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