Intermediate Algebra Assignment for 1/15

We revisited solving quadratic equations today, now with the capability of evaluating negative radicands!

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Intermediate Algebra Assignment for 1/14, plus Test Warning

As we continue to explore the use of i to represent the square root of -1, and the consequences that such a definition involves, we revisited the topic of rationalizing today, and noted that since i is a square root, the rules of Simplest Radical Form require that we not leave i in the denominator of a fraction.

Our test on Unit 4 will be on Friday, January 18th. Please do not be absent on that day! If you know for some reason that you will be absent on that day, please arrange a time before the 18th to take the test! Otherwise, we will have to schedule a time for you to take the test during exam week.

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Intermediate Algebra Assignment for 1/11

More work with imaginary numbers today, in particular simplifying expressions that involve multiplying them or with higher powers. We saw in the videos we watched yesterday that powers of i don’t increase like other real numbers, but instead cycle through the numbers 1, i, -1, -i, and then back to 1 again.

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Intermediate Algebra Assignment for 1/10

We’ve started the second section of Unit 4, learning about complex and imaginary numbers. This is a new category of number, much like irrational or negative numbers, that mathematicians developed to handle equations that they previously had no ability to solve. We watched two videos to introduce this topic, but I recommend you watch the full story found here.

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Intermediate Algebra Assignment for 1/4, plus Quiz Warning

Still more work with simplifying radical expressions today, now with expressions that include variable components. The method of dealing with these terms, fortunately, is fairly straightforward.

We will have a quiz on our work in this unit so far on Tuesday, January 8th.

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Intermediate Algebra Assignment for 1/3

Radical expressions aren’t just for undoing powers of two, there are in fact roots for every conceivable power you might use as an exponent. Our lesson today was evaluating “n-th” (pronounced “ennth”) roots.

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Intermediate Algebra Assignment for 1/2

We expanded on the specifics of Simplest Radical Form today by adding the requirement that expression written in SRF have no radical expressions in their denominator. The process of tweaking expressions to accomplish this is called rationalizing.

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Intermediate Algebra Assignment for 12/20

Yesterday we discussed adding/subtracting radicals (and a bit of dividing). Today is multiplying

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Intermediate Algebra Assignment for 12/19

We have started Unit 4, a unit working extensively with radical expressions. We can treat these expressions as a class of numbers in their own way, with their own “rules” for adding, subtracting, multiplying, and dividing them. Today we started with adding/subtracting.

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Intermediate Algebra Assignment for 12/13, plus Test Warning

The last bit of new material for this unit takes us back to the connection between the roots/solutions of a quadratic and the x-intercepts of its graph. This relationship exists even with polynomials of higher degrees, which means we can use that relationship to factor using its roots! We introduced two tasks today:

  • Using the known roots of a polynomial to write the polynomial, and
  • Using the graphing calculator to find the zeroes, and by extension the factors, of the polynomial.

These are the last two new items, in addition to everything else you’ve learned this unit, that will appear on your Unit 3 test on Tuesday, December 18.

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Intermediate Algebra Assignment for 12/12

We reviewed the key features of parabolas today, but this time from an algebraic perspective. We’ve already seen that the roots of the parabola (aka the x-intercepts or the zeroes) are the solutions we get from the quadratic equation. We saw today that the equation for the Axis of Symmetry can be obtained from the standard form of a quadratic equation using the formula x = –b/(2a). And since the vertex is on the axis of symmetry, the x-coordinate of the vertex is that same value (and the y-value is obtained by plugging that x-value into the equation).

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Intermediate Algebra Assignment for 12/10

We took a moment today to pause and look back on the three methods of solving quadratic equations that we have discussed: factoring, the quadratic formula, and the square root method. We discussed when each method might be most efficient, but reinforced that point that the quadratic formula is always a valid solution method.

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Intermediate Algebra Assignment for 12/7

The third method of solving quadratics is to simply use the square root, but there’s a danger here: you still have two solutions. The + is built into the quadratic formula, but it still needs to be added here. And that falls to you, the solver!

Today’s lesson also included a brief revisit to word problems, this time resulting in a quadratic equation.

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Intermediate Algebra Assignment for 12/5

We did some more work with the quadratic formula today, specifically with simplifying the radical expressions we sometimes get when we apply it.

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Intermediate Algebra Assignment for 12/3

More work with solving quadratic equations today, this time with equations that did not factor. Our solution? The quadratic formula.

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Intermediate Algebra Assignment for 11/30

Part 1 of the unit was on graphing quadratic functions and identifying the key features of the parabolas we create. Part 2 is more algebraic, focused on solving quadratic equations by hand (and eventually finding those key features without the graph). Today was a review of factoring and how that method of algebraic manipulation allows us to solve these equations.

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Intermediate Algebra Assignment for 11/20

Today was Day 3 of the Desmos-based activities we’ve been using in class to re-introduce ourselves to parabolas. In class yesterday, many of you had some difficulty in properly describing parabolas or in identifying features of parabolas to ask about in order to guess which one your partner had chosen. This shows us that there is a need for proper vocabulary when describing these entities. Today’s lesson reviewed that vocabulary.

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Intermediate Algebra Assignment for 11/6

For the last major lesson of the unit, we are looking at solving rational equations. I made a notes sheet for today’s lesson and a custom video for reviewing it here.

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Intermediate Algebra Assignment for 10/30

We’ve moved on to the next phase of the rational expressions unit: Complex Fractions. Don’t be intimidated by their name! These are expressions that involve “nested fractions,” meaning the numerator and denominator of the expression are both fractions (or a sum/difference of fractions) themselves.

Remember the basic process for simplifying these beastly expressions:

  1. Combine fractions in the numerator (finding a lowest common denominator and so on) so you have one single rational expression
  2. Combine fractions in the denominator (LCD, etc.)
  3. Keep the top fraction, flip the bottom fraction, and change the operation to multiplication (KFC)
  4. Simplify.

There are several videos online you could watch with more examples. I recommend this one and its follow-up here. The video posted here is also good. If you want more, search for “Simplifying Complex Fractions”

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Intermediate Algebra Assignment for 10/24

We started a mastery quiz in class today, and we will spend some more time finishing it tomorrow. This will end up pushing our traditional quiz to Monday, October 29. Make a note.

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