A)
R = (C - d)/K
6
What should you do when a quadratic equation has a negative 'c' value when attempting to factorize?
Answer
(B)
Find two numbers with different signs.
7
In the expression x² - 6x + 9, what is the result of factoring?
Answer
(B)
(x-3)(x-3)
8
In the equation y = mx + c, what does 'm' represent?
Answer
(B)
The slope
9
What's the significance of the sign of the 'b' term (coefficient of the x term) in the quadratic equation?
Answer
(B)
It affects the x-coordinate of the vertex.
10
What is the main goal when using substitution to solve simultaneous equations?
Answer
(C)
To eliminate one of the variables.
11
What's the first step when solving an equation using the quadratic formula?
Answer
(A)
Identify the values of a, b, and c.
12
Solve: 1/3x - 1 = 5
Answer
(C)
18
13
How is the value of the subject variable changed in the equation by doing addition or subtraction?
Answer
(B)
The value of the subject variable may change.
14
How many possible solutions are there for a quadratic equation?
Answer
(B)
Two
15
If 2x - 7 = 9, what is the value of x?
Answer
(C)
16
16
Identify the errors that commonly occur when solving equations with fractions:
Answer
A
B
C
17
When factorizing, what sign should the factors of 'c' have if 'c' is positive and 'b' is negative?
Answer
(B)
Both negative.
18
What happens to the roots of the equation if the discriminant is negative?
Answer
(C)
There are no real roots.
19
In the context of solving simultaneous equations, what does the term 'elimination' refer to?
Answer
(A)
Adding or subtracting the equations to remove a variable
20
Which are the common steps in the factorization method?
Answer
A
C
D
21
Which of the following methods are suitable for solving the equation: x² - 4 = 0?
Answer
(D)
All of the above.
22
Which of the following is a suitable example for using factorization?
Answer
(A)
x² + 2x + 1 = 0
23
If the sides of a triangle are a, b, and c. If a = 3, b = 4, and c = 5, what kind of triangle is it?
Answer
(C)
Right
24
If 4x + 8 = 20, what is the value of x?
Answer
(A)
3
25
Solve for x: 4(x - 2) = 16
Answer
(A)
2
26
What does 'c' represent in the standard quadratic equation ax² + bx + c = 0?
Answer
(C)
The constant term
27
Which technique is appropriate for solving equations of the form (x - a)(x + b) = 0?
Answer
(C)
Setting each factor equal to zero
28
What is the slope-intercept form of a linear equation?
Answer
(B)
y = mx + b
29
What is the solution to the equation: x/5 - 2 = 3?
Answer
(B)
25
30
What is the most reliable method for solving quadratic equations, especially when factorization is difficult or impossible?
Answer
(C)
The quadratic formula.
31
What is the method for solving the equation: (x-2)(x+3) = 0?
Answer
(C)
Setting each factor to zero.
32
If the length of a rectangle is 12 and the perimeter is 36, what is the width?
Answer
(A)
6
33
What step immediately follows isolating the variable when solving for the subject of a formula?
Answer
(C)
Using inverse operations to eliminate terms on the same side as the variable.
34
If the perimeter of a square is 20, what is the length of one side?
Answer
(B)
5
35
How should you handle the case when a quadratic equation's discriminant is zero?
Answer
(D)
Only one real solution, a repeated root.
36
Solve the equation: 2x - 4 = x + 1
Answer
(A)
5
37
What is the next step in solving 5x - 4 = 11?
Answer
(B)
Add 4 to both sides
38
What is the area of a rectangle if the length is 10 cm and the width is 5 cm?
Answer
(B)
50 sq cm
39
When solving for a variable, what operations are considered 'inverse' operations?
Answer
(B)
Subtraction and division
40
When solving a quadratic equation by factorization, what should you do if 'c' is negative and you have an equation like x² + bx + c = 0?
Answer
(B)
Find two numbers with different signs that multiply to give 'c' and add to give 'b'.
41
When solving for x in the equation 5x = 20, what is the correct step?
Answer
(B)
Divide both sides by 5
42
What is the main goal of solving simultaneous equations?
Answer
(C)
To find values for both variables that satisfy both equations.
43
Solve for x: x/2 + 5 = 9
Answer
(C)
8
44
What is the value of x in the equation 2x + 5 = 11?
Answer
(A)
3
45
What would be the result of the equation x² = 9 by using the method of "difference of two squares"?
Answer
(C)
x = 3 or -3
46
If a is 7 and b is 4, what is the value of (a+b) * a ?
Answer
(A)
77
47
What is the simplified form of the expression: 3(x + 2) - x?
Answer
(A)
2x + 6
48
What is the y-intercept of the linear equation y= -2x + 5?
Answer
(B)
5
49
What is the primary goal when solving a system of simultaneous equations?
Answer
(B)
To find the points of intersection.
50
If 3x - 5 = 4, what is x?
Answer
(B)
1