Download Math 0320 Final Exam Review

Math 0320 Final Exam Review
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Factor out the GCF using the Distributive Property.
1) 6x3 + 9x
1)
Objective: (6.1) Factor Out GCF
2) 3x2 y6 + 15x2 y5
2)
Objective: (6.1) Factor Out GCF
Factor by grouping.
3) 40r2 + 25ry - 8xr - 5xy
3)
Objective: (6.1) Factor by Grouping
4) x2 + 5x + xy + 5y
4)
Objective: (6.1) Factor by Grouping
Factor, if possible, using the difference or sum of squares. If a polynomial is not factorable, write "prime."
5) 100 - y2
5)
Objective: (6.2) Factor Sum or Difference of Squares
6) 49x2 + 4
6)
Objective: (6.2) Factor Sum or Difference of Squares
Factor the trinomial completely using the general factoring strategy. If a trinomial is not factorable, write "prime."
7) 8x3 + 18x2 + 9x
7)
Objective: (6.3) Factor Using General Strategy
8) 24x3 - 104x2 - 80x
8)
Objective: (6.3) Factor Using General Strategy
Determine if the trinomial is a perfect square trinomial. If it is, factor it. If it is not, write "prime."
9) z 2 - 2z + 1
9)
Objective: (6.4) Factor Perfect Square Trinomial
10) 25x2 + 30x + 9
10)
Objective: (6.4) Factor Perfect Square Trinomial
Factor the polynomial completely using the general factoring strategy. If the polynomial is not factorable, write "prime."
11) y3 + 49y2 + 50y
11)
Objective: (6.5) Factor Out Common Factor
12) 3(x - 2) - a(x - 2)
12)
Objective: (6.5) Factor Out Common Factor
1
Simplify the rational expression.
3x - 15
13)
x2 - 25
Math 0320 Final Exam Review
13)
Objective: (7.1) Simplify Rational Expression
14)
5x - 2
15x2 + 4x - 4
14)
Objective: (7.1) Simplify Rational Expression
Multiply the rational expressions and write the answer in lowest terms.
21m 5 p2 m - p
15)
·
m+p
3m 8 p
15)
Objective: (7.2) Multiply Rational Expressions
16)
d3 + 125
d2 - 7d
·
d- 7
d2 - 5d + 25
16)
Objective: (7.2) Multiply Rational Expressions
Divide the rational expressions and write the answer in lowest terms.
2k2 + 17k + 21
6k2 + 17k + 12
17)
÷
9k2 - 24k + 16
9k2 - 16
17)
Objective: (7.2) Divide Rational Expressions
18)
x2 + 7x + 10
10 + 3x - x2
÷
x2 + 10x + 25
2x2 - 50
18)
Objective: (7.2) Divide Rational Expressions
Simplify using the product rule for radicals.
19) 490
19)
Objective: (8.1) Simplify Using Product Rule
20)
500
20)
Objective: (8.1) Simplify Using Product Rule
Simplify. Assume that all variables represent real numbers.
49m 2
21) n2
21)
Objective: (8.1) Simplify Square Root
22)
(x - 1)2
22)
Objective: (8.1) Simplify Square Root
2
Math 0320 Final Exam Review
Multiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
23) 5y · 35y
23)
Objective: (8.2) Multiply Square Roots
3x3 ·
24)
6x2
24)
Objective: (8.2) Multiply Square Roots
Divide. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
96
25)
25)
6
Objective: (8.2) Divide Square Roots
26)
3 200
2
26)
Objective: (8.2) Divide Square Roots
Solve and write the solution using set notation.
27) -7x - 10 = x + 4
27)
Objective: (8.3) Solve Equation Containing Square Root (Square Binomial)
x+1=
28)
x+5
28)
Objective: (8.3) Solve Equation Containing Square Root (Square Binomial)
Simplify using the product rule or quotient rule for radicals. Write the answer in simplified radical form. Assume that all
variables represent positive real numbers.
3
29) 135
29)
Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule
30)
5
32 x 4 y28
30)
Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule
Evaluate.
31) 272/3
31)
Objective: (8.5) Evaluate with Rational Exponents
32)
16 1/2
9
32)
Objective: (8.5) Evaluate with Rational Exponents
Find the functional value and write the answer as an ordered pair.
33) h(x) = 3x2 - 7x - 4, h(-5)
Objective: (9.1) Find Functional Value (Number)
3
33)
34) f(t) = -3t3 + 6t2 - t - 41, f(-2)
Math 0320 Final Exam Review
34)
Objective: (9.1) Find Functional Value (Number)
Find the functional value.
35) g(x) = 2x2 - 5x - 3, g(x - 1)
35)
Objective: (9.1) Find Functional Value (Variable Expression)
36) f(x) = 8x + 8,
f(a + h) - f(a)
h
36)
Objective: (9.1) Find Functional Value (Variable Expression)
Find the following function and its domain.
4
3x
and g(x) =
. Find (f + g)(x).
37) Let f(x) =
x-2
x2 - 4
37)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
38) Let f(x) = 2x2 - 3 and g(x) = 7x - 4. Find (f - g)(x).
38)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
39) Let f(x) = 5x2 - 2 and g(x) = 4x + 1. Find (f · g)(x).
39)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
40) Let f(x) = 5x + 1 and g(x) = 2x - 5. Find
f
(x).
g
40)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
Perform the indicated operations and write the answer in the standard form a + bi.
41) (-9 + 14i) - (5 - 2i)
41)
Objective: (10.1) Add or Subtract Complex Numbers
42) (-6 - 7i) + (12 + 4i)
42)
Objective: (10.1) Add or Subtract Complex Numbers
43) (7 - 4i)(7 + 4i)
43)
Objective: (10.1) Multiply or Divide Complex Numbers
44)
1 - 2i
7+i
44)
Objective: (10.1) Multiply or Divide Complex Numbers
Solve using the Zero Factor Property.
45) x(6x - 1) = 0
45)
Objective: (10.2) Solve Using Zero Factor Property
4
46) 7x2 + 19x - 6 = 0
Math 0320 Final Exam Review
46)
Objective: (10.2) Solve Using Zero Factor Property
Solve using the Square Root Property.
81
47) x2 =
49
47)
Objective: (10.2) Solve Using Square Root Property
48) (3s + 9)2 = 64
48)
Objective: (10.2) Solve Using Square Root Property
Solve by completing the square.
49) 3x2 + 15x = - 18
49)
Objective: (10.2) Solve by Completing the Square
50) x2 + 6x = 31
50)
Objective: (10.2) Solve by Completing the Square
Solve using the Quadratic Formula.
51) 5x2 + 8x = 4
51)
Objective: (10.3) Solve Using Quadratic Formula
52) 17x2 - 2x = 0
52)
Objective: (10.3) Solve Using Quadratic Formula
5
Answer Key
Testname: MATH_0320_FINAL_SPRING_2014_II_REVIEW
1) 3x(2x2 + 3)
2) 3x2 y5 (y + 5)
3)
4)
5)
6)
7)
8)
(8r + 5y)(5r - x)
(x + 5)(x + y)
(10 + y)(10 - y)
Prime
x(2x + 3)(4x + 3)
8x(3x + 2)(x - 5)
9) (z - 1)2
10) (5x + 3)2
11) y(y2 + 49y + 50)
12) (3 - a)(x - 2)
3
13)
x+5
14)
1
3x + 2
15)
7pm - 7p2
m 3 (m + p)
16) d2 + 5d
k+ 7
17)
3k - 4
18) -2
19) 7 10
20) 10 5
m
21) -7
n
22) |x - 1|
23) 5y 7
24) 3x2 2x
25)
26)
27)
28)
29)
30)
31)
32)
4
30
{-2}
{4}
3
3 5
5
2y5 x4 y3
9
4
3
33) (-5, 106)
34) (-2, 9)
35) 2x2 - 9x + 4
36) 8
7x + 8
, D = {x x
37)
(x - 2)(x + 2)
-2 and x
2}
6
Answer Key
Testname: MATH_0320_FINAL_SPRING_2014_II_REVIEW
38) 2x2 - 7x + 1, D = ( , )
39) 20x3 + 5x2 - 8x - 2, D = (
40)
5x + 1
,D= x x
2x - 5
5
2
, )
41) -14 + 16i
42) 6 - 3i
43) 65 + 0i
1
3
i
44)
10 10
45) 0,
1
6
46) -3,
2
7
47) -
9 9
,
7 7
48) -
17
1
,3
3
49) {-3, -2}
50) {-3 - 2 10, -3 + 2 10}
2
51) -2,
5
52) 0,
2
17
7