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Mathematics for IGCSE & O level - Algebraic Manipulation (Section 7)

1
What do you need to check when factorizing expressions of the form ax² + bx + c?
Answer
A
B
C
2
What is the result of (x + 4)(x - 4)?
Answer
(C)
x^2 - 16
3
Which of the following can be factorized using the difference of two squares method?
Answer
(B)
4x² - 25
4
Solve for x: 2x - 7 = 5.
Answer
(D)
9
5
What is the sum of the interior angles of a triangle?
Answer
(B)
180 degrees
6
What is the area of a circle with a radius of 7?
Answer
(C)
49π
7
If a = 2 and b = 3, what is the value of 3a + 2b?
Answer
(B)
11
8
What is the solution to the equation 3x + 1 = 7?
Answer
(B)
2
9
Simplify the expression: 4a + 2b - a + 3b.
Answer
(A)
3a + 5b
10
What is the simplified form of -5(x - 2)?
Answer
(A)
-5x + 10
11
Simplify 2a - 3b + 5a + b
Answer
(A)
7a - 2b
12
Which of the following are like terms?
Answer
A
C
13
Which of the following is the simplified form of the expression 3x + 2x - x?
Answer
(B)
5x
14
Solve for x: x/3 + 2 = 5
Answer
(C)
9
15
What is the result of expanding (x + 5)^2?
Answer
(C)
x^2 + 10x + 25
16
What's the simplified form of 3(x+y) - 2y?
Answer
(A)
3x + y
17
What is the result of expanding (x - 4)(x + 2)?
Answer
(A)
x^2 - 2x - 8
18
If a = 3, what is the value of 2a^2 - 4?
Answer
(B)
18
19
Which rule is used when simplifying algebraic expressions?
Answer
(C)
Collect all the positive terms and all the negative terms separately.
20
What is the meaning of "Factorizing an algebraic expression"?
Answer
(A)
Factoring means to factor fully to make sure you have found all the common factors and that the expression in the brackets will not factorize further.
21
What is the expanded form of (x - 2)(x - 3)?
Answer
(A)
x^2 - 5x + 6
22
Which of the following is a factor of 15x + 9?
Answer
(B)
3
23
What is the factored form of 4x^2 - 16?
Answer
(B)
(2x+4)(2x-4)
24
Expand and simplify: 4(x - 1) - (2x + 3)
Answer
(A)
2x - 7
25
What is the simplified form of 3(a+b) - (a-b)?
Answer
(B)
2a + 2b
26
Which of the following is a simplified form of x + 2x - 3x?
Answer
(A)
0
27
What is the perimeter of a rectangle with length 8 and width 5?
Answer
(B)
26
28
What is the result of (3x + 2y) - (x - y)?
Answer
(A)
2x + 3y
29
Which of the following is a factor of 10x + 20?
Answer
(B)
5
30
What is the area of a triangle with base b and height h?
Answer
(B)
1/2bh
31
Which of the following is a linear equation?
Answer
(B)
2x + 3 = 7
32
Which of the following is the expansion of (2x - 1)(x + 4)?
Answer
(A)
2x^2 + 7x - 4
33
Which of these expressions is a perfect square trinomial?
Answer
(B)
x² - 4x + 4
34
Which statements are true about the use of completing the square method?
Answer
A
B
C
D
35
What is the minimum value of the expression x² - 4x + 5?
Answer
(A)
1
36
Expand (x + 2)(x + 2)
Answer
(B)
x^2 + 4x + 4
37
Simplify: 4(x + 3).
Answer
(B)
4x + 12
38
If a = 4, what is the value of 3a - 5?
Answer
(B)
12
39
What is the result of expanding (a-b)^2?
Answer
(C)
a^2 - 2ab + b^2
40
What is the area of a square with sides of length 's'?
Answer
(C)
s^2
41
In the expression ax²+bx+c, how would you identify factors of the form if a != 1?
Answer
(C)
Determine the factors of ac.
42
What expression does the following describe: If apples cost $2 each and you bought 'a' apples?
Answer
(B)
2a
43
What is the result of simplifying 8x - 3y + 2y - x?
Answer
(A)
7x - y
44
The formula for the area of a circle is πr^2. If r=3, find the area.
Answer
(C)
9π
45
Which of the following is a factor of 6x + 9?
Answer
(C)
3
46
The perimeter of a rectangle is given by the formula 2(l+w). If l=5 and w=3, what is the perimeter?
Answer
(D)
15
47
Which of the following is the simplified form of 5a * 2b?
Answer
(B)
10ab
48
What is the formula for calculating the area of a parallelogram?
Answer
(B)
base * height
49
Simplify: 2(3x + 4y) - (x - y).
Answer
(B)
5x + 7y
50
If a quadratic expression can be written as the difference of two squares, which of these expressions CANNOT be a term in it?
Answer
(C)
5