This year in Pre-Calculus was a journey that had its high points and low points. Here are the top five things I learned.

1.) Rationalizing the denominator, It is a concept that is very easy to mess up. Whether it is not multiplying by the conjugate or leaving a negative on the bottom it is something that has to be done with extreme care

1. take the conjugate of the denominator
2. multiply both the numerator and the denominator by the conjugate
3. distribute everything
4. simplify if necessary
5. multiply by -1 if the denominator is negative

2.) Geometric sequences with percent values, this is a concept that is very applicable to real-life situations

If you get a 5% raise you use (1.05)

If something depreciates by 20% you use (0.80 or 1-0.20)

3.) Graphing quadratic and linear equations, one of the most important skills in Pre-Calculus 11, because it appears in multiple units, it’s involved in absolute values, reciprocal functions, and inequalities.

4.) Completing the square with fractions, one of the concepts I struggled with the most.

(I had to work out my own strategy for this)

1. put brackets around everything with an “x”
2. to find the square number take your fraction, divide by two then square that number
3. bring it out and multiply by the coefficient
4. take your circle number and put it on the square

5.) Graphing reciprocal functions

1. plot your original parent function

2. locate asymptotes that will be at y=1 and y=-1

3. graph the hyperbolas