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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 3)

1
What are the terms of the bracket (x+5) which when multiplied give x²+10x+25?
Answer
(B)
(x+5)
2
Expand (x - 6)(x + 6)
Answer
(B)
x² - 36
3
Which expressions can be factored using the difference of squares?
Answer
A
C
4
What expression results from completing the square of x² + 6x + 5?
Answer
(B)
(x + 3)² - 4
5
Simplify: 15z - (8z + 4)
Answer
(A)
7z - 4
6
What is the result of factorizing x² - 16?
Answer
(A)
(x + 4)(x - 4)
7
In the factorization of x² - 5x + 6, what are the two numbers that multiply to 6 and add up to -5?
Answer
(B)
-2 and -3
8
What is the factored form of 10x + 15?
Answer
(A)
5(2x + 3)
9
Which expression is equivalent when factorizing 18r - 30s?
Answer
(D)
All of the above
10
If the expansion of a bracket resulted in the expression x² + 2x + 1, what were the original brackets?
Answer
(C)
(x + 1)(x + 1)
11
What is the result of expanding 2(x + 3)?
Answer
(B)
2x + 6
12
Expand 7(x + 1)
Answer
(C)
7x + 7
13
Simplify 7u - 4u + 8v - 2v
Answer
(B)
3u + 6v
14
What are the factors of x² - 25?
Answer
(C)
(x + 5)(x - 5)
15
Which is the complete square form for x² + 2x - 3?
Answer
(A)
(x + 1)² - 4
16
Simplify: 2y + 5z - y - 3z
Answer
(B)
y + 2z
17
When factoring quadratic expressions of the form x² + bx + c where 'c' is positive, what can be inferred about the signs of the factors?
Answer
(B)
The factors have the same sign.
18
What is the factored form of x² - 16?
Answer
(D)
(x - 4)(x + 4)
19
Factorize 48x + 72
Answer
(B)
8(6x + 9)
20
Expand 4(2x - 5)
Answer
(B)
8x - 20
21
If the perimeter of a rectangle is given by 2l + 2w, what is the perimeter of a rectangle with l = 5 and w = 3?
Answer
(B)
16
22
What is the result of completing the square on the expression x² + 12x + 30?
Answer
(A)
(x + 6)² - 6
23
If you have an equation x² - 6x + 9 = 0, what are the solutions to this quadratic equation?
Answer
(B)
x = 3
24
Factorize 15x + 25
Answer
(A)
5(3x + 5)
25
A rectangle has a length of 'a' and a width of 'b'. What is the formula for the area of the rectangle?
Answer
(C)
a * b
26
Which of the following options can be used when simplifying more complex brackets?
Answer
A
B
C
27
What is the purpose of using algebraic expressions?
Answer
(B)
To represent mathematical relationships and solve problems.
28
What is the expanded form of (5x + 2)(3x - 4)?
Answer
(A)
15x² - 14x - 8
29
To factor the expression 4x² - 9, what method is applied?
Answer
(B)
Difference of squares
30
Which algebraic expression represents '5 less than a number x'?
Answer
(C)
x - 5
31
What is 5(x - 1) when expanded?
Answer
(C)
5x - 5
32
What is the simplified form of a + a + b + b + b?
Answer
(A)
2a + 3b
33
What is the result of expanding -3(x + 5)?
Answer
(A)
-3x - 15
34
Simplify: 8a - 5b + 2a + 7b
Answer
(A)
10a + 2b
35
Factorize 20x + 30
Answer
(B)
10(2x + 3)
36
What is the correct procedure for simplifying algebraic expressions?
Answer
(D)
All of the above.
37
What is the complete square form of x² + 6x + 5?
Answer
(A)
(x + 3)² - 4
38
A triangle has a base of 'b' and a height of 'h'. What is the formula for its area?
Answer
(C)
1/2 * b * h
39
Which of the following statements is true when factoring an expression using the form ax² + bx + c?
Answer
A
B
C
40
Which of these is a perfect square trinomial?
Answer
(B)
x² + 6x + 9
41
What is the standard form of a quadratic equation?
Answer
(B)
ax² + bx + c = 0
42
Expand (x + 10)(x - 10)
Answer
(B)
x² - 100
43
Which of these expressions is a difference of squares?
Answer
(B)
4x² - 9
44
Factorize 24x + 36
Answer
(C)
12(2x + 3)
45
What is the equivalent expression after correctly factorizing 50x - 75?
Answer
(A)
25(2x - 3)
46
For the expression 2x² + 7x + 3, what numbers are required to factor by trial and error?
Answer
(C)
6 and 1
47
What is the expanded form of (3x - 4)(x + 2)?
Answer
(C)
3x² + 2x - 8
48
What type of expression is represented by a² + 2ab + b²?
Answer
(B)
Perfect square trinomial
49
The expression x²-14x+49 can be obtained by multiplying a bracket by itself, what is that bracket?
Answer
(D)
(x-7) and (x-7)
50
Which expression is correct when expanding (2x - 1)(x + 4)?
Answer
(A)
2x² + 7x - 4