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Worksheets

Algebra 2 Fall 2021 Midterm Review

Total questions: 41

Worksheet time: 3hrs 25mins

Name
Class
Date
1.
Simplify: 
(10+ 15i)-(48 - 30i)
a)
58 - 45i
b)
58 - 15i
c)
-38 - 15i
d)
-38 + 45i
2.
Simplify: 
(7 + 2i)(9 - 6i)
a)
75-24i
b)
63 - 24i  - 12i2
c)
51 - 24i
d)
58 + 60i
3.
What does i2 = ?
a)
-1
b)
√-1
c)
1
d)
-√1
4.
Simplify
2i - 7i + 10
a)
-5i+10
b)
5i
c)
9i+10
d)
5i+10
5.
Simplify
3i - (4 + 7i)
a)
-4 + 10i
b)
21 - 12i
c)
4 - 10i
d)
-4 - 4i
6.
Find the sum.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
7.
Multiply
(2i)(3i)
a)
5i
b)
-5
c)
6i
d)
-6
8.
Multiply
(3i)(-2+4i)
a)
-6+12i
b)
-12-6i
c)
-2+7i
d)
12+6i
9.
Multiply: 
(4 – 3i)(7 + 2i)
a)
A.  22 - 13i
b)
B.  28 - 19i
c)
C.  34 - 13i
d)
D.  -34 - 29i
10.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
11.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

12.
a)
b)
c)
d)
13.
a)
b)
c)
d)
14.

Solve by taking the square root:

x2 = 49

a)

-7

b)

7

c)

49

d)

±7

15.

x2 -4 = 77

a)

9

b)

-9

c)

No Real Solutions

d)

±9

16.

Solve the equation using square root method.

  3x29=3\ 3x^2-9=3  

a)

x = 9 or x = -9

b)

no solutions

c)

x = 2 or x = -2

d)

x = 81 or x = -81

17.
solve:  
4x2+16x+15=0
a)
-5/2,-3/2
b)
(2x+5)(2x+3)
c)
-10,-6
d)
5/2, 3/2
18.
Solve      3x2 - 192 = 0
a)
-32 or 32
b)
No Solution
c)
-8 or 8
d)
-64 or 64
19.
Solve:
X2 - 3 =6X + 10
a)
X = 7, -1
b)
X = -7, 1
c)
X = -7, -1
d)
No Solution
20.
Solve -2x2 + 4x = 9
a)
(2 - i√14)/2   ,   (2 + i√14)/2
b)
(2 - i√-56)/2   ,   (2 + i√-56)/2
c)
(2 - i√-14)/2   ,   (2 + i√-14)/2
d)
(2 - √14)/2   ,   (2 + √14)/2
21.
Solve x2 - 5x + 10 = 0
a)
(5 - i√15)/2  ,  (5 + i√15)/2
b)
(5 - √15)/2  ,  (5 + √15)/2
c)
(5 - i√65)/2  ,  (5 + i√65)/2
d)
(5 - √65)/2  ,  (5 + √65)/2
22.
What would be the leading coefficient if this this polynomial was written in standard form?
a)
8
b)
-4
c)
-1
d)
1
23.
The end behavior can be written as x --> infinity, y --> ___ and as x --> - infinity, y --> ___. 
a)
infinity, infinity
b)
-infinity, - infinity
c)
infinity, - infinity
d)
- infinity, infinity
24.
What is the end behavior as x → -∞ f(x)→ ?
a)
-∞
b)
25.
(3x2+xy-5y2) + (2x2-xy+3y2)
a)
5x2-2xy+8y2
b)
5x2-2y2
c)
5x2+2y2
d)
5x2+2xy-8y2
26.
What is the degree of the polynomial 3x4 + 2x2 + 5x ?
a)
1
b)
2
c)
3
d)
4
27.
What is the degree of the polynomial 17x + 4
a)
0
b)
1
c)
2
d)
3
28.
When a polynomial is written in standard form, the coefficient of the first term is called the _____________.
a)
Boss coefficient
b)
Leading coefficient
c)
Best coefficient
d)
Greatest common coefficient
29.

 f(x)=x3+x224x+36f\left(x\right)=x^3+x^2-24x+36  
Which of the following is NOT a zero of this polynomial

a)

-6

b)

-1

c)

2

d)

3

30.

A polynomial has roots of -4, 1, and 6. What is the polynomial in factored form?

a)

(x+4)(x-1)(x-6)

b)

(x-4)(x+1)(x+6)

c)

 4x2+x+6-4x^2+x+6  

d)

 x33x222x+24x^3-3x^2-22x+24  

31.

Is the leading coefficient for the polynomial shown positive or negative?

a)

Negative

b)

Positive

c)

Cannot be determined

32.

How many zeroes (real and imaginary) does the polynomial have?

a)

2

b)

3

c)

4

d)

5

33.

Which of the following does not represent a polynomial?

a)

4 real zeros; 5 imaginary zeroes

b)

1 real zero; 6 imaginary zeroes

c)

3 real zeroes; 4 imaginary zeroes

d)

8 real zeroes; 2 imaginary zeroes

34.

The polynomial given by: y = 3x2 + 9x5 − 4 + 10x8 + 2x9 will have exactly how many zeroes?

a)

5

b)

2

c)

9

d)

8

35.

The degree of a polynomial always represents the:

a)

end behavior

b)

y-intercept

c)

number of zeroes

d)

quartography

36.
What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
37.
What are the roots of the polynomial function?
y = (x + 2)(x - 7)3
a)
-2, 7 multiplicity 3
b)
-2, 7, 3
c)
2, -7 multiplicity 3
d)
2, -7, 3
38.

Which function might have the given graph?

a)

f(x) = (x - 6)(x + 4)2

b)

f(x) = (x - 6)2(x + 4)

c)

f(x) = (x + 6)2(x - 4)

d)

f(x) = x(x - 6)(x + 4)

39.

Which function has zeros: x=0, x=5(multiplicity of 3) and x=-6.

a)

f(x) = 9x(x + 5)3(x - 6)

b)

f(x) = 3(x - 5)3(x + 6)

c)

f(x) = -7x(x - 5)3(x + 6)

d)

f(x) = (x - 3)(x - 5)(x + 6)

40.

2x3 - 5x2 + 3x + 7 ÷ x - 2

a)

2x3 - x2 + x + 9

b)

2x2 - x + 1

c)

2x2 - x + 1 + 9/(x - 2)

d)

2x2 - 9x - 15 - 23/(x - 2)

41.

Divide (4x³ - 2x² - 3) by (2x² - 1).

a)

2x - 1 + (2x - 4)/(2x2 - 1)

b)

2x + 3 + (x - 3)/(2x2 - 1)

c)

2x - 1

d)

2x + 3 + (3x-5)/(2x2 - 1)