WorksheetsAlgebra 2 - Midterm Review - Units 1-3
Total questions: 62
Worksheet time: 4hrs 9mins
Name
Class
Date
1.
Solve for a by factoring.
a2 + 2a - 24 = 0
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
2.
Solve by factoring: 5x2 + 13x + 6 = 0
a)
x = -2 and x = -3/5
b)
x = 2 and x = 3/5
c)
x = -2 and x = 3/5
d)
x = 2 and x = -3/5
3.
Solve using square roots.
a)
±81
b)
±9
c)
±3
d)
No real solution
4.
Solve using square roots.
5b2 - 4 = 41
5b2 - 4 = 41
a)
b = 9, b = -9
b)
b = 3, b = -3
c)
b = 8, b = -8
d)
no solution
5.
What are the solutions?
a)
0 and 8
b)
-2 and -4
c)
3 and -1
d)
2 and 4
6.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
7.
Solve using the Quadratic Formula.
a)
A
b)
B
c)
C
d)
D
8.
Simplify √-48
a)
4i
b)
-4√3
c)
4i√3
d)
12i
9.
Solve a2 - a - 20 = 0
a)
-4, 5
b)
5, 4
c)
d)
10.
Find the value of c that makes x2 + 16x + c a perfect square.
a)
-64
b)
64
c)
8
d)
16
11.
8r3 + 16r2
a)
4r2(2r + 4)
b)
8r2(r + 2)
c)
8(r3 + r2)
d)
4(r3 + 2r2)
12.
2x3y8 + 6x4y2 + 10x5y10 what is the GCF?
a)
2x3y2
b)
x3y2
c)
2
d)
-x3y2
13.
Factor Completely: 4k2+24k+36
a)
(2k+6)2
b)
(2k-6)2
c)
(2k-6)(2k+6)
d)
4(k+3)2
14.
Factor 8w5 - 48w4 + 72w3
a)
8w3 (w - 3) (w - 3)
b)
8w3 (w + 3) (w - 3)
c)
8w3 (w2 - 6w + 9)
d)
8w3 (w + 3) (w - 2)
15.
Factor: 27x3 + 8
a)
(3x + 2)(9x2 - 6x + 4)
b)
(9x + 2)(3x2 + 18x + 4)
c)
(3x2+4)(9x + 2)
d)
(27x + 8)(x2 - 216x + 64)
16.
What is the factored form of x³+7x²-2x-14
a)
(x²-2)(x-7)
b)
(x²+2)(x-7)
c)
(x²+2)(x+7)
d)
(x²-2)(x+7)
17.
Simplify. Write your answer in standard form:
(3x³+9x²-2x)−(7x³-6x²+1)
(3x³+9x²-2x)−(7x³-6x²+1)
a)
10x³+15x²-3x
b)
-4x³+3x²-2x+1
c)
-4x³+15x²-2x-1
d)
-4x³+15x²-2x+1
18.
Simplify the product. Write the answer in standard form.
(3x-5)(2x-3)
(3x-5)(2x-3)
a)
6x²-5
b)
6x²-19x+15
c)
6x²-10x-15
d)
6x²-10x+15
19.
Simplify the product. Write the answer in standard form.
(y+6)(6y²+9y-8)
(y+6)(6y²+9y-8)
a)
49y³
b)
36y²+55y-48
c)
6y³+36y²+54y-48
d)
6y³+45y²+46y-48
20.
What are the factors of
25x2 - 81?
25x2 - 81?
a)
(5x - 9)(5x + 9)
b)
(5x - 9)(5x - 9)
c)
(5x + 9)(5x + 9)
d)
Cannot be factored
21.
Classify this polynomial by its degree and number of terms: x2 + 6
a)
Linear polynomial
b)
Quadratic trinomial
c)
Quadratic binomial
d)
Cubic binomial
22.
Classify this polynomial by its degree and number of terms: x3 + 2x + 6
a)
Cubic polynomial
b)
Quadratic binomial
c)
Quadratic trinomial
d)
Cubic trinomial
23.
x4+2
a)
Quadratic binomial
b)
Quadratic monomial
c)
Quartic binomial
d)
Quartic trinomial
24.
What is the leading coefficient of the polynomial?
7x5 - 9x2 + 6x
7x5 - 9x2 + 6x
a)
7
b)
5
c)
9
d)
2
25.
Classify the polynomial by the highest degree.
-3x + 1
-3x + 1
a)
constant
b)
linear
c)
quadratic
d)
cubic
26.
What does the prefix TRI- mean?
a)
To attempt
b)
A triangle
c)
Many
d)
Three
27.
f(x) = 2x3 - 3x2 + 4x -10
State the maximum number of turns the graph of f(x) could make.
a)
3
b)
2
c)
1
d)
0
28.
f(x) = -3x4 + x3 - 2x2 + x - 1
What is the y-intercept of f(x)?
a)
(-1, 0)
b)
(0, -1)
c)
(-3, 0)
d)
(0, -3)
29.
f(x) = x3 - 3x2 - 4x
Find the zeros of f(x).
a)
{-4, 0, 1}
b)
{-1, 4}
c)
{-1, 0, 4}
d)
{-4, 1}
30.
f(x) = -3x4 + x3 - 2x2 + x - 1
State the maximum number of turns the graph of f(x) could make.
a)
3
b)
4
c)
2
d)
1
31.
Which function has this end behavior?
a)
-x2-3x+1
b)
-x3+2x2+3
c)
x4+3x3-4x+1
d)
x5-4x4+2x2-1
32.
What is the degree?
a)
Positive
b)
Negative
c)
Odd
d)
Even
33.
What is the leading coefficient?
a)
Positive
b)
Negative
c)
Odd
d)
Even
34.
Match the graph to the function
a)
f(x)= -x2+3x+2
b)
f(x) = -x3+2
c)
f(x) = x3+2
d)
f(x) = ⅓x⁴-5x²+2
35.
If a zero of a polynomial function has multiplicity 4 that means:
a)
The x intercept is at (4, 0)
b)
The graph will "bounce back" at that zero
c)
The graph will "pass through" at that zero
d)
Zeros cannot have multiplicity of 4
36.
Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0
*a positive leading coefficient
*zeros: 9, 3, -2, 0
a)
y = x(x - 9)(x - 3)(x + 2)
b)
y = x(x + 9)(x + 3)(x - 2)
c)
y = -x(x - 9)(x - 3)(x + 2)
d)
y = -x(x + 9)(x + 3)(x - 2)
37.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
38.
Expand:
(x - 2y)3
(x - 2y)3
a)
x3 - 8y3
b)
x2 - 4xy + 4y2
c)
x3 + 6x2y + 12xy2 + 8y3
d)
x3 - 6x2y + 12xy2 - 8y3
39.
Find the 4th term in the expansion of (4x-3)5.
a)
5760
b)
-4320x2
c)
5760x3
d)
-4320
40.
What is the 4th row of Pascal's Triangle?
a)
1 3 3 1
b)
1 4 8 4 1
c)
1 2 1
d)
1 4 6 4 1
41.
What is the 6th term in the expansion of (x + 3)5?
a)
243
b)
x5
c)
243x5
d)
90x3
42.
What is the Binomial expansion of (x + 1)5 ?
a)
x5 + 5x4 + 10x3 + 10x2 + 5x + 1
b)
x5 + 5x4 + 15x3 + 15x2 + 5x + 1
c)
x5 + 6x4 + 15x3 + 15x2 + 6x + 1
d)
x5 + 1
43.
When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).
a)
14x-10
b)
-8x+2
c)
2x+2
d)
2x-2
44.
When f(x) = x2+9 and g(x) = x-9, find f(x)-g(x).
a)
x2+x+9
b)
x2-x+9
c)
x2-x
d)
x2-x+18
45.
When f(x) = 4x+8 and
g(x) = x+3, find
f(x) * g(x).
g(x) = x+3, find
f(x) * g(x).
a)
4x2+24
b)
4x2+20x+24
c)
4x2+12x+24
d)
4x2+4x+24
46.
f(n)=x2+1
g(n)=2x-5
Find f(n)-g(n)
g(n)=2x-5
Find f(n)-g(n)
a)
x2-2x+6
b)
-x2+2x+4
c)
-x2-2x-6
d)
x2-2x-4
47.
h(x) = 3x + 3
g(x) = -4x + 1
Find (h + g)(10)
hint: add h(x) and g(x), then plug in 10
a)
-6
b)
6
c)
82
d)
-72
48.
a)
-4x4 - 10x3 - 8x - 20
b)
-4x3 - 4x2 0 8x - 8
c)
-x3 - 11x2 - 30x
d)
x3 - 11x2 + 30x
49.
Simplify this expression.
a)
-5x10
b)
4x4 + 18x6
c)
-6x4 + 16x2
d)
4x4 - 9x2
50.
Divide the polynomial by the monomial.
a)
2x8-8x2-28x
b)
2x8-2x2-7x
c)
8x7-8x-28x
d)
2x7 -2x -7
51.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
52.
(2x3 + 7x2 - 6x - 8) ÷ (x + 4)
a)
2x2 - x - 2
b)
2x3 - x2 - 2x
c)
2x2 + 15x + 54 + 208/x+4
d)
2x3 + 15x2 + 54x + 208
53.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
54.
What is the remainder when dividing (x3 - 3x2 - 10x + 24) by x+3?
a)
-4
b)
8
c)
0
d)
3
55.
i66
a)
1
b)
i
c)
-1
d)
-i
56.
Simplify:
-3i(4 + 2i)
-3i(4 + 2i)
a)
6 - 12i
b)
6 + 12i
c)
-12i - 6i2
d)
-12i + 6i2
57.
Simplify:
(2 - 3i)(5 + 4i)
(2 - 3i)(5 + 4i)
a)
22 - 7i
b)
22 + 7i
c)
22 - 7i2
d)
22 + 7i2
58.
Simplify:
(4 + 7i) - (3 + 2i)
(4 + 7i) - (3 + 2i)
a)
1 + 5i
b)
7 + 9i
c)
1 + 9i
d)
-1 + 5i
59.
(4-5i)(4+5i)
a)
41
b)
-9
c)
41+40i
d)
-9+40i
60.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
61.
Simplify
(-6 - 2i)2
(-6 - 2i)2
a)
32
b)
36-4i
c)
36+24i
d)
32+24i
62.
Write the polynomial in standard form given the following zeros. x = -2, 1, 4
a)
f(x) = (x+2)(x-1)(x-4)
b)
f(x) =x3 - 3x2 - 6x + 8
c)
f(x) = x3 + 8
d)
f(x) = x3 - 3x2 + 8
100 %
