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Mathematics for IGCSE & O level - Equations (Section 4)

1
If 2x + 5 = 15, what is the value of x?
Answer
(A)
5
2
What does a positive discriminant imply regarding the roots of a quadratic equation?
Answer
(A)
Two real and distinct roots.
3
What type of equations can be solved using factorization?
Answer
(B)
Quadratic equations that can be expressed as a product of linear factors.
4
If two quantities A and B are equal, and two other quantities C and D are equal, then what is the consequence?
Answer
(D)
All of the above
5
How can you solve 2x + 3y = 7 and x - y = 1 using substitution?
Answer
A
B
6
If the product of two binomials results in x² - 9, what is the result of the binomials?
Answer
(C)
(x + 3)(x - 3)
7
Which of the following must you find to use the quadratic formula?
Answer
A
D
8
When solving a quadratic equation by completing the square, what do you aim to create?
Answer
(A)
A perfect square trinomial.
9
When working with the equation x² + 4x - 5 = 0, what would the next step be after correctly identifying the values of a, b, and c, is to:
Answer
(B)
Substitute the values into the quadratic formula.
10
What is the first step when using factorization to solve a quadratic equation like x² + 5x + 6 = 0?
Answer
(B)
Identify two numbers that add up to 5 and multiply to 6.
11
If the perimeter of a rectangle is given by 2l + 2w, and l=6, w=3, what is the perimeter?
Answer
(A)
9
12
How can you describe a quadratic equation that cannot be solved by factorization?
Answer
(D)
All of the above.
13
If a = 4 and b = -2, what is the value of a^2 + b?
Answer
(B)
12
14
Which is the appropriate situation to use the quadratic formula?
Answer
(B)
When it is not possible to factor a quadratic.
15
What is one of the advantages of using factorization over completing the square?
Answer
(B)
It avoids fractions and square roots.
16
What is the first step when changing the subject of a formula?
Answer
(C)
Simplify and collect terms.
17
What are the key elements needed when using the quadratic formula to solve an equation?
Answer
A
B
18
Solve for x: -2x + 5 = 15
Answer
(A)
-5
19
In a triangle, the angles are x, 2x, and x + 20. What is the value of x?
Answer
(D)
35
20
In a problem involving the area of a rectangle, which formula is frequently employed?
Answer
(C)
A = l * w
21
Which of the following statements is TRUE about solving simultaneous equations graphically?
Answer
(A)
The solution is the point where the lines intersect.
22
Write an equation for the statement: The cost (C) of renting a car is a fixed charge (K) plus the number of days (d) multiplied by the daily rate (R).
Answer
(A)
C = K + dR
23
If you are given the equation 3x - 2y = 6 and y = x - 5, what is the most efficient way to solve this system?
Answer
(C)
Using the substitution method.
24
What does 'completing the square' method involve to solve a quadratic equation?
Answer
(A)
Add and subtract the square of half the coefficient of x.
25
If a car travels at 60 miles per hour, how far will it travel in 3 hours?
Answer
(C)
180 miles
26
Which elements are necessary to compute the solutions to a quadratic equation using the quadratic formula?
Answer
B
D
27
What does 'a' represent in the standard quadratic equation ax² + bx + c = 0 ?
Answer
(C)
The coefficient of the x² term
28
In the quadratic formula, what is the purpose of the square root?
Answer
(C)
To find the x-intercept.
29
Which of the following statements is correct about the roots of a quadratic equation?
Answer
A
B
30
What is the value of x in the equation x/3 - 1 = 4?
Answer
(B)
15
31
Solve the equation: 5x - 2 = 13
Answer
(B)
1
32
Solve for x: 2x + y = 7 and 3x - y = 3
Answer
(A)
x = 2, y = 3
33
What is the value of x in the equation x/4 + 2 = 8?
Answer
(A)
24
34
What are the solutions to a quadratic equation also known as?
Answer
(C)
The roots or zeros
35
What does the discriminant of a quadratic equation help determine?
Answer
(C)
The number and nature of the roots (real or complex).
36
Write an expression for the total of these lengths, in centimeters: x+6, x, x-1.
Answer
(A)
3x+5
37
If one angle of a triangle is 90 degrees, what type of triangle is it?
Answer
(D)
Right
38
What should be used to find the roots of an equation?
Answer
(B)
Factor the equation and set each factor equal to zero.
39
If A=πr^2, and the radius (r) is 3, what is the area?
Answer
(B)
9π
40
If the area of a square is 25, what is the length of one side?
Answer
(B)
5
41
What is another term for the solutions to a quadratic equation?
Answer
(C)
Roots
42
If 3x - 8 = 10, what is the value of x?
Answer
(A)
6
43
If x=30 and y=10, what is the value of x - y?
Answer
(C)
20
44
If the base of a triangle is 8 cm and the height is 6 cm, what is its area?
Answer
(B)
24 cm^2
45
What is the first step in solving 2(x + 3) - 5 = 7?
Answer
(C)
Distribute the 2
46
Which operation is the inverse of squaring?
Answer
(D)
Taking the square root
47
What is the general form of a quadratic equation?
Answer
(B)
ax² + bx + c = 0
48
What is the main goal of solving quadratic equations?
Answer
(C)
To find the x-intercepts (roots or zeros) of the corresponding parabola.
49
Which of the following are necessary steps to change the subject of a formula?
Answer
A
B
C
50
Which of the following expressions is equivalent to 4(x + 2)?
Answer
(B)
4x + 8