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Online tutoring for MATH 110N students
www.khanacademy.org
WHAT IS KHAN ACADEMY? www.khanacademy.org
Khan Academy is a free, online, educational community which offers
lessons, videos, and so much more in a variety of subjects. Many
students use Khan Academy as a supplemental resource to learn and
reinforce their math skills. Each topic has a group of videos and
exercises to help explain what it is and how to do it, like a teacher
would in a classroom. These exercises reflect what is taught in the
videos and can be done as many times as you’d like.
USING KHAN ACADEMY
To start learning and find what you’re looking for, check the playlist
below and then search for things in the search bar of Khan Academy.
When you search for something, you will notice that it could reference
a Video (represented by on the playlist) or a Skill (represented by
on the playlist). So if you’re looking to learn how to add and subtract
negative numbers, you can search for the video “Adding numbers with
different signs” (which is 5 minutes and 33 seconds long); make sure
when you find it that it brings you to a video. If you then want to
practice exercises relating to this topic, you can then search for
“Adding and subtracting negative numbers” which is an exercise set
with 3-5 problems in it.
“What to Search” is what you type in the search bar. What you are
looking for is written exactly as shown here and is case-sensitive;
remember that a symbol means “Video” and a symbol means
“Skill”.
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Topics
What to Search
-Fractional Exponents & Radicals
16
3
1
8
205
2873
51
53
-Radical Equations
xx 285
2
-Imaginary Number i
(9 + 2i)(8 – 3i)
1
2
i
-The Quadratic Formula
a
acbb
x
2
4
2
-Completing the Square
82
2
xx
using
2
2
b
Introduction to rational exponents (4:59)
How to rewrite a radical expression as a single exponential
term (example) (4:01)
Understanding fractional exponents
Simplifying radicals (9:44)
Simplifying square roots (5:35)
Simplifying square roots
Simplifying square roots 2
Adding and simplifying radicals (7:56)
Adding and subtracting radicals
Multiply and simplify a radical expression 2 (3:07)
How to rationalize a denominator (10:17)
Solving radical equations (3:10)
Solving radical equations 3 (4:21)
Radical equations
Introduction to i and imaginary numbers (5:19)
Adding and subtracting complex numbers
Multiplying complex numbers (5:31)
Multiplying complex numbers
Dividing complex numbers (4:57)
Dividing complex numbers
How to use the quadratic formula (16:31)
Using the quadratic formula
Solving quadratic equations by completing the square
(14:05)
Solving quadratics by completing the square 1
3
-Parabolas (Vertex, Intercepts,
Minimum, Maximum)
Standard Form Formula
a
b
x
2
-Pythagorean Theorem
222
cba
-Sine, Cosine, Tangent, and their
Reciprocals
-Radians Degrees & Quadrants
rs
180
3602
135
4
3
36
11
55
Finding the vertex of a parabola example (5:39)
Vertex of a parabola
Graphing a parabola in vertex form (3:16)
Graphing parabolas in vertex form
Multiple examples graphing parabolas using roots and
vertices (16:04)
Graphing parabolas in standard form
The Pythagorean theorem intro (10:45)
Pythagorean theorem 1 (4:32)
Pythagorean theorem
Basic trigonometry (9:16)
Example: Using soh cah toa (4:04)
Trigonometry 0.5
Basic trigonometry II (12:11)
Trigonometry 1
Secant (sec), cosecant (csc) and cotangent (cot) example
(4:43)
Reciprocal trig functions
Introduction to radians (10:50)
Rotation by radians and quadrants (3:50)
Example: Converting degrees to radians (7:01)
Example: Converting radians to degrees (3:19)
Degrees to radians
Radians on the unit circle
Finding arc length from radian angle measure (2:38)
Example: Radian measure and arc length (3:29)
Radians and arc length
Unit circle manipulative (1:45)
Unit circle intuition
Example: Calculator to evaluate inverse trig function (3:27)
Evaluating inverse trig functions
Inverse trig word problems
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-Law of Sines and Cosines
C
c
B
b
A
a
sinsinsin
Abccba cos2
222
Baccab cos2
222
Cabbac cos2
222
-Graphing Sin and Cos
BxAy sin
BxAy cos
AAmplitude
B
Period
2
Law of sines (5:57)
Law of sines for missing angle (5:33)
Law of sines
Law of cosines (4:37)
Law of cosines to determine grade (6:40)
Law of cosines
Midline, amplitude and period of a function (4:57)
Example: Amplitude and period (8:20)
Example: Amplitude and period transformations (12:51)
Example: Amplitude and period cosine transformations
(10:42)
Example: Figure out the trig function (6:30)
Graphs of sine and cosine
-Manipulation of Trigonometric and
Pythagorean Identities
cos
sin
tan
sin
cos
cot
1cossin
22
22
csccot1
22
sectan1
Examples using Pythagorean identities to simplify
trigonometric expressions (3:06)
Manipulating trig expressions with pythagorean identities
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Sample Exam for Algebra & Trigonometry MATH 110
1. Simplify:
144
49
2. Simplify:
3
2
125
3. Simplify:
3
1
8
4. Simplify:
2873
5. Simplify:
20545
6. Simplify:
48512227
7. Rationalize:
53
51
8. Solve:
xx 285
2
9. Solve:
524 xx
10. Solve:
xx 22
6
11. Simplify:
)7)(34( ii
12. Rationalize:
31
32
13. Use the Quadratic Formula to solve: 2x
2
+ 6x + 3 = 0
14. Use the Quadratic Formula to solve: x
2
+ 4x + 5 = 0
15. Complete the Square: x
2
+ 2x = 8
16. Complete the Square: x
2
– 8x + 2 = 0
7
17. Find the Vertex:
35162
2
xx
18. Graph. Find the Vertex, y-intercept, x-intercept(s):
9)4(
2
xy
19. Graph. Find the Vertex, y-intercept, x-intercept(s):
86
2
xxy
8
20. Use the Pythagorean Theorem to solve for x:
21. Write the ratios for following trigonometric functions:
sin
csc
cos
sec
tan
cot
22. Convert to degrees:
5
2
23. Convert to radians:
225
24. Solve the right triangle; round all angles to the nearest degree:
9
25. Solve the triangle using the Law of Sines to start:
26. Solve the triangle using the Law of Cosines to start :
27. Graph one period of: y = sin2x
10
28. Graph one period of: y = -3cos½x
29. Simplify:
2222
cotsincostan
30. Simplify:
csc
1
sec
tan
