Chapter 8



Chapter 8

Simplifying Log Expressions

- Using Inverse Properties: Class example log327x = 3x

- Convert from Log to Exponential form, and back and forth

- Know your log properties, apply them with variables and numbers.

Solving Logs

- Make same bases ( 4x + 2 = 82x style

- Exponentiating both sides ( log3(x + 2) = 4 style

- Log both sides ( 3x + 2 = 10 style

- No Calculator, leave in terms of logs.

- No negative or 0 inside logs, so DOUBLE CHECK

Find the inverse of a log function

- Base of log by itself is 10

- Base of ln is e

Growth or decay word problem. Remember growth is (1 + r), decay is (1 – r), and r is the rate in DECIMAL form

Simplify exponential expressions, like 8.3 I think.

Graph exponential functions

- Cheap way is to plug in numbers

- Quick way is identify horizontal asymptote, growth or decay

Chapter 9

Graphs: Know how to find HA and VA for both simple and other rational functions.

Simplifying expressions

- Make sure you remember how to factor

- Don’t forget to flip for division

- When adding or subtracting, be careful with the signs and distribute carefully

Solving

- Cross multiply and solve, or multiply by LCD

- Double check your work, make sure the denominator does not equal 0.

Chapter 10

You HAVE to be able to complete the square!!!!

You HAVE to be able to identify conics.

Knowing the general equations will help, remember to make ellipses and hyperbolas equal to 1.

Make sure you know all forms, how to identify centers, vertices, co-vertices, and which way things open, wide\tall, etc.

Chapter 11

Write arithmetic and geometric sequences

- They might give you the numbers, and you figure out a1, d or r, and plug into formula

- They might give you random terms like a5 and a12 and you have to figure out the info.

- If you understand the information and know how to eliminate choices, it will help.

Find sums

- Arithmetic, know the formula, how to find n, first term, and last term.

- Geometric sum formula, no calculator, so know how to set up.

- Infinite geometric sum formula, know how to find a1, r, and know when it is no sum. The terms may be in sigma notation, or listed out. If listed out, remember “…” means infinity.

Recursive

- Know how to find the next term.

- Be able to identify is a sequence is arithmetic or geometric, and apply the right formula

Chapter 12

Combinations vs Permutations

- Know the formulas

- Permutations, order matters, jobs/positions implies permutations (captain and assistant captain, editor and assistant editor, president and vice president, roles in a play)

- Conbinations, order does not matter (4 captains, 3 members)

- For combinations, watch out for at least or at most

- At least examples involve roller coaster from test and homework

- At most example involve pizza toppings from notes.

There is some basic probability – Please read the problem carefully

There is an experimental probability problem – Please read the problem carefully

Binomial probability – That formula where you use it to figure out things like 7 heads out of 10 flips. The numbers will be manageable because you have no calculator.

Probability formulas, you will have one.

P(A or B) = P(A) + P(B) – P(A and B)

P(A and B) = P(A) * P(B)

P (A and B) = P(A) * P(B|A)

If you notice, you use the add formula if there is an ‘or’. Otherwise, it’s the multiplication formula.

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