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Math - 21 - Prep Lessons

The document outlines prerequisite topics for Math 21, covering pre-algebra, functions, and trigonometry. It includes specific skills such as simplifying expressions, solving equations, evaluating functions, and understanding trigonometric identities. Additionally, it provides practice questions for each topic to reinforce learning.

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jgjeon0901
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20 views3 pages

Math - 21 - Prep Lessons

The document outlines prerequisite topics for Math 21, covering pre-algebra, functions, and trigonometry. It includes specific skills such as simplifying expressions, solving equations, evaluating functions, and understanding trigonometric identities. Additionally, it provides practice questions for each topic to reinforce learning.

Uploaded by

jgjeon0901
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Math 21 Prerequisite Topics

1. Pre-algebra topics

(a) Simplifying Expressions (cancelling, adding, subtracting, multiplying expressions)


(b) Special Products
(c) Factoring
(d) Laws of Exponents
(e) Laws of Logarithms
(f) Solving Equations and inequalities (Linear, quadratic, rational, exponential, and logarithmic)

2. Functions

(a) Domain, range, x- and y- intercepts


(b) Evaluating functions
(c) Odd and Even functions
(d) Graphs and properties of common functions
• Linear Functions
• Quadratic Functions
• Cubic Functions
• Polynomial Functions
• Exponential function
• Logarithmic functions
• Trigonometric functions

3. Trigonometry

(a) Identities (Pythagorean, ratio, reciprocal, sum and difference, double angles)
(b) Evaluating trigonometric/circular functions
(c) Solving trigonometric and inverse trigonometric equations
(d) Trigonometric functions (domain and range, graph)
(e) Inverse trigonometric functions (domain, range, graph)
(f) Evaluating inverse trigonometric functions

1
Prep Questions

1. Simplify the following:


4x + 8
(a)
2x + 4
(b) (3x − 2y)2
(c) (a − b)3
x2 − 4x + 4
(d)
x2 + x − 6
(2x2 y 3 )3
(e)
4x3 y 2 − 2x2 y
2. Simplify (2x)−3 and 2x−3 .

3. Evaluate/Simplify the following:


3 0
(a) 0
vs 3
(b) 24 + 2−3
(c) e0 and 30
(d) ln 1, log 1, and log3 1
(e) log2 0 =?
(f) log3 3, ln e, and log 10
1
(g) log3 9 and log3 ( 81 )
(h) cos 45◦ , cos 3π
4
, tan(− π4 )
7π
(i) Find the trig values of θ = 6
and θ = − 2π
3
.

4. Solve for x:

(a) 3x2 − 8x + 3 = 0
1 4
(b) =
2x + 5 2x − 1
2
(c) x − 4 = 0
(d) |7 − 2x| = 9
(e) 2x + 3 = 8
(f) 2 cos(2x) − 1 = 0
(g) 4 sin2 (x) − 3 = 0
√
5. What is the difference between the solution set of x2 = 4 and x = 4?

6. Let f (x) = −2x2 + 5x + 3.

(a) What is f (−1)? f (2x)?


(b) Find the x and y intercept/s of f (x)
(c) Find the domain, range, then graph.

7. Graph the following. Identify the domain, range, and important points.

(a) y = x
(b) y = x2

2
(c) y = x3
(d) y = |x|
(e) y = ex
(f) y = ln(x)
(g) y = cos x
(h) y = sin x
(i) f (x) = −2x + 4
(j) y = ( 12 )x − 3
(k) y = log2 (x) + 3

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