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