Mathematics for IGCSE & O level - Algebraic Manipulation (Section 4)
1
A rectangle has a length of '3x' and a width of '2y'. What expression represents its area?
Answer
(B)
6xy
2
What should you do first when presented with a factoring problem?
Answer
(B)
Identify and factor out any common factors
3
What is the result of expanding -7(2x + 1)?
Answer
(B)
-14x - 7
4
What is the result of expanding (3x + 2)(x - 5)?
Answer
(A)
3x² - 13x - 10
5
When factoring a quadratic expression of the form x² + bx + c, and if 'c' is negative, what do you know about the signs of the two numbers you are looking for?
Answer
(C)
The numbers have different signs
6
In the expression x² - 7x + 10, what two numbers add to -7 and multiply to 10?
Answer
(A)
-5 and -2
7
How many terms are in a trinomial?
Answer
(C)
Three
8
What is the result of expanding (3x - 1)(2x + 5)?
Answer
(A)
6x² + 13x - 5
9
What is a key characteristic of a perfect square trinomial?
Answer
(B)
It can be factored into two identical binomials.
10
To complete the square of x² + 8x + ___, what value goes in the blank?
Answer
(C)
16
11
A rectangle has length 'p' and width 'q'. What is the area?
Answer
(A)
pq
12
What are the factors of x² + 7x + 12?
Answer
(B)
(x + 3)(x + 4)
13
For the expression x² + 4x - 21, after identifying factors, what will be the signs of the numbers?
Answer
(C)
One is positive and one is negative
14
What is a² - 4 factorized?
Answer
(C)
(a - 2)(a + 2)
15
Which expression is equivalent to factorizing 16a - 24b?
Answer
(D)
All of the above.
16
What is the result of expanding and simplifying (x + 2)(x - 3)?
Answer
(A)
x² - x - 6
17
Which expression is an example of the difference of two squares?
Answer
(B)
x² - 9
18
Simplify: -3x + 5y + 2x - y
Answer
(A)
-x + 4y
19
What is the first step in factoring the expression 2x² + 4x - 6?
Answer
(B)
Factor out the common factor
20
Which are the numbers whose product is 12 and sum is 7?
Answer
(B)
3 and 4
21
What is the result of expanding (2x + 3)(x - 1)?
Answer
(A)
2x² + x - 3
22
What are the matching brackets that equal x²+4x+4?
Answer
(D)
(x+2) and (x+2)
23
Which strategy is best to employ when the coefficient of the x² term is not 1?
Answer
A
B
C
24
What is the factored form of x² - 100?
Answer
(C)
(x + 10)(x - 10)
25
A rectangle has a width of 'm' and a length of '3m'. What is its area?
Answer
(A)
3m²
26
Simplify 9y - (4y + 2)
Answer
(A)
5y - 2
27
What is the result of expanding (x + 2)(5x - 3)?
Answer
(A)
5x² + 7x - 6
28
Simplify: 5a + 3b - 2a + b
Answer
(B)
3a + 4b
29
For expressions in the form ax² + bx + c, when is the middle term negative?
Answer
(C)
When one factor of c is positive and one is negative and the larger magnitude factor is negative
30
What is the simplified form of 4p - 2p + 3q - q?
Answer
(B)
2p + 2q
31
What are the factors of x² - 1?
Answer
(C)
(x-1)(x+1)
32
Consider the expression 2x² + 4x - 6. What is the first step to factor this expression?
Answer
(A)
Factor out the common factor of 2.
33
When factoring a quadratic expression, how do you confirm your factored form is correct?
Answer
(A)
Multiply the factors to see if you get the original expression.
34
The expression x² + 8x + 16 can be expressed as the product of two brackets, one of which is (x+4). What is the other bracket?
Answer
(A)
(x + 4)
35
In the expression 3x² - 6x - 9, what is the common factor?
Answer
(B)
3
36
Simplify: 12a - (4a + 3)
Answer
(A)
8a - 3
37
What is the factored form of x² - 8x + 15?
Answer
(C)
(x - 5)(x - 3)
38
What is the correct way to expand a bracket with a negative number?
Answer
(B)
-2(x + 3) = -2x - 6
39
Which expressions can be simplified by completing the square?
Answer
A
B
C
40
Which expression, when factored, would result in (x - 5)(x + 2)?
Answer
(B)
x² - 3x - 10
41
What is the factored form of x² - 14x + 49?
Answer
(B)
(x - 7)²
42
What is the algebraic representation of 'a number w decreased by 9'?
Answer
(B)
w - 9
43
Expand 2(3x + 5)
Answer
(B)
6x + 10
44
Factorize 9x + 18
Answer
(A)
9(x + 2)
45
In the process of factoring, what does it mean to 'complete the square'?
Answer
(B)
To add or subtract a constant to create a perfect square trinomial
46
What are the factors of x² - 36?
Answer
(C)
(x + 6)(x - 6)
47
Simplify: 20b - (7b - 6)
Answer
(A)
13b + 6
48
Which of the following is a correctly factored expression for 3x + 6y?
Answer
(A)
3(x + 2y)
49
Which of the following is the correct algebraic representation for 'three times a number x'?
