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Final Review 2019

Total questions: 54

Worksheet time: 3hrs 40mins

Name
Class
Date
1.

x2 - 9

a)

(x + 3)2

b)

(x + 3) (x - 3)

c)

(x - 3)2

d)

x + 3(x - 3)

2.

x2 - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)2

d)

x + 4(x - 4)

3.

4x2 - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)2

c)

(2x + 5)2

d)

2x + 5(2x - 5)

4.

25x2 - 36y2

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)2

d)

(5x - 6y)2

5.

4x2y2 - 1

a)

(2 + xy) (2 - xy)

b)

(2x + y) (2x - y)

c)

(2xy + 1) (2xy - 1)

d)

(2y + x) (2y - x)

6.

64x2 - 81y2

a)

(8x + 7y) (8x - 7y)

b)

(8x + 9y) (8x - 9y)

c)

(6x + 7y) (6x - 7y)

d)

(6x + 9y) (6x - 9y)

7.

4x2 - 16

a)

4(2x + 4) (x - 2)

b)

4(4x + 2) (x - 2)

c)

(2x + 4) (2x - 4)

d)

4(x + 2) (x - 2)

8.

49x2 - 144y2

a)

(7x + 16y) (7x - 16y)

b)

(7x + 12y)2

c)

(12x + 7y) (12x - 7y)

d)

(7x + 12y) (7x - 12y)

9.

x4 - 100y2

a)

(x2 + 10y) (x2 - 10y)

b)

(x + 10y) (x - 10y)

c)

(x + 10y) (x3 - 10y)

d)

(x3 + 10y) (x - 10y)

10.

169x2y6 - 196w4z8

a)

(13xy3 + 14w2z4) (13xy3 - 14w2z4)

b)

(13xy2 + 14w3z4) (13xy2 - 14w3z4)

c)

(13xy6 + 14w2z4) (13xy6 - 14w2z4)

d)

(13x2y + 14w3z4) (13x2y - 14w3z4)

11.

121x2y6z8 - 225w4

a)

(11xy4z4 + 15w) (11xy2z4 - 15w)

b)

(11x2y3z4 + 15w) (11x2y3z4 - 15w)

c)

(11xy3z4 + 15w2) (11xy3z4 - 15w2)

d)

(11xy3z + 15w2) (11xy3z3 - 15w2)

12.

We can't factor using difference of two square this

25x2 - 51y2. Why?

a)

Because 51 is not a perfect cubed number.

b)

Because 51 is not a perfect squared number.

c)

Because 25 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

13.

We can't factor using difference of two square this

49x2 + 4y2. Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

14.

Which of these can factor using difference of two squares?

a)

144x2 - 49y2

b)

x2 + 4x - 12

c)

100x2 + 20x + 1

d)

14x - 16

15.

Which one is false about the difference of two squares?

a)

We can factor that it is addition sign.

b)

We can factor that it is a perfect squared number (Example: x2, 25, 49)

c)

Formula: a2 - b2 = (a + b) (a - b)

d)

We can factor that it is minus sign.

16.
Is this a perfect square trinomial?
x2 + 16x + 64
a)
Yes
b)
No
17.
Is this a perfect square trinomial?
x2 + 18x + 9
a)
Yes
b)
No
18.
Factor: x2 + 24x + 144
a)
(x + 12)2
b)
(x + 9)2
c)
(x + 15)2
d)
(x + 13)2
19.
Factor: x2 - 4x + 4
a)
(x + 2)2
b)
(x - 2)2
c)
(x + 4)2
d)
(x - 4)2
20.
Which of the following is a perfect square trinomial?
a)
x2 – 4x – 4 
b)
x2 – 6x – 9 
c)
x2 + 6x – 9 
d)
x2 – 4x + 4 
21.
Put into standard form: (x - 3)2
a)
x2 + 3x + 9
b)
x2 - 3x - 9
c)
x2 + 6x - 9
d)
x2 - 6x + 9
22.
Put into standard form: (x + 6)2
a)
x2 + 6x + 12
b)
x2 + 6x + 36
c)
x2 + 12x + 6
d)
x2 + 12x + 36
23.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
24.
Complete the Square
x2 + 6x = 5
a)
(x + 3)2 = 5
b)
(x + 6)2 = 9
c)
(x + 3)2 = 14
d)
(x + 6)2 = 14
25.
Solve the equation by completing the square and then finding the roots. 
x2+ 6x - 4 = 36
a)
x = -7, 7
b)
x = 4, -10
c)
x = -4 +- √7
d)
x = 10, -4
26.

Solve the following quadratics equation by completing the square...


x2 + 4x - 1 = 0

a)

x = -2 ± √5

b)

x = -5 ± √2

c)

x = 2 ± √5

d)

x = -5 ± √5

27.
What is the first step to solving THIS equation by completing the square?
a2 + 10a + 21 = 0
a)
Set the equation equal to zero
b)
Divide 10 by 2 and add the result to both sides
c)
Add a2 and 10a together
d)
Subtract the 21
28.
Factor:
 b2 + 8b + 7
a)
(b + 4)(b + 3)
b)
(b + 6)(b + 1)
c)
(b + 7)(b +1)
d)
prime
29.
Factor:
 x² - 4x + 24
a)
prime
b)
(x + 6)(x - 4)
c)
(x - 8)(x - 3)
d)
(x - 12)(x - 2)
30.
Factor Completely:  3n² - 15n + 18
a)
(n - 2)(n - 3)
b)
3(n + 2)(n + 3)
c)
(3n - 9)(n - 2)
d)
3(n - 3)(n - 2)
31.
Factor Completely:  15t² - 27t - 6
a)
3(5t +1)(t - 2)
b)
(3t - 6)(5t + 1)
c)
3(5t - 1)(t + 2)
d)
(15t + 6)(1t - 6)
32.
Factor Completely:  6x² + 5x - 6
a)
6(x + 1)(x - 6)
b)
(6x + 6)(x - 1)
c)
(2x - 3)(3x + 2)
d)
(3x - 2)(2x + 3)
33.
Factor:  n2 - 2n + 1
a)
(n + 1)(n - 1)
b)
(n + 1)²
c)
prime
d)
(n - 1)²
34.
Factor Completely:  5v2 - 30v + 40
a)
(5v - 8)(v + 5)
b)
(5v + 5)(v - 8)
c)
5(v - 4)(v - 2)
d)
5(v + 8)(v - 5)
35.
Factor:
 2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
36.
Factor:
 4h² - 17h + 4
a)
(2h - 2)²
b)
4(h + 4)(h + 1)
c)
(2h - 2)(2h + 2)
d)
(h - 4)(4h - 1)
37.
Factor Completely:  2r2 - 44r + 242
a)
2(r - 11)2
b)
(2r - 11)2
c)
2(r - 11)(r + 11)
d)
2(r + 11)2
38.
Factor Completely:  16b2 + 60b - 100
a)
(4b + 20)(4b - 5)
b)
(16b - 20)(b + 5)
c)
(4b + 10)(4b - 10)
d)
4(b + 5)(4b - 5)
39.
Factor:  x16  -  y36
a)
(x4  -  y6)(x4  +  y6)
b)
(x8  -  y18)(x2  +  y2)
c)
(x8  -  y18)(x8  +  y18)
d)
prime
40.
Factor:
 x2 - 15x + 50
a)
(x - 10)(x - 15)
b)
(x - 10)(x - 5)
c)
(x - 25)2
d)
(x - 5)2
41.
Factor:  -4 + x2
HINT - Rearrange the problem
a)
(2 + x)(2 - x)
b)
(-2 + x)(2 - x)
c)
4(x + 1)(x - 1)
d)
(x + 2)(x - 2)
42.

Determine the values of a, b, and c for the quadratic equation:

4x2 – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

43.

What is this formula?

a)

This is the standard formula.

b)

This is the quadratic formula.

c)

This is the square root formula.

d)

This is the Pythagorean formula

44.

Use the quadratic formula to solve 2x2 + 2x - 12.

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

45.

Use the quadratic formula to find the solutions for

y = -x2 - 5x + 12

a)

No Real Solution

b)
c)
d)
46.
QUESTION 5
a)
A
b)
B 
c)
C 
d)
D 
47.

What should you do first in solving this equation?

x2 + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

48.
a)
A
b)
B
c)
C
d)
D
49.

Solve using the quadratic formula...

9x2 = 4 + 7x

a)
b)
c)
d)

No solution

50.
Simplify.
a)
-5i
b)
5
c)
5i
d)
-5
51.

Another way to express √-1 is?

a)

1

b)

-1

c)

i

d)

0

52.

(6+i)(-3+6i)

a)

3+7i

b)

-18+6i

c)

-24+6i

d)

-18+12i

53.
a)
A
b)
B
c)
C
d)
D
54.
a)
A
b)
B
c)
C
d)
D

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