Name:
Trigonometry
& Related Topics
Fundamentals Review Packet
This packet is intended to review some previously learned concepts that
are essential to success in TART. In addition to the review in class, you
should also utilize TLC and chapters 1 and 2 in your text as needed.
Directions: You may take notes and complete the homework directly in this packet.
You are expected to show all work and may not use a calculator to help you answer
the questions unless directed to do so.
Section I: Pre-Algebra/ Algebra 1

Operations with Real Numbers: You need to know how to add, subtract, multiply, and divide any
combination of real numbers (integers, fractions, radicals, etc).
Examples: Evaluate each expression without a calculator.
a. -9 + 17 = __________
b. 4 – 12 = __________
c. -6  -8 = __________
d. -18 ÷ -6 = __________
4
e. 3  = __________
5
f.
1 7
 = __________
10 18
i.
2 3
 = __________
11 4
g.
2 3
 = __________
11 4
h.
2 3
 = __________
11 4
Notes:

Solving Linear Equations: You need to know how to solve a linear equation in one variable.
Examples: Solve each equation and show all work in the space provided.
a. 7x – 4 = -18
b. -5(x – 8) = - 100
c. 2(3x + 1) = 10 – 4x
Notes:

Properties of Exponents: You need to know when to add, subtract, or multiply exponents. You also
need to know the properties of zero and negative exponents.
Examples: Simplify each expression without using a calculator.
a. g  g = __________
3
5
b.
y9
= __________
y7
 w
c.  
2
3
= __________
Notes:
1

Graphing Linear Equations: You need to know how to graph a line from an equation in any form
(slope-intercept, point-slope, standard) using the slope and a point or using the intercepts.
a. 3x + y = 8 [table of values]
X
b. 2x – 3y = 12 [by slope and y-intercept]
Y
Notes:

Operations with Polynomials: You need to know how to use the Distributive Property along with
combining like terms to add, subtract, and multiply polynomials.
Examples: Simplify each expression completely without using a calculator.
a. (-r3 + 5r2 + 9r + 3) + (r3 – 8r – 1)
b. (4u3 – u2 + 9u + 22) – (u3 + 3u2 + 12u – 15)
c. 6m2(8m4 – m2 + 7)
d. (4n + 11)(n – 8)
Notes:
2
SECTION I: HOMEWORK
Directions: Simplify each expression completely without using a calculator. Show work as needed in the
space provided.
2 5
1

2
1. 43  4-5
2.
3.
5 6
5
4.
 2x y 
2
5 3
7. (x – 9)(3x + 2)
5.
3 5

8 9
6.

8


2
8. (3x2 + 5x) + (x2 – 2x – 8)
Directions: Solve each linear equation for “n”. Show all work in the space provided.
9. 6(n + 4) = 12
10. 7n – 10 = 5n + 14
11. 9n = 2(3n + 7) – 4n
Directions: Graph each linear equation on the grid provided.
12. y = 13 x  7
13. 2x + 4y = 8
3
Section II: Geometry

Simplifying and Rationalizing Radical Expressions: You need to know how to simplify a radical
expression. You also need to know how to rationalize the denominator of a fraction.
Examples: Simplify each radical completely
a.
8
b.
75
b.
1
2
Examples: Rationalize and simplify
a.
1
3
Notes:

Pythagorean Theorem: You need to know when and how to apply the Pythagorean Theorem to any
right triangle to find a missing side length.
a.
b.
4
5
5
Notes:

Coordinate Geometry –You need to know how to plot points on a coordinate grid. You also need to
know how to find the distance, midpoint, and/or slope between any two given ordered pairs.
Example: Plot the points (9, 4) and (-1, 5) on the grid provided. Use the points to find the distance
between the points, the midpoint of the segment that connects the points and the slope of the line
through the points.
Distance =_____________
Midpoint =_____________
Slope =_____________
Notes:
4
SECTION II: HOMEWORK
Directions: Simplify each expression completely. Show work as needed in the space provided.
2
1. 40
2. 7 18  4 2
3.
6
Directions: Find the length of the missing side. Show work as needed and simplify your answers
completely. Please do not answer with an approximate decimal value (i.e. do not use your calculator to
round irrational answers).
4.
5.
6.
4
8
17
8
8
8
Directions: Find the distance, midpoint, and slope between the two given points. You may plot the points if
you find it helpful, but it isn’t necessary. Grids are provided for those who want to plot the points.
7. (0, 3) and (3, -1)
8. (-4, -3) and (5, 2)
Distance =_____________
Distance =_____________
Midpoint =_____________
Midpoint =_____________
Slope =_____________
Slope =_____________
5
Section III: Algebra 2

Functions: You need to know how to determine if an equation or graph represents a function. You
also need to know how to find the inverse of a function.
a.
To determine if a graph represents a function…
b. To find the inverse of a function…
Example: Find the inverse of function f(x) = 2x – 5

Factoring: You need to know how to factor an expression by GCF, difference of two squares,
grouping, and/or other methods and patterns.
Examples: Factor each expression
a. x2 + 9x + 20
b. n2 – 100
c. 2t2 – 8t + 30
Notes:

Solving Quadratic Equations: You need to know how to solve a quadratic equation by factoring or
applying the Quadratic Formula.
Example: Solve the equation y2 – 8y – 20 = 0 using the Quadratic Formula and check your answer by
solving the equation using factoring.
6

Operations with Rational Expressions: You need to know how to add, subtract, multiply, divide,
and simplify rational expressions.
Examples: Simplify the expressions completely. You may want to look back at page 1 section I to
review operations with fractions.
a.
2 1

x 3
b.
x 3

8 4y
SECTION III: HOMEWORK
Directions: Find the inverse of each given function. Write your answer using function notation.
1. f(x) = 3x – 9
2. g(x) = x3 + 1
Directions: Solve each equation by factoring. Show all work.
3. x2 + 8x – 20 = 0
4. 10x2 = 100x
Directions: Solve each equation by using the Quadratic Formula. Show all work.
7. x2 + 7x + 10 = 0
8. x2 – 2x = 8
7