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