Algebra 2

2^2x-1 = 8
log₂(7x + 9) = 1
9^x = (1/3)^2x-4
ln(2x + 5) = ln(3x - 3)
The number of new chain saws sold t years after the introduction of a new model is given by the function y = 2300 ln(8t + 3). How many chain saws will be sold 5 years after the new model is introduced? Round your answer to the nearest whole number.

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Unit 7 - Rational Functions

Terms to Know

Terms to Know:

complex conjugate
polynomial
coefficient
quadratic
theorem
Descartes
synthetic
fraction
factor
function
constant

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 7.1: Inverse Variation

Section 7.2: Graphing Rational Functions

Section 7.3: Multiplying and Dividing Rational Expressions

Section 7.4: Adding and Subtracting Rational Expressions

Section 7.5: Solving Rational Equations

Important Questions: Answer the following Questions

The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.

x = -1, y = 29
x = 8, y = 11
x = 3, y = 12
x = 3/7, y = 7/6

Perform the indicated operation.

(6a²/b) / (3a⁴/5b²)
[(t² + 4t - 21) / (t² + t - 12)] - [6 / (t - 4)]
[(x² - 2x - 35) / (x² - 4x - 21)] / [(x² + 9x + 20) / (x² - x - 12)]
[p² / (p + 6)] x [(p² + 11p + 30) / (p² + 6p)]
(7m²/3n⁵) x (8n⁶/10m⁴)
For Valentine’s Day, a chocolate store plans to produce a chocolate-covered strawberry in the shape of a heart. The initial cost for the store to produce this item is $560. The store estimates that it will cost $0.84 to make one heart-shaped chocolate-covered strawberry. How many of the heart-shaped chocolate-covered strawberries must the company produce before the average cost for the item is $1.25? Round your answer to the nearest whole number.

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Unit 8 - Sequences and Series

Terms to Know

Terms to Know:

Sequence
Terms
Finite Sequence
Infinite Sequence
Rule
Series
Summation Notation
Sigma Notation
Factorial

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 8.1: Defining and Using Sequences and Series

Section 8.2: Analyzing Arithmetic Sequences and Series

Section 8.3: Analyzing Geometric Sequences and Series

Section 8.4: Finding Sums of Infinite Geometric Series

Section 8.5: Using Recursive Rules With Sequences

Important Questions: Answer the following Questions

Write a recursive rule for the sequence. Then find a₄.

-2, -7, -12, -17, ...
r = 1/5, a₁ = 125
a_n = 3 - 2n
2, 9, 37, 149, ...

You recently have been offered a job that pays you a monthly salary of $3500 and guarantees you a monthly raise of $180 during your first year on the job.

Find the general term of this arithmetic sequence.
What will your monthly salary be at the end of your first year of work?
In preparation to buy a new video game that costs $65, your friend plans on saving money each month for the purchase of the game. Your friend initially starts her savings with $10 in January, and plans on saving 10% more during each successive month. After what month will your friend be able to purchase the video game?

Find the next term in the pattern and then write a rule for the nth term.

2, 9, 16, 23, ...
-3, 6, -9, 12, ...
1/5, 2/10, 3/15, 4/20, ...

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Unit 9 - Trigonometric Ratios and Functions

Terms to Know

Terms to Know:

arccosine
arctangent
cotangent
arcsine
trigonometric function
trigonometric
radian
cosecant
inverse function
cosine
secant
function
sine
tangent
angle
adjacent

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 9.1: Right Triangle Trigonometry

Section 9.2: Angles and Radian Measure

Section 9.3: Trigonometric Functions of Any Angle

Section 9.4: Graphing Sine and Cosine Functions

Section 9.5: Graphing Other Trigonometric Functions

Section 9.6: Modeling With Trigonometric Functions

Section 9.7: Using Trigonometric Identities

Section 9.8: Using Sum and Difference Formulas

Important Questions: Answer the following Questions

Evaluate the given trigonometric function using the graph above for Questions 1-4.

sin Θ
cos Θ
tan Θ
cot Θ

Verify the identity.

sin² x + sin² x cot² x = 1
1 - [cos² x / (1 + sin x)] = sin x

Evaluate.

cot(495°)
sec(-240°)

Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.

-560°
170°

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Unit 10 - Probability

Terms to Know

Terms to Know:

Probability
Distribution
Outcome
Function
Event
Statistics
Percentage
Sum
Mean

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 10.1: Sample Spaces and Probability

Section 10.2: Independent and Dependent Events

Section 10.3: Two-Way Tables and Probability

Section 10.4: Probability of Disjoint and Overlapping Events

Section 10.5: Permutations and Combinations

Section 10.6: Binomial Distributions

Important Questions: Answer the following Questions

You spin a spinner that has equal spots numbered 1–8. Find the probability of the event described.

1. You spin a 4.

2. You spin a composite number.

3. You spin a multiple of 2.

4. You spin a number less than 1.

Evaluate the expression.

5. ₁₂P₅

6. ₇C₄

7. ₁₃C₇

8. ₉P₄

A small bag contains 6 pennies, 5 nickels, 3 dimes, 5 quarters, and 2 one-dollar coins.

9. You choose one coin at random from the bag. What is the probability that you choose a one-dollar coin or a dime?

10. You choose one coin at random, do not replace it, and then choose a second coin at random. What is the probability that you choose a quarter followed by another quarter?

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