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

1
What is the GCF (Greatest Common Factor) of the expression 4x² + 8x + 12?
คำตอบ
(B)
2
2
Expand (x - 1)(x + 1)
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(B)
x² - 1
3
Which expression is a perfect square trinomial?
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(A)
x² + 4x + 4
4
Expand (x + 7)(x - 7)
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(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?
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(A)
0
6
The algebraic expression for 'the product of a number z and 8' is...
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(C)
8z
7
What is the algebraic expression for 'the product of a and b'?
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(C)
ab
8
Which expression is a perfect square trinomial?
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(B)
x² - 6x + 9
9
How do you represent 'the sum of a number y and 7' algebraically?
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(C)
y + 7
10
What is the minimum value of the expression (x-3)² + 4?
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(C)
4
11
What is the product of 4 and x, written in algebraic form?
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(B)
4x
12
Expand -3(x - 2)
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(B)
-3x + 6
13
When expanding -3(a + 2), what is the resulting expression?
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(B)
-3a - 6
14
Which expression is the result of a difference of squares factorization?
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(B)
x² - 4
15
Expand 8(x - 3)
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(B)
8x - 24
16
What is the primary goal of algebraic manipulation?
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(B)
To simplify expressions and solve equations.
17
Simplify: 4p - 7q + 2p + 5q
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(A)
6p - 2q
18
Which factors create the expression x² + 12x + 36 when multiplied together?
คำตอบ
(D)
(x+6) and (x+6)
19
What must be considered before trying to factor a quadratic equation?
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(C)
Any common factors
20
Expand (x - 2)(x + 2)
คำตอบ
(B)
x² - 4
21
Expand -2(4x + 3)
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(A)
-8x - 6
22
Expand (x - 1)(x + 1)
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(B)
x² - 1
23
In the context of algebraic manipulation, what is 'difference of two squares'?
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(B)
An expression in the form a² - b².
24
What are the common factors of 6x² and 12x?
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A
B
C
D
25
Which expression is correctly factorized for 30c - 45d?
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(D)
All the above.
26
What does the term 'collecting like terms' mean?
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(B)
Combining terms with the same variable and power.
27
Simplify: 6a + 2b - 3a + 5b
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(C)
3a + 7b
28
What is the simplified form of 7x - (2x + 3)?
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(B)
5x - 3
29
What is the algebraic term for 'the difference between a number and 6'?
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(B)
x - 6
30
If a square has sides of length 's', what expression represents its perimeter?
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(B)
4s
31
In completing the square, what does adding and subtracting the same value do?
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(B)
Maintains the equality of the expression.
32
Which expression is equivalent to 24x + 36y?
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(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?
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(B)
Both negative
34
Factorize 28x + 42
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(B)
14(2x + 3)
35
What is the result of expanding -5(x + 4)?
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(A)
-5x - 20
36
What is the relationship between the factored form and the completed square form of a quadratic expression?
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(B)
The completed square form is a special case of factored form
37
What is the simplified form of 3a - a + 2b - b?
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(A)
2a + b
38
Which expression is equivalent to 14m - 21n when factorized?
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(A)
7(2m - 3n)
39
Simplify: 5a - 2b + 3a + b
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(A)
8a - b
40
When simplifying algebraic expressions, what are 'like terms'?
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(B)
Terms that have the same letter in the same combination of letters.
41
What is the factored form of 9x² - 30xy + 25y²?
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(B)
(3x - 5y)²
42
What are the factors of x² - 64?
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(C)
(x + 8)(x - 8)
43
Which expression represents a perfect square trinomial?
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(B)
x² - 2x + 1
44
What is the algebraic representation of 'y divided by 4'?
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(D)
y/4
45
Simplify: 11m - (3m + 2)
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(B)
8m - 2
46
What is the expanded form of (4x - 3)(2x + 1)?
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(B)
8x² - 2x - 3
47
What is a perfect square trinomial?
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(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?
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(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?
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(B)
x² - 4
50
How many terms are in a trinomial?
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(C)
Three