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