# Algebra II—Semester B

We put the "function" in "dysfunctional."

Yeah, that's right. Algebra's back for round two—and this time, it means business.

It's beefed up its stock of algebraic weapons—from inverse functions to conic sections—so it's going to take a whole lot more than the quadratic formula to get this guy to cry uncle. Good thing you've got Shmoop on your side. (And it doesn't hurt that you've been pumping a bit of iron yourself.)

Semester B is all about building, analyzing, and interpreting functions of all kinds. We'll get to know the end behavior of functions and describe it using numbers, words, and interpretive dance. Once we've learned about functions and their inverses (a.k.a. evil twins), we'll delve deep into logarithms, trigonometry, and conic sections. Finally, we'll end the semester with statistics and probability. Well, *probably*.

We've got activities, quizzes, projects, and more that cover:

- graphing, analyzing, and interpreting different types of functions;
- building and modeling with functions;
- logarithms, trigonometric functions, and conic sections;
- the normal distribution and real-world applications of statistics;
- combinations, permutations, and probability.

P.S. Algebra II is a two-semester course. You're looking at Semester B, but you can check out Semester A here.

## Course Breakdown

### Unit 6. Interpreting Functions

In this unit, we'll talk about how to identify a function type, how to set rules to make a function make sense in a real-world situation, and even how to compare multiple functions at once. (It's like comparing apples and oranges—except that it can actually be done.) By the time you're through with this unit, you'll be able to interpret and model with just about any function you come across.

### Unit 7. Building Functions

In this unit, we'll take a look at some particular types of functions, and see what exactly they can do. Whether they're linear or quadratic, polynomial or rational, even or odd, they all have interesting properties, and alone and together, they can be used to model different processes and phenomena in the world. And, unlike Transformers, functions don't have to pretend to be a truck or an airplane or a school bus half the time.

### Unit 8. Logarithmic, Exponential, and Trigonometric Functions and Conic Sections

We won't lie to you: we've packed a lot into this unit. We'll start off with logarithms and exponents and their rules. Soon after, we'll move onto the unit circle and trigonometric functions and finish up with conic sections. It might feel like we're on a sine-shaped roller coaster for a while, but at least we aren't going around in circles—or ellipses.

### Unit 9. Statistics

In this unit, we'll run the statistical gamut—from summary stats and the normal distribution to populations, samples, and simulations. We'll lay down the foundation for properly collecting real-world data and even get our hands dirty summarizing it. By the end of it all, your head will be fit to burst with all kinds of statistical knowledge.

### Unit 10. Probability

This unit is all about taking what we know about a situation and making the best possible guesses and extrapolations about it that we can. Some will be wrong, but we're also betting that a good number of them will be right! And given that our universe is a giant floating bubble of randomness and chaos, we think being able to predict events through math is pretty neat.

## Sample Lesson - Introduction

#### Lesson 4: Translating Between Logarithms in Any Base

(Source)

We've seen how important it is for a lot of our rules that bases of two pieces match. But what if they don't? Do we have any recourse if our logarithms can't communicate? We sure do. It's a little tool that works a bit like a translator. We put in pieces of what we know, and it spits out our log's equivalent in a brand new base. It's even better than Google Translate! (But don't tell it we said so. In any language.)

Changing bases is really just a one step process. It's just like changing shoes. (And way less confusing than changing phone service providers.) It follows this basic pattern:

log_{b} *x *=

In this scenario, the new base we were after was *a*. To get a real number out of this, we have to put it into a calculator, which is sort of a bummer. But when bases change, it's pretty unusual to end up with a whole number. Get your calculators warmed up and let's do a little translating. Vamanos! (Google Translate tells us this means, "Going all of us now!" Close enough.)

- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 10, 11, 12
- Course Type: Basic
- Category:
- Math

- Prerequisites:

Algebra II—Semester A

Geometry—Semester A

Geometry—Semester B

Algebra I—Semester A

Algebra I—Semester B

Just what the heck is a Shmoop Online Course?

Courses Tutorial

### Common Core Standards

The following standards are covered in this course:

CCSS.Math.Content.HSF-BF.A.1CCSS.Math.Content.HSF-BF.B.3

CCSS.Math.Content.HSF-BF.B.4

CCSS.Math.Content.HSF-BF.B.5

CCSS.Math.Content.HSF-IF.B.4

CCSS.Math.Content.HSF-IF.B.5

CCSS.Math.Content.HSF-IF.B.6

CCSS.Math.Content.HSF-IF.C.7

CCSS.Math.Content.HSF-IF.C.8

CCSS.Math.Content.HSF-IF.C.9

CCSS.Math.Content.HSF-LE.A.2

CCSS.Math.Content.HSF-LE.A.4.1

CCSS.Math.Content.HSF-LE.A.4

CCSS.Math.Content.HSF-LE.A.4.2

CCSS.Math.Content.HSF-LE.A.4.3

CCSS.Math.Content.HSF-TF.A.1

CCSS.Math.Content.HSF-TF.A.2.1

CCSS.Math.Content.HSF-TF.A.2

CCSS.Math.Content.HSF-TF.B.5

CCSS.Math.Content.HSF-TF.C.8

CCSS.Math.Content.HSG-GPE.A.3.1

CCSS.Math.Content.HSG-GPE.A.3

CCSS.Math.Content.HSS-IC.A.1

CCSS.Math.Content.HSS-IC.A.2

CCSS.Math.Content.HSS-IC.B.3

CCSS.Math.Content.HSS-IC.B.4

CCSS.Math.Content.HSS-IC.B.5

CCSS.Math.Content.HSS-IC.B.6

CCSS.Math.Content.HSS-ID.A.1

CCSS.Math.Content.HSS-ID.A.2

CCSS.Math.Content.HSS-ID.A.3

CCSS.Math.Content.HSS-ID.A.4

CCSS.Math.Content.HSS-ID.B.6

CCSS.Math.Content.HSS-MD.B.6

CCSS.Math.Content.HSS-MD.B.7

F-IF.7e

F-IF.7c

F-IF.7b