# Quiz on Friday

There will be a quiz on properties of exponents on Friday. This will cover all material in 5-1, 6-1, and 6-2, but not the material on inverse functions.

# End of First Quarter

The first quarter officially ended November 8. I will accept work towards the first quarter marking period until I leave the building on Friday, November 10. The last official grade of the first quarter are the reteaching sheets I handed out on Monday; the Kuta worksheets assigned on Wednesday will count toward the second quarter.

# Complex numbers / quadratic test

There is a test on complex numbers and quadratics on Friday, November 3. This test will be worth 50 pts.

# Chapter 3 Test

The chapter three test will be Thursday, Oct. 19. This test will cover solving and graphing linear systems and inequalities, as well as basic matrix operations.

# Delta Math

All students are expected to join the appropriate class on Delta Math. There will be assignments; students are also encouraged to use the resources for additional study.

To join your class, go to https://www.deltamath.com/

If you have an existing account, log on and add my teacher code; if you don’t, create one. The teacher code is 559492

There is an assignment that is automatically assigned when you join. To receive full credit, complete a total of 10 total problems (of 16 assigned). Additional exercises earn extra credit. However, only the first four problems you complete in each section will be counted. This assignment is due Monday, October 16.

All students are expected to join the Khan Academy Algebra II class. There will be assignments; students are also encouraged to use this resource for further study.

To join Mr. Hartzer’s class, login at https://www.khanacademy.org and select “Coaches”. Then enter this under “Join a class”: VR3JMK94

Note that you will not automatically receive assignments that were given before you joined; I’ll have to assign them to you manually.

The first required assignment is on matrices. You must complete a total of four points worth of exercises for full credit; additional exercises earn extra credit! Note that for this assignment, you must complete the exercise, but you don’t have to get 100%.

This is due Friday, October 13.

1 point exercises
Matrix Dimensions
Matrix Elements

2 point exercises
Multiply Matrices by Scalars

4 point exercise
Multiply Matrices

# Chapter 3 Quiz

The chapter 3 quiz has been moved to Friday, Sept. 29, due to the two half-days. It will still cover the same material (up to solving three-variable systems), even though we will start matrices on Thursday.

# Chapter 3 Quiz

The chapter 3 quiz is currently planned for Thursday, September 28.

The quiz covers graphing and solving two-variable linear systems, graphing linear inequalities, and solving three-variable linear systems. This is a five-question open-ended quiz.

# Welcome Back!

Welcome back to Hamtramck High School. This year, I’ll be teaching Algebra II, so I already know quite a few of you from last year, in Geometry. For those of you in Honors Algebra II, the main difference is that we’ll be digging in deeper, while keeping to the same pace.

On this website, you’ll find the daily PowerPoints (after you’ve seen them in class), as well as daily topics and information on any classwork or homework.

# The Volume of a Sphere

Here is a quick explanation for the formula of the volume of a sphere. This is based on the proof known to the Ancient Greeks.

For this, consider three objects:

1. A cylinder;
2. A cone with the point  on the bottom;
3. A hemisphere with the flat side down.

Each object has a height of r and a radius of r.

Take a slice of each object at some height h. The exposed surface (cross-section) will be a circle.

For the cylinder, the radius of this exposed circle will be r, because the radii of all circular cross-sections is r. So the area of the circle for the cylinder at height h is πr2.

For the cone, the radius of this exposed circle will be h, so the area is πh2.

By definition, each point on the hemisphere is r units away from the center. Each point on the exposed circle is at a height of h. Using the Pythagorean Theorem, the radius of the exposed circle is the square root of (r2-h2), so the area is π(r2-h2).

Note that this is the difference between the cylinder and the cone: This is the key.

Since, for each cross-section of the three objects, the area for the cylinder is equal to that of the cone plus that of the hemisphere, it must be the case that the volume of a cylinder is equal to the volume of a cone and the volume of a hemisphere, when all objects have the same radius and height.

We know the formula for the volume of a cylinder: πr2h. If h = r, then πr3.

We know the volume of a cone is one-third of this, so the volume of a hemisphere is two-thirds of this, 2πr3/3. The volume of a sphere is twice that of a hemisphere, that is, 4πr3/3.