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