Mathematics for IGCSE & O level - Algebraic Manipulation (Section 6)
1
What is the correct factorization of 7x + 14?
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(B)
7(x + 2)
2
If the sales tax is 8% on a $50 item, what is the total cost?
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(B)
$58
3
Simplify 6x - 4y + 2x + 9y
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(A)
8x + 5y
4
What does it mean to expand an expression?
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(B)
To remove parentheses by multiplying.
5
What is the greatest common factor (GCF) of 24 and 36?
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(D)
12
6
If x= -2, what is the value of x^2 - 3x?
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(C)
10
7
What expression represents the area of a triangle?
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(C)
1/2 * base * height
8
What is the simplified form of (2x + 1) + (3x - 2)?
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(A)
5x - 1
9
What is the result of (x + 2)(x - 2)?
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(B)
x^2 - 4
10
Which of these is the expanded form of (x + 2)(x + 1) ?
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(A)
x^2 + 3x + 2
11
Which of these expressions are equivalent?
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A
C
D
12
What is the coefficient of x in the expression 5x - 3?
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(D)
5
13
When factorizing x² + bx + c and 'c' is positive, what is the rule for the signs of the factors?
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(D)
Both factors have the same sign as the coefficient of 'b'.
14
If x = -3, what is the value of x + 5?
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(B)
2
15
What is the simplified expression for: 5(2x + 3) + 2x?
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(B)
12x + 15
16
If a square has a perimeter of 20, what is its area?
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(C)
25
17
If a pentagon has five sides, and each side has length 3, what is its perimeter?
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(C)
15
18
Solve for x: 4x + 7 = 27
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(A)
5
19
If a = 2 and b = 3, what is the value of 2a + b?
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(B)
7
20
In the expression ax² + bx + c, if the coefficient of 'a' is not 1, what is the first step to factorize?
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(B)
Find two numbers that multiply to ac and add to b.
21
What is the result of completing the square for x² - 4x + 5?
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(A)
(x - 2)² + 1
22
Which of the following is an example of like terms?
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(C)
5x and -x
23
Which expression represents the total cost if apples cost $1.50 each and you buy 'n' apples?
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(B)
1.50n
24
If the coefficient of x in the middle term of a quadratic expression is negative, what does that indicate about the resulting factors when completing the square?
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(B)
The sign in the bracket will be negative.
25
What is the expansion of 4(2x - 1)?
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(A)
8x - 4
26
What is the expanded form of (x+y)(x-y)?
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(B)
x^2 - y^2
27
If x + y = 7 and x - y = 3, what is the value of x?
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(C)
5
28
When completing the square, what must be added and subtracted to an expression of the form x² + bx?
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(C)
(b/2)² and -(b/2)²
29
If the perimeter of a rectangle is 2l + 2w, and the length is 7 and the width is 3, what is the perimeter?
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(C)
20
30
If a car travels at 60 miles per hour, how far will it travel in 'h' hours?
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(A)
60h miles
31
Which of the following expressions are correctly expanded?
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A
B
D
32
Which is the expanded form of (2x + 1)(x - 2)?
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(A)
2x^2 - 3x - 2
33
What is the simplified form of 4(x - 1) + 2x?
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(A)
6x - 4
34
What is the value of 2(x + 1) when x = 4?
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(C)
10
35
What is the result of (x + 2)(x + 3)?
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(A)
x^2 + 5x + 6
36
Which methods can be applied in order to factorize the quadratic expressions?
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A
B
C
D
37
Simplify: 7x - 3y + 2x + 5y.
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(A)
9x + 2y
38
What is the product of (2x + 1) and (x - 3)?
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(A)
2x^2 - 5x - 3
39
Which of the following is the correct factorization of 3x + 9?
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(A)
3(x + 3)
40
Which of the following simplifies to the expression 3x + 9?
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(A)
3(x + 3)
41
If a square has a side length of 'a', what expression represents its perimeter?
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(B)
4a
42
What is the expanded form of (x-1)(x+3)?
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(A)
x^2 + 2x - 3
43
Expand and simplify: (x+1)(x-5)
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(A)
x^2 - 4x - 5
44
When factorizing x² + bx + c and 'c' is negative, what is the rule for the signs of the factors?
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(C)
The factors must have different signs.
45
When factorizing 3x² - 6x - 9, which is the correct step to start with?
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(B)
Look for the common factor.
46
Expand (x+4)(x+1)
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(A)
x^2 + 5x + 4
47
Which expression is equivalent to x/4 = 7?
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(C)
x = 28
48
What's the area of a rectangle with a length of 9 and a width of 4?
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(C)
36
49
What expression is equivalent to 3(x + 2)?
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(C)
3x + 6
50
What is the simplified expression of 2x + 3y - x + y?
