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?
Απάντηση
A
B
C
2
What is the result of (x + 4)(x - 4)?
Απάντηση
(C)
x^2 - 16
3
Which of the following can be factorized using the difference of two squares method?
Απάντηση
(B)
4x² - 25
4
Solve for x: 2x - 7 = 5.
Απάντηση
(D)
9
5
What is the sum of the interior angles of a triangle?
Απάντηση
(B)
180 degrees
6
What is the area of a circle with a radius of 7?
Απάντηση
(C)
49π
7
If a = 2 and b = 3, what is the value of 3a + 2b?
Απάντηση
(B)
11
8
What is the solution to the equation 3x + 1 = 7?
Απάντηση
(B)
2
9
Simplify the expression: 4a + 2b - a + 3b.
Απάντηση
(A)
3a + 5b
10
What is the simplified form of -5(x - 2)?
Απάντηση
(A)
-5x + 10
11
Simplify 2a - 3b + 5a + b
Απάντηση
(A)
7a - 2b
12
Which of the following are like terms?
Απάντηση
A
C
13
Which of the following is the simplified form of the expression 3x + 2x - x?
Απάντηση
(B)
5x
14
Solve for x: x/3 + 2 = 5
Απάντηση
(C)
9
15
What is the result of expanding (x + 5)^2?
Απάντηση
(C)
x^2 + 10x + 25
16
What's the simplified form of 3(x+y) - 2y?
Απάντηση
(A)
3x + y
17
What is the result of expanding (x - 4)(x + 2)?
Απάντηση
(A)
x^2 - 2x - 8
18
If a = 3, what is the value of 2a^2 - 4?
Απάντηση
(B)
18
19
Which rule is used when simplifying algebraic expressions?
Απάντηση
(C)
Collect all the positive terms and all the negative terms separately.
20
What is the meaning of "Factorizing an algebraic expression"?
Απάντηση
(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)?
Απάντηση
(A)
x^2 - 5x + 6
22
Which of the following is a factor of 15x + 9?
Απάντηση
(B)
3
23
What is the factored form of 4x^2 - 16?
Απάντηση
(B)
(2x+4)(2x-4)
24
Expand and simplify: 4(x - 1) - (2x + 3)
Απάντηση
(A)
2x - 7
25
What is the simplified form of 3(a+b) - (a-b)?
Απάντηση
(B)
2a + 2b
26
Which of the following is a simplified form of x + 2x - 3x?
Απάντηση
(A)
0
27
What is the perimeter of a rectangle with length 8 and width 5?
Απάντηση
(B)
26
28
What is the result of (3x + 2y) - (x - y)?
Απάντηση
(A)
2x + 3y
29
Which of the following is a factor of 10x + 20?
Απάντηση
(B)
5
30
What is the area of a triangle with base b and height h?
Απάντηση
(B)
1/2bh
31
Which of the following is a linear equation?
Απάντηση
(B)
2x + 3 = 7
32
Which of the following is the expansion of (2x - 1)(x + 4)?
Απάντηση
(A)
2x^2 + 7x - 4
33
Which of these expressions is a perfect square trinomial?
Απάντηση
(B)
x² - 4x + 4
34
Which statements are true about the use of completing the square method?
Απάντηση
A
B
C
D
35
What is the minimum value of the expression x² - 4x + 5?
Απάντηση
(A)
1
36
Expand (x + 2)(x + 2)
Απάντηση
(B)
x^2 + 4x + 4
37
Simplify: 4(x + 3).
Απάντηση
(B)
4x + 12
38
If a = 4, what is the value of 3a - 5?
Απάντηση
(B)
12
39
What is the result of expanding (a-b)^2?
Απάντηση
(C)
a^2 - 2ab + b^2
40
What is the area of a square with sides of length 's'?
Απάντηση
(C)
s^2
41
In the expression ax²+bx+c, how would you identify factors of the form if a != 1?
Απάντηση
(C)
Determine the factors of ac.
42
What expression does the following describe: If apples cost $2 each and you bought 'a' apples?
Απάντηση
(B)
2a
43
What is the result of simplifying 8x - 3y + 2y - x?
Απάντηση
(A)
7x - y
44
The formula for the area of a circle is πr^2. If r=3, find the area.
Απάντηση
(C)
9π
45
Which of the following is a factor of 6x + 9?
Απάντηση
(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?
Απάντηση
(D)
15
47
Which of the following is the simplified form of 5a * 2b?
Απάντηση
(B)
10ab
48
What is the formula for calculating the area of a parallelogram?
Απάντηση
(B)
base * height
49
Simplify: 2(3x + 4y) - (x - y).
Απάντηση
(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?
Απάντηση
(C)
5