This document provides a 15 problem review for students taking Calculus with Analytic Geometry. It covers important topics like trigonometric functions and their relationships, converting between degrees and radians, the unit circle, graphing rational functions, solving equations involving exponents and logarithms, and more. Students are instructed to attempt each problem on their own before checking the answers provided to assess their understanding. Additional resources are also included for topics needing more review.

1. F O R C A L C U L U S W / A N A LY T I C G E O M E T R Y M T H 1 7 3
ARE YOU READY?

2. ARE YOUR READY
• The following Power Point will consist of15 math problems that
every student should be accustomed to solving before entering into
the following class. Students should attempt to solve each problem
on their own than check their answers (see last page) to see how
they did. Instructional links will be provided in case the students
needs additional help.
• Most professors of Calculus with Analytic Geometry will tell you that
the trigonometry portion of the course is the most important
prerequisite of the course and is often overlooked by students. See
the link below for quick review of trigonometry
http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

3. PROBLEM 1
Know Your Trig Functions & Their Relationships

4. PROBLEM 2
Know The Relationship Between The Trig Functions and
the Right Triangle
cos 𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
tan 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
cot 𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
sec 𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
csc 𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

5. PROBLEM 3
Converting the following degree to radians by multiplying
by
𝜋
180
30°

6. PROBLEM 4
Knowing the basic angles in degrees and radians
Degrees 0 30 45 60 90 180 270 360
Radians 0

7. PROBLEM 5
Knowing The Unit Circle.

8. PROBLEM 6
Use the Leading Coefficient Test to determine the end
behavior of the graph.
−4𝑥3
𝑥 − 1 2
(𝑥 + 5)

9. PROBLEM 7
Using Long Division of Polynomials Divide
(𝑥2
+10𝑥 + 21) 𝑏𝑦 (𝑥 + 3)

10. PROBLEM 8
Find The Vertical Asymptote of The Rational Function
𝑥
𝑥2 − 9

11. PROBLEM 9
Find The Horizontal Asymptote of The Rational Function
4𝑥2
2𝑥2 + 1

12. PROBLEM 10
A ball is thrown vertically upward from the top of the
Leaning Tower of Pisa (190 ft) with an initial velocity of 96
ft/sec. During which time period will the ball’s height
exceed that of the tower?

13. PROBLEM 11
Write each equation in its equivalent exponential form:
2 = log5 𝑥
Write each equation in its equivalent logarithmic form:
𝑏3 = 8

14. PROBLEM 12
Solve The Equation By Completing The Square
𝑥2
+ 10𝑥 − 4 = 0

15. PROBLEM 13
Rationalize The Denominator
8
1 − 5

16. PROBLEM 14
Solve the equation (check the proposed solution)
7 +
48
𝑎 − 8
=
6𝑎
𝑎 − 8

17. PROBLEM 15
Perform The Indicated Operations (without calculator)
2
3
+
1
4
=
2
3
−
1
4
=
2
3
÷
1
4
=
2
3
×
1
4
=

18. ANSWERS
1) The Graph Falls To The Left and Falls To Right
2) x+7
3) Vertical asymptotes at x = 3, x = -3
4) Horizontal asymptote y = 2
5) Between (0,6) seconds
6) 52
= 𝑥, 3 = log𝑏 8
7) 𝑥 = −5 ± 29
8) −2 1 + 5
9) a = 8, However, there is no solution since the following would
yield a division by zero.
10)
11
12
,
5
12
,
8
3
,
1
6