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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 6)

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