Study Guide for Math 0995 Final
Unit 1
1) List all the factors of 24 1,2,3,4,6,8,12,24
2) Write the prime factorization of 500 2*2*5*5*5
3) Craig and Edie both have night jobs. Craig has every fifth night off and Edie has every seventh
night off. How often will they have the same night off? Every 35th night
4) Find the LCM of 4, 14, and 35 140
5) Write the fraction 5/6 as an equivalent fraction with a denominator of 24
20
24
6) Simplify the fraction 162/354 27/59
9 2
∙
7) Multiply
8) Divide
3
10) Add
1
4
÷
4
9) Subtract
9/20
8 5
5
8
+
1
24
−
1
3
9
20
18
7/40
7/12
11) Determine which sets the number -4.454545… belongs to. List all that apply.
 Natural Numbers
 Whole Numbers
 Integers
 Rational Numbers X
 Irrational Numbers
 Real Numbers X
12) Determine which sets the number -2 belongs to. List all that apply.
 Natural Numbers
 Whole Numbers
 Integers X
 Rational Numbers X
 Irrational Numbers
 Real Numbers X
13)
Simplify the expression 3[(2
– 4) – ( -5 – 8)] + 62 69
14) Simplify
9+ |2−1|+ 22
8−6
7
15) If x = -3 and y = -5, evaluate the expression and simplify the result.
2y- 8
3+ 4x
-2
16) Suppose a deep-sea diver dives from the surface to 159 feet below the surface. He then dives
down 14 more feet. Use positive and negative numbers to represent this situation. Then find the
diver’s present depth.
173 feet below the surface
17) Simplify |15| + (−10)2
18) Simplify -3
2
+ [−10 − (−7)] 112
9
19) Simplify -10w – w – 11 + 4w + 2 -7w - 9
20) Simplify (11g – 3) – (2g + 8) 9g - 11
(-4x y) (-xy )
21) Simplify
4
3
4x5y4
−2
22) Simplify using positive exponents
(𝑥 2 𝑦)
(𝑥 3 𝑦2 )3
1
𝑥 13 𝑦 8
23) Simplify (2a2 +3a – 1) – (4a2 + 5a + 6) -2a2 – 2a - 7
24) Find the product. (4y2 – y + 2)(y2 – 2y – 1) 4y4 – 9y3 – 3y – 2
25) Divide
26) Divide
9𝑦 2 +12𝑦−15
3𝑦
3𝑦 + 4 −
9k4 +12k3 - 4k -1
3k2 -1
5
𝑦
3k2 + 4k + 1
27) Factor out the greatest common factor.
x7 y8 + x5 y4 - x5 y9 - x3 y3 x3y3 ( x4y5 + x2y – x2y6 – 1)
28) Factor by grouping. 5x2 – 10xy – 4x + 8y (5x – 4)(x -2y)
29) Completely Factor. 8x2 – 14xy + 3y2 (2x-3y)(4x-y)
30) Completely Factor. 9y2 – 4 (3y-2)(3y+2)
x3 + 8x2
x2 + 3x - 40
31) Simplify
32) Find the product, then simplify.
33) Find the quotient, then simplify.
𝑥2
(𝑥−5)
x2 +12x + 35 x2 - 3x - 4 (𝑥+5)(𝑥+1)
×
x2 + 4x - 32 x2 + 5x -14 (𝑥+8)(𝑥−2)
( x + 6)
2
x2 - 36
¸
x-6
6x - 36
34) Perform the indicated operation. Simplify if possible.
6(𝑥+6)
(𝑥−6)
11x
x -1
10x +10 x +1
1
10
35) Simplify the following radicals
a.
3
1
b. √𝑥 10
√−125
c. √64
x5
-5
36) Simplify.
1/8
121 3⁄2
a. 811⁄4
c. 𝑑4⁄5 ∙ 𝑑9⁄5
b. (144)
3
1331/1728
13
15
37) Simplify √121𝑥 𝑦
d^13/5
11𝑥 6 𝑦 7 √𝑥𝑦
38) Simplify
3
3
3
√24𝑥 − √81𝑥 − √3𝑥
Unit 2
1) Is - 49 a solution to the equation
𝑥+4
5
= −5 no
2) In one U.S. city, the taxi cost is $1 plus $1.10 per mile. If you are traveling from the airport, there
is an additional charge of $2.50 for tolls. How far can you travel from the airport by taxi for
$31.00? 25 miles
3) Solve the equation -2(y – 6) + 7y = 9y – 4 y = 4
4) Solve the equation. | 5x – 4 | = 21 x=5, -17/5
5) Solve the equation. | 6n +7 | + 5 = 2 No Solution
6) An object is thrown upward from the top of a 208-foot building with an initial velocity of 192 feet
per second. The height h of the object after t seconds is given by the quadratic equation
h = -16t 2 +192t + 208.
When will the object hit the ground?
13 seconds
7) Solve the equation. x2 + 2x – 63 = 0
X = 7, -9
1
30
-1 = 2
x +15
x - 225
8) Solve.
x=
1±√721
2
9) Solve.
x- 11-10x = -22
X = -11
10) Solve. 256 = 64
X = 1/3
11) Solve. (x + 3)2 = 75
X = -3±5√3
12) Solve. y2 + 5y – 4 = 0
3x
Y=
x+1
−5±√41
2
-5y = 4y - 6
2
13) Solve
Y = -2, 3/4
14) Solve the inequality. Write your answer in interval notation.
2(x+ 4)-8 > -3(x- 4)+13
[5,∞)
15) Nick and Jessica are celebrating their 50th anniversary by having a reception at a local reception
hall. They have budgeted $5,000 for their reception. If the reception hall charges a $70 cleanup
fee plus $35 per person, find the greatest number of people that they may invite and sill stay
within their budget.
140 people
16) Solve the inequality. Write your answer in interval notation.
[1, 9/2]
10 + 4x-11 £17
Unit 3
1) Is this a function? Find the domain and range of the graph.
It is a function, D: (-∞, ∞) , R: (-∞, ∞)
2) Find f(5) if f (x) = 2x2 +3x- 4,
61
3) Graph the linear equations.
a) 9x – 3y = 18 The graph is a line with a y-int of -6 and a slope of 3
b) y – 8 = 0 The graph is a horizontal line at y = 8
c) x + 6 = 0 The graph is a vertical line at x = -6
4) What are the x and y intercepts of the line 4x – 6y = 24
(6, 0) (0, -4)
5) Find the slope of a line that goes through the points (2, 7) and (8, 1)
-1
6) Determine if the lines are parallel, perpendicular or neither.
18 + 8x = 9y
9x + 8y = -8
Perpendicular
7) Find an equation of the line passing through the pair of points. Write the equation in slopeintercept form. (4, 9) and (3, 5) y = 4x +1
8) Write an equation in slope-intercept form of the line that contains the point (-1, 2) and is
perpendicular to the line y = 2x – 8. Y = -1/2x +3/2
9) Graph the function. Give the domain and range.
f (x) = x- 3 +1
The graph is a “v” with a center at (3, 1)
10) Use your graphing calculator to solve the inequality.
(-∞, -4)  (0, 4)
x3 <16x
11) The equation
x3 - 4x = 4x2 + 5 has one solution. Use your graphing calculator to find
the solution to the equation.
x=5
ì5x - 4y = 9
í
12) Solve the system of equations.
î3- 2y = -x
(5, 4)
ì3x + 4y = -6
13) Solve the system of equations. í
î5x + 3y =1
(2, -3)
14) Write the standard equation for the circle whose center is at (4, 1) and whose radius is 3.
(x - 4)2 + (y – 1)2 = 9
15) Find the center and radius of the circle below. Then graph the circle.
( x+ 2) + ( y-1) =1
2
2
Center (-2, 1) Radius 1 then graph
16) Find the center and radius of the circle below. Then graph the circle.
2
2
Center (-4, -1) Radius: 5 then graph
x + y +8x+ 2y-8 = 0