MrE's Algebra Blog

Algebra 1a: CST Review

Square Roots: The `sqrt(25) = 5`.

The `sqrt(5)` can be approximated as somewhere between the `sqrt(4)` and the `sqrt(9)`.

`sqrt(9)=3`

`sqrt(5) = ?`

`sqrt(4)=2`, so `sqrt(5)` is closer to `sqrt(4)` than `sqrt(9)`.  A good guess could be 2.2?

Pythagorean Theorem: Only works for right – triangles. The 3 sides of the triangle are `a`, `b`, and `c`. `a` and `b` are the short sides and `c`, the side OPPOSITE the right angle is called the hypotenuse.

The theorem states:

`c^2= a^2 + b^2` (if you know the 2 smaller sides, `a` and `b`)

or

`a^2 = c^2 – b^2` (if you know the hypotenuse, `c` and side `b`)

or

`b^2 = c^2 – a^2` (if you know the hypotenuse, `c` and side `a`)

SNOW DAY #5

Algebra 1a: Chapter 9, Lesson 2, page 405.

Compound Sentences

Conjunctions and Disjunctions are like Intersections and Unions (respectively) from lesson 9-1. A disjunction of 2 statements is formed by connecting them with the word “or”. A disjunction is true when one OR both statements are true.

A conjunction of 2 statements is formed by connecting them with the word “and”. A conjunction is true when both statements are true.

Two of tonight’s homework problems solved by MrE are here! Just click it!

Snow Days #3 and #4!

Algebra 1a: Chapter 9, Lesson 1, page 400.

Sets, Intersections and Unions

A set is a well-defined collection of objects called members or elements.

• Roster notation LISTS the members of the set.
• Set-Builder Notation gives a DESCRIPTION of how the set is built.

The intersection of 2 sets `A` and `B`, written `A ∩ B` is the set of all members that are COMMON to both sets. We say ” A intersection B”.

The union of 2 sets `A` and `B`, written `A ∪ B` is the set of all members that are in `A` or `B` or in both. If an intersection is EMPTY, we say the intersection is the empty set which is symbolized as `∅`.

All of these concepts are described here too with examples!

Two of tonight’s homework problems solved by MrE are here! Just click it!

Algebra 1a Benchmark #6 – Chapter 8 TODAY!

Algebra 1a: Chapter 8 REVIEW! Make sure that you review:

1. Motion Problems

REMEMBER, diagrams are great to get you to understand what you are looking for. The tables in the book are also good techniques. The more pictures or diagrams you have, the better chance you have of understanding what steps you have to go through! GO SLOW!!

Here are some links to excellent D-R-T examples at the PurpleMath website. Its easier to link to these than show you the same thing!

2. Digit and Coin word problems.

Just remember to write the coin problems with the d (dime), q (quarter), n (nickel) preceeded by the value of the coin remembering that the d, q or n stand for the number of that type of coin. For example, `.05n + .10d = 2.05`. You can then multiply both sides by `100` to clear the decimals.

Remember too, that any 2-digit number can be expressed as `10x + y` where `x` is the digit in the tens place and `y` is the digit in the one (units) place. For example, the number `23` can be written as `10 * 2 + 3`. If we reverse the digits in the original number, the new number can be expressed as `10y + x`. The reverse of `23`, `32` can be written as `10 * 3 + 2`.

Here is a link for some examples of coin problems and here is a link for digit type problems (about 1/2 the way down the page)!

3. Solving Systems of Equations by Graphing

A set of equations for which a common solution is sought is called a SYSTEM OF EQUATIONS. A solution of a system of 2 equations in 2 variables (x, y) is an ordered pair that makes both equations true.

Take 2 linear equations and graph them (with at least 2 points for each linear equation) and where they INTERSECT is a “SOLUTION” to BOTH equations.

Pretty simple to do, but it can be time consuming in that you have to have graph paper and a ruler and some time ….

Here is a link with LOTS of examples from purplemath.com. It goes on for 2 pages so make sure that you see them both!

Algebra 1a: Chapter 8 Review

Review of Benchmark #6 began today and continues on Monday. Make sure your questions on the review are covered and you know HOW to solve these!

Ask questions!

Algebra 1a: Chapter 8, Lesson 6, page 387.

Digit and Coin word problems.

Just remember to write the coin problems with the d (dime), q (quarter), n (nickel) preceeded by the value of the coin remembering that the d, q or n stand for the number of that type of coin. For example, `.05n + .10d = 2.05`. You can then multiply both sides by `100` to clear the decimals.

Remember too, that any 2-digit number can be expressed as `10x + y` where `x` is the digit in the tens place and `y` is the digit in the one (units) place. For example, the number `23` can be written as `10 * 2 + 3`. If we reverse the digits in the original number, the new number can be expressed as `10y + x`. The reverse of `23`, `32` can be written as `10 * 3 + 2`.

Here is a link for some examples of coin problems and here is a link for digit type problems (about 1/2 the way down the page)!

Two of tonight’s homework problems solved by MrE are here! Just click it!

Algebra 1a: Chapter 8, Lesson 5, page 380.

Motion Problems

D-R-T Problems (otherwise known as DIRT problems). `D` is the distance, `R` is the rate (or speed like miles per hour [mph] or kilometers per hour [kph] or feet per second [ft/sec]) and `T` is the time. Be careful and make sure that if the rate is in mph, then the time has to be in hours. If the rate is in feet/sec, then the time has to match and be in seconds as well.

For those type of problems that have 2 people starting off, remember that the first person’s time is `t`, but the second person (who leaves later) actually has `t – x` time where x is the time delay of the second person leaving. For example if one person leaves at `t` and the second leaves 2 hours later, then the second person’s time is `t – 2`.

REMEMBER, diagrams are great to get you to understand what you are looking for. The tables in the book are also good techniques. The more pictures or diagrams you have, the better chance you have of understanding what steps you have to go through! GO SLOW!!

Here are some links to excellent D-R-T examples at the PurpleMath website. Its easier to link to these than show you the same thing!

Two of tonight’s homework problems solved by MrE are here! Just click it!