Monthly Archives: May 2018

Week 15 – Solving Rational Expressions

This week in math we learned how to actually solve the equation (solving for x)

 Here’s how to do it.

for example number one, 

  1. I cross multiplied to simplify
  2. I got my variable on one side of the equation
  3. I isolated “x”
  4. REMEMBER TO LIST NON-PERMISSIBLE VALUES

for example number two, it’s a bit more complicated

  1. Get the factor to have a common denominator
  2. Instead of making just the denominator common multiply everything by the common denominator (Numerator and Denominator)
  3.  Cancel out zero pairs (when a factor in the numerator is equivalent to the factor on the denominator)
  4. Expand (FOIL)
  5. Get variables on one side of the equation.
  6. Isolate for “x”
  7. LIST NON-PERMISSIBLE VALUES.

Things to remember;

  • Only cross-multiply when there are two values.
  •  Make sure to cancel out zero pairs
  • Multiply the whole thing by the common denominator

 

Week 14 – Multiplying and Dividing Rational Expressions

In earlier previous grades we learned to solve and simplify rational and irrational expressions and equations. A lot of people panic when they see expressions that include fractions, myself included. But it doesn’t need to be hard.

First, vocabulary learned in previous years.

  • Denominator
  • Numerator
  • Multiplying the reciprocal
  • Simplifying
  • Equivalent expressions
  • Factoring

All this vocabulary and concepts are still useful. But now we are including fractions!

By now we have learned how to factor expressions, if not remember

Common

Difference of squares

Pattern

Easy

Ugly

Example;

There is a new concept that relates to previous a pre-calculus unit similar to restrictions, known as non-permissible values. Non-permissible are basically x values that make the expression untrue or make it equal to nothing. If you did 6/0, you wouldn’t get an answer

Week 12 – Solving Absolute Value Equations Algebraically

A couple of weeks ago we learned how to solve absolute value equations by using algebra.

 

Verifying is how you can check for extraneous roots (Roots that give you a different answer). Make sure you remember it’s in absolute value form, so there’s never any negative values, if there’s ever any negative  you know that there are no solutions. If the left side does not equal the right side it’s an extraneous root.

Week 13 – Graphing Reciprocal Quadratic Functions.

Last week we learned about how to graph reciprocal functions.

The steps to solve.

1.) Graph the parabola

2.) Locate the invariant points

3.) Find the asymptotes

 

Three types of Quadratics

Positive Slope, Positive y-intercept

 

It never touches (0,0)

so no invariant points

 

Positive slope (can be negative), y-intercept=0

The asymptotes are touching the parabola

Positive or Negative Slope, opposite y-intercept

 

 

 

 

Candy Lab – Chemistry 12

Purpose of the lab: To find the (pH) and the molarity (M) of acids in a substance.

Materials: 

Candy (Blue Powder – Citric Acid) 10g.

(2) 50mL Beakers (H20) and (0.1M NaOH).

Drops of Phenolphthalein (C20H14O4).

A Flask.

a 10 mL measuring tube.

Funnel.

Burette.

Titration Stand w/ clamp.

Procedure:

1.) Weight out (10g) of candy (citric acid) on the scale.

2.) Combine the candy with H20 so the candy dissolves.

3.) Pour (10mL) of (water + citric acid) solution into the flask.

4.) Place 3-4 drops (C20H1404) in the flask.

5.) Carefully pour NaOH into the burette. Make sure the starting levels at 0.

6.) Slowly drop NaOH into the flask with your previous solution, once a color change is apparent, stop the flow of the NaOH.

7.) Recording and keep recording the quantity of NaOH that was added to the solution.

Photos: 

Results and Calculations:

Analysis:

My partner and my’s result was very close to the actual pH of citric acid as we got a pH of 3.13 and the actual pH was 3.2, the reason it was so close is that the pieces of blue powder were able to dissolve to make our solution very pure. Reasons, why our resulting pH was not exact, was that the particles did not dissolve completely. Another reason why our pH’s didn’t perfectly align is that we may have added more NaOH to the solution in the flasks, accuracy played a vital part in our results and we could have tried to be more precise in our procedure.

Week 11 – Graphing Linear Inequalities.

This last week we learned how to graph different types of equations

Grade 10 question

y=x+7

Now we are looking to solve this as an inequality

y>x-4

Right now we have 50% chance of getting it right

But by testing the inequality by putting 2 points in as a check (verify)

I like to use the points (0,0)

y=x-4

0, 0-4

0>-4 (CORRECT)

so the side would shaded in including (0,0)