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