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