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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 5)

1
When factoring x² + 4x + 4, what is the factored form?
Answer
(A)
(x + 2)(x + 2)
2
When using the difference of squares method, how many terms must the expression have?
Answer
(B)
Two
3
What is the next step after factoring out the common factor of 3 from 3x² - 12?
Answer
(B)
Apply the difference of squares to the remaining terms
4
Given that x²-18x+81 is the product of the brackets. What bracket multiplied by itself gives this expression?
Answer
(B)
(x-9)
5
What is the simplified form of a + a + a + a?
Answer
(B)
4a
6
What is the result when you factor the GCF from an expression like 5x² + 10x + 15?
Answer
(C)
5(x² + 2x + 3)
7
What is the area of a rectangle with width '2x' and length 'x+3'?
Answer
(B)
2x² + 6x
8
What is the first step when factoring the expression 3x² - 12?
Answer
(C)
Factor out the common factor
9
When completing the square for the expression x² - 4x + 5, the number to add and subtract inside the parentheses is:
Answer
(C)
4
10
Which of the following is NOT a method used in algebraic manipulation?
Answer
(D)
Solving for inequalities
11
Which of these expression is a perfect square trinomial?
Answer
(A)
x² + 2x + 1
12
For the expression x² + bx + c, if 'c' is negative, which is true about the factors?
Answer
(C)
One factor is positive and one is negative.
13
In a quadratic equation of the form ax² + bx + c = 0, what does the 'c' term represent?
Answer
(C)
The constant term
14
When the coefficient of a is not 1, which methods are best for factoring ax² + bx + c?
Answer
A
B
C
15
What is the common factor to pull out of 3x² - 9x + 6?
Answer
(B)
3
16
What is the simplified form of 2z + 3z - w + 4w?
Answer
(B)
5z + 3w
17
For the expression x² + 8x + 16, what is the factored form?
Answer
(B)
(x + 4)(x + 4)
18
Expand (x + 4)(x - 4)
Answer
(B)
x² - 16
19
When factoring 5x² - 15x - 20, what is the common factor that can be initially extracted?
Answer
(A)
5
20
When factoring a quadratic expression x² + bx + c, if both 'b' and 'c' are positive, what can you infer about the factors?
Answer
(A)
Both factors are positive.
21
In the expression 2x² + 5x + 3, to factor, what should you look for first?
Answer
(A)
A common factor
22
What do you have to do to the expression 2x² - 8 before attempting to factor it?
Answer
(B)
Factor out the GCF (2)
23
What is the result of expanding -2(x - 3)?
Answer
(B)
-2x + 6
24
Consider the expression x² + 6x + 8. What are the two numbers that multiply to 8 and add to 6?
Answer
(A)
4 and 2
25
What is the result of expanding 2(x - 4) + 3x?
Answer
(A)
5x - 8
26
What's the solution of 5x + 2 = 17?
Answer
(C)
4
27
Which statement is true about completing the square?
Answer
(B)
It involves arranging the x-terms as a square.
28
What is the simplified value of (2x + 3) + (x - 1)?
Answer
(A)
3x + 2
29
What is the greatest common factor (GCF) of 12 and 18?
Answer
(C)
6
30
Which expression is equivalent to -3(x - 2) + 4x?
Answer
(A)
x + 6
31
Simplify: (x+3)(x-3)
Answer
(C)
x^2 - 9
32
What is the value of y, if 2y + 4 = 10?
Answer
(A)
3
33
Which expression results after applying distributive property on 3(2a + 4b - 1)?
Answer
(B)
6a + 12b - 3
34
Which expression is equivalent to x^2 - 9?
Answer
(C)
(x + 3)(x - 3)
35
What is the factored form of 25x² - 49?
Answer
(A)
(5x - 7)(5x + 7)
36
Which of these represents a 'perfect square' trinomial?
Answer
A
B
37
Identify the expression that is the same as x^2 - 4
Answer
A
D
38
What is the meaning of the word "coefficient"?
Answer
(C)
A number multiplied by the variable in an algebraic term.
39
Which of the following is equivalent to -2(x - 3)?
Answer
(B)
-2x + 6
40
If a = -1, what is the value of a^2 + 2a?
Answer
(B)
-1
41
What is the factored form of x^2 + 6x + 9?
Answer
(A)
(x+3)(x+3)
42
Which of the following is the simplified form of -4(2x - 1)?
Answer
(B)
-8x + 4
43
What are like terms?
Answer
(B)
Terms with the same variables raised to the same powers
44
What is the result of expanding (a + b)(a - b)?
Answer
(B)
a^2 - b^2
45
What is the area of a triangle with base 6 cm and height 4 cm?
Answer
(B)
12 cm^2
46
What is the expansion of (x+y)(x-y)?
Answer
(B)
x^2 - y^2
47
What is 2(x + 3) - x?
Answer
(A)
x+6
48
What is the formula to calculate the area of a rectangle?
Answer
(A)
length * width
49
What is 3a + 2b - a + b equal to?
Answer
(A)
2a + 3b
50
If the side of a square is 's', what is its area?
Answer
(B)
s^2