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