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