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