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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 1)

1
If an expression has a negative 'c' value in the quadratic equation ax² + bx + c, what does that indicate about the signs of the factors?
Answer
(C)
The factors have different signs.
2
Given the expression x²-6x+9, one of the brackets is (x-3). What is the other?
Answer
(B)
(x-3)
3
What is the factored form of x² - 10x + 25?
Answer
(B)
(x - 5)²
4
What is the purpose of simplifying an algebraic expression?
Answer
(B)
To rewrite it in a more concise form.
5
Which of the following is a correct factorization for 42a - 63b?
Answer
(D)
All of the above
6
If expanding a pair of brackets gives x² - 4x + 4, which of the following could be one of the pair of brackets?
Answer
(D)
(x-2) and (x-2)
7
If an expression can be written in the form of a² - b², which method can be applied?
Answer
(B)
The difference of squares
8
Expand 6(2x - 1)
Answer
(C)
12x - 6
9
The expression x² - 9 can be factored using which method?
Answer
(B)
The difference of two squares
10
What are the factors of y² - 49?
Answer
(C)
(y + 7)(y - 7)
11
Simplify: 5k + 3k - 2l + 7l
Answer
(A)
8k + 5l
12
Factorize 35x + 49
Answer
(A)
7(5x + 7)
13
Simplify m + m + m + n + n
Answer
(A)
3m + 2n
14
Which operation is used to simplify an algebraic expression?
Answer
(C)
Addition, subtraction, multiplication, and division
15
Expand (x + 5)(x - 5)
Answer
(B)
x² - 25
16
What is (x + 3)(x - 3) expanded?
Answer
(B)
x² - 9
17
Which operation is performed first when simplifying an expression with multiple operations and parentheses?
Answer
(C)
Parentheses
18
Which is the result of 8x - (3x - 5)?
Answer
(B)
5x + 5
19
Expand 3(x - 4)
Answer
(C)
3x - 12
20
Which expression correctly factorizes 36p - 54q?
Answer
(D)
All of the above.
21
How do you find the value to add inside the parenthesis to complete the square in x² + bx + c?
Answer
(B)
Divide b by 2 and square the result.
22
Expand 4(x + 2)
Answer
(B)
4x + 8
23
If 'c' is negative in a quadratic expression, what can you say about the signs of the numbers you seek to factor the expression?
Answer
(D)
They will have opposite signs.
24
In the context of algebraic manipulation, which of the following statements is correct?
Answer
(D)
Algebraic terms can be multiplied together, and the multiplication sign can be omitted, depending on the context.
25
If an expression can be factored by completing the square, what is the resulting form?
Answer
(B)
A perfect square trinomial
26
When simplifying an expression like 3x + 2x - x, what is the result?
Answer
(A)
4x
27
When factorizing an expression, what is a common factor?
Answer
(B)
A number or letter that divides an expression.
28
Expand 5(3x - 2)
Answer
(B)
15x - 10
29
Simplify 10x - (5x + 7)
Answer
(A)
5x - 7
30
Which of the following represents a correct factorization for 24a - 36b?
Answer
(D)
All of the above
31
Which of the following is a correct example of expanding a single bracket?
Answer
(B)
3(x + 2) = 3x + 6
32
If you have the expression 4x² + 12x + 9, what is its factored form?
Answer
(A)
(2x + 3)(2x + 3)
33
What is the first step when simplifying an algebraic expression?
Answer
(B)
Collect like terms.
34
What are the factors of x² - 81?
Answer
(C)
(x + 9)(x - 9)
35
Which expression is equivalent to factorizing 4x + 8?
Answer
(B)
4(x + 2)
36
What is the result of expanding -4(x - 1)?
Answer
(B)
-4x + 4
37
What is the factored form of the expression x² - 49?
Answer
(C)
(x - 7)(x + 7)
38
If the sides of a square are 'x', then which expression represents its area?
Answer
(B)
x²
39
Simplify: 9m + 4n - 5m - 2n
Answer
(A)
4m + 2n
40
What are the two numbers that multiply to -12 and add to +1?
Answer
(C)
3 and -4
41
Simplify: 7x - 3y + 2x + 4y
Answer
(A)
9x + y
42
Which expression is correctly simplified form for x + x + x?
Answer
(B)
3x
43
Simplify: 14y - (6y + 5)
Answer
(A)
8y - 5
44
Which of the following are methods for simplifying brackets?
Answer
A
B
C
45
Which of the following techniques are frequently used when factoring a quadratic equation?
Answer
A
B
C
D
46
What is the factored form of the quadratic expression x² - 10x + 24?
Answer
(A)
(x-6)(x-4)
47
What is the factored form of 4x² - 25?
Answer
(B)
(2x + 5)(2x - 5)
48
What is the result of expanding (x - 7)(2x + 1)?
Answer
(A)
2x² - 13x - 7
49
Factorize 60x + 75
Answer
(B)
15(4x + 5)
50
When factoring a quadratic expression ax² + bx + c, what are you looking for when 'c' is positive?
Answer
A
B
C