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Chapter 4 Review

Total questions: 47

Worksheet time: 12hrs 45mins

Name
Class
Date
1.

Determine whether each statement is true or false. If it is false, give a counter example.


The sum of two imaginary numbers is an imaginary number.

a)

True

b)

False: i + i

c)

False: (1 - i)+(1 + i)

d)

False: 2i + (3 - 4i)

2.

Determine whether each statement is true or false. If it is false, give a counter example.


The product of two pure imaginary numbers is a real number.

a)

True

b)

False: 2i(2i)

c)

False: i(i)

d)

False: i + i

3.

Determine whether each statement is true or false. If it is false, give a counter example.


A pure imaginary number is an imaginary number

a)

True

b)

False: 2i

c)

False: 1 + 2i

d)

False: 3

4.

Determine whether each statement is true or false. If it is true, give an example. If it is false, give a counter example.


A complex number is a real number.

a)

True

b)

False: 1 + 2i

c)

False: 2i

d)

False: 3 + 0i

5.

Which student made a mistake and what is their mistake?

4 lines
6.

Solve by factoring.

x2 + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

7.

Solve by factoring. (what do they have in common)

n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

8.

The solutions of the quadratic equation

x2+12x+35=0 are (hint: find the zeros) FACTOR

a)

x = -5 or x = -7

b)

x = 5 or x = 7

c)

x = -35 or x = -1

d)

x = -9 or x = -4

9.
Solve by taking square roots:
5m2 + 1 = 6
a)
m = 0
b)
m = 1 or -1
c)
m = √7
d)
m = 7/5 m = -7/5
10.

Solve x2− 4 = 0 (solve using square roots)

a)

2 and -2

b)

4 and -4

c)

16 and -16

d)

8 and -8

11.

solve using square roots

a)

±81

b)

±9

c)

±3

d)

No real solution

12.

What is standard form of a quadratic Equation?

a)

Ax2 + Bx + C = 0

b)

Ax2 + B + Cx = 0

13.

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

14.

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

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

15.

Use the quadratic formula to find the solutions for

y = -x2 - 5x + 12

a)

No Real Solution

b)
c)
d)
16.
QUESTION 5
a)
A
b)
c)
d)
17.
a)
A
b)
B
c)
C
d)
D
18.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
19.
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
20.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
21.
When do you use the plus or minus symbol?
±
a)
After taking the square root of both sides
b)
After adding the square to both sides
c)
After taking half of b
d)
After setting the equation equal to zero
22.
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
23.
Complete the square for
x2 + 12x + ____
a)
x2 + 12x + 144
b)
x2 + 12x + 36
c)
x2 + 12x - 36
d)
x2 + +12x - 144
24.
What should be added to both sides of the following equation to complete the square?
x2 + 12x = 5
a)
12
b)
6
c)
36
d)
5
25.
The discriminant is
a)
aX2  + bX  +  c
b)
b - 4ac
c)
b2 - 4ac
d)
b2 + 4ac
26.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
27.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
28.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

29.

What is the discriminant of -2x2 − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

30.

What is the discriminant for 5x2 + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

31.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

32.

A function has a discriminant of 25.

______________

How many real solutions does it have?

a)

0

b)

1

c)

2

d)

5

33.

Determine the value of the discriminant and name the nature of the roots for the following:

x2 + 7x + 13

Remember: b2 - 4ac

a)

400, 2 real root

b)

0, 1 real root

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

34.
Simplify √-4
a)
2i
b)
-2i
c)
2
d)
4i
35.
Simplify -√-48
a)
4i√3
b)
-4i√3
c)
i√48
d)
-48i
36.
i13
a)
-1
b)
1
c)
i
d)
-i
37.
(-3i)(i)(5i)
a)
15i
b)
-15i
c)
-15i3
d)
15i3
38.
(3i)(-2+4i)
a)
-6+12i
b)
-12-6i
c)
-2+7i
d)
12+6i
39.
Multiply: 
(4 – 3i)(-7 – 2i)
a)
A.  -23 + 13i
b)
B.  -23 - 29i
c)
C.  -34 + 13i
d)
D.  -34 - 29i
40.
Simplify: 
(10+ 15i)-(48 - 30i)
a)
58 - 45i
b)
58 - 15i
c)
-38 - 15i
d)
-38 + 45i
41.
Find the solution.
a)
(2,3) and (3,4)
b)
(-3,-15) and (4,-8)
c)
(-3,10) and (8,4)
d)
(-8,3) and (-4,10)
42.

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

no solutions

d)

All of the above

43.

Solve the depicted system algebraically

a)

(0,-7) and (1, 6)

b)

(0,-7) and (1, -6)

c)

(0, 7) and (1, -6)

d)

(-7,0) and (1, -6)

44.

The graph shows the height y (in feet) of an apple x sections after it is tossed in the air with an initial velocity of 32 ft per second. The linear function represents an arrow shot through the apple. After how many seconds does the arrow hit the apple? Check the reasonableness of the solution(s). You may use the model given below where v0 is the initial velocity and h0 is the initial height.



  

 f(x) = 16x2+v0x +h0f\left(x\right)\ =\ -16x^2+v_0x\ +h_0  

a)

10 seconds

b)

1.75 seconds

c)

3 seconds

d)

14.25 seconds

45.

Which inequality is represented by the graph?

a)

y > (x - 3)² - 3

b)

y ≥ (x + 3)² - 3

c)

y > (x + 3)² - 3

d)

y ≥ (x - 3)² - 3

46.

a)

A

b)

B

c)

C

47.

Have your attempted to complete the Quadratic Formula proof to practice reading math?

a)

yes

b)

no