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