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.
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
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:
logb 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.)
Sample Lesson - Reading
Reading 8.4: Drop the Base (and Add a New One)
There are some bases we really, really like (10, e, and 2 come to mind) and others we just don't have much use for. This reading introduces us to our mathematical gift receipt. It's how we get to take back the base we don't have much use for and walk out with one we really needed. Remember last Christmas when Aunt Enid gave you a golf ball cleaner and you swapped it for some killer headphones? Same concept.
Changing out a base all comes down to one simple equation:
logb x =
Just remember that the old base always goes on the bottom. It's like we're stomping it into the ground because we hate it so much and want to get rid of it. If you have a less violent way of remembering, go with that one. Also remember that this will give you a regular, probably-not-whole number, not a log. For simplicity and accuracy, it's best to avoid changing a base if you can.
Sample Lesson - Activity
Activity 8.4c: Problem Set
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 10, 11, 12
- Course Type: Basic
Algebra II—Semester A
Algebra I—Semester A
Algebra I—Semester B
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:CCSS.Math.Content.HSF-BF.A.1