This week we started our final unit of precalc 11 which is Trigonometry.
we leaned the Sine law and the cos law
and CAST
week17 in pc
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Category Archives: Math 11
week 14 in pc
This week in precalc 11 we learned about reciprocal functions and asymptotes.
Reciprocal Functions have invisible no-go lines where the two lines can not touch, they are called the horizontal/vertical asymptotes.
week 13 in Pc
This week in Pre-Calc we learned about absolute value functions and solving absolute value equations.
The main thing to know is that if it is an absolute value equation it can never be negative.
Ex
Since it can never ever be negative you have to flip up the negative points when you graph it.
week 12 in pc
This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.
When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a prefect point, you will not be able to be completely accurate. To solve get everything equal to zero.
Example:
- y = x2 – 5x + 7
- y = 2x + 1
Make both equations into “y=” format:
They are both in “y=” format, so Set them equal to each other
x2 – 5x + 7 = 2x + 1
Simplify into “= 0” format (like a standard Quadratic Equation)
Subtract 2x from both sides: x2 – 7x + 7 = 1
Subtract 1 from both sides: x2 – 7x + 6 = 0
Start with: x2 – 7x + 6 = 0
Rewrite -7x as -x-6x: x2 – x – 6x + 6 = 0
Then: x(x-1) – 6(x-1) = 0
Then: (x-1)(x-6) = 0
Which gives us the solutions x=1 and x=6
Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers
The matching y values are:
- for x=1: y = 2x+1 = 3
- for x=6: y = 2x+1 = 13
Our solution: the two points are (1,3) and (6,13)
week 11 in pc
This week in Pre Calculus 11 we learned about Graphing Linear Inequalities in two variables. The solutions to these inequalities are represented by a boundary line and shading one side of the line.
Ex:
key notes
choosing any coordinate (the easy one is 0,0) and seeing if the statement is true or false.
week10 in pc11
This week has been a review week.
The thing that I think are difficult is infinite geometric series.
At first I do not know what is difference between sequence and series, now I know sequence is list and series is sum .
key notes:
week 9 in pc
Something I’ve learned this week is about domain and range.
At first I am so confused with domain and range, then I asked teacher.
that is what I learned from week 9.
week 8 in pc
This week in pc we analyzed the quadratic function. In the equation each variable represents something that can change the graph.
positive sign, the graph moves up, negative sign, the graph moves down.
positive sign, the graph moves right, negative sign, the graph moves left.
positive sign, the graph opens up, negative sign, the graph opens down.
greater than 1, the graph is stretched vertically, between 0 and1,
the graph is compressed vertically.
week 7 in pc11
This week we learned discriminants. A discriminant is a part of the quadratic formula and can determine the number of solutions in a quadratic equation without solving the equation.The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:
The “±” means you need to do a plus AND a minus, so there are normally TWO solutions
The blue part (b2 – 4ac) is called the “discriminant”, because it can “discriminate” between the possible types of answer. If it is positive, you will get two normal solutions (two real roots), if it is zero you get just ONE solution (one root), and if it is negative you get imaginary solutions (unreal roots).
that is what I learned from week 7
week 6 in pc11
this week we learned how to solve quadratic equation.
we had 3 ways to solve quadratic equations.
example:
Completing the square and quadratic formula can be used in any quadratic equations. Some quadratic equations cannot be solved by factoring.
that is what I learned from week 6.