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
- take the conjugate of the denominator
- multiply both the numerator and the denominator by the conjugate
- distribute everything
- simplify if necessary
- 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)
- put brackets around everything with an “x”
- to find the square number take your fraction, divide by two then square that number
- bring it out and multiply by the coefficient
- 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
