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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 2)

1
What is the GCF (Greatest Common Factor) of the expression 4x² + 8x + 12?
Answer
(B)
2
2
Expand (x - 1)(x + 1)
Answer
(B)
x² - 1
3
Which expression is a perfect square trinomial?
Answer
(A)
x² + 4x + 4
4
Expand (x + 7)(x - 7)
Answer
(B)
x² - 49
5
For the expression x² - 8x + 16, what is the value of the constant term when the expression is written in the completed square form (x - a)² + b?
Answer
(A)
0
6
The algebraic expression for 'the product of a number z and 8' is...
Answer
(C)
8z
7
What is the algebraic expression for 'the product of a and b'?
Answer
(C)
ab
8
Which expression is a perfect square trinomial?
Answer
(B)
x² - 6x + 9
9
How do you represent 'the sum of a number y and 7' algebraically?
Answer
(C)
y + 7
10
What is the minimum value of the expression (x-3)² + 4?
Answer
(C)
4
11
What is the product of 4 and x, written in algebraic form?
Answer
(B)
4x
12
Expand -3(x - 2)
Answer
(B)
-3x + 6
13
When expanding -3(a + 2), what is the resulting expression?
Answer
(B)
-3a - 6
14
Which expression is the result of a difference of squares factorization?
Answer
(B)
x² - 4
15
Expand 8(x - 3)
Answer
(B)
8x - 24
16
What is the primary goal of algebraic manipulation?
Answer
(B)
To simplify expressions and solve equations.
17
Simplify: 4p - 7q + 2p + 5q
Answer
(A)
6p - 2q
18
Which factors create the expression x² + 12x + 36 when multiplied together?
Answer
(D)
(x+6) and (x+6)
19
What must be considered before trying to factor a quadratic equation?
Answer
(C)
Any common factors
20
Expand (x - 2)(x + 2)
Answer
(B)
x² - 4
21
Expand -2(4x + 3)
Answer
(A)
-8x - 6
22
Expand (x - 1)(x + 1)
Answer
(B)
x² - 1
23
In the context of algebraic manipulation, what is 'difference of two squares'?
Answer
(B)
An expression in the form a² - b².
24
What are the common factors of 6x² and 12x?
Answer
A
B
C
D
25
Which expression is correctly factorized for 30c - 45d?
Answer
(D)
All the above.
26
What does the term 'collecting like terms' mean?
Answer
(B)
Combining terms with the same variable and power.
27
Simplify: 6a + 2b - 3a + 5b
Answer
(C)
3a + 7b
28
What is the simplified form of 7x - (2x + 3)?
Answer
(B)
5x - 3
29
What is the algebraic term for 'the difference between a number and 6'?
Answer
(B)
x - 6
30
If a square has sides of length 's', what expression represents its perimeter?
Answer
(B)
4s
31
In completing the square, what does adding and subtracting the same value do?
Answer
(B)
Maintains the equality of the expression.
32
Which expression is equivalent to 24x + 36y?
Answer
(D)
All of the above
33
If an expression is in the form x² + bx + c, and if 'b' is negative and 'c' is positive, what are the signs of the factors?
Answer
(B)
Both negative
34
Factorize 28x + 42
Answer
(B)
14(2x + 3)
35
What is the result of expanding -5(x + 4)?
Answer
(A)
-5x - 20
36
What is the relationship between the factored form and the completed square form of a quadratic expression?
Answer
(B)
The completed square form is a special case of factored form
37
What is the simplified form of 3a - a + 2b - b?
Answer
(A)
2a + b
38
Which expression is equivalent to 14m - 21n when factorized?
Answer
(A)
7(2m - 3n)
39
Simplify: 5a - 2b + 3a + b
Answer
(A)
8a - b
40
When simplifying algebraic expressions, what are 'like terms'?
Answer
(B)
Terms that have the same letter in the same combination of letters.
41
What is the factored form of 9x² - 30xy + 25y²?
Answer
(B)
(3x - 5y)²
42
What are the factors of x² - 64?
Answer
(C)
(x + 8)(x - 8)
43
Which expression represents a perfect square trinomial?
Answer
(B)
x² - 2x + 1
44
What is the algebraic representation of 'y divided by 4'?
Answer
(D)
y/4
45
Simplify: 11m - (3m + 2)
Answer
(B)
8m - 2
46
What is the expanded form of (4x - 3)(2x + 1)?
Answer
(B)
8x² - 2x - 3
47
What is a perfect square trinomial?
Answer
(B)
A trinomial that results from squaring a binomial.
48
What is the correct strategy to factor an expression like ax² + bx + c when 'a' is not equal to 1?
Answer
(C)
Use trial and error or factoring by grouping.
49
Which of the following expressions can be factored using the difference of two squares method?
Answer
(B)
x² - 4
50
How many terms are in a trinomial?
Answer
(C)
Three