Top 5 Things
a. 1.3 Geometric Sequences
b. 3.4 Developing and Applying the Quadratic Formula
c. 3.5 Interpreting the Discriminant
d. 5.5 Solving System of Equations Algebraically
e.6.4 The Sine Law
a. 1.3 Geometric Sequences
Q:Why it is important?
A:We learn about this because we encounter geometric sequences in real life, and sometimes we need a formula to help us find a particular number in our sequence.
Q:How to use it?
A:We define our geometric sequence as a series of numbers, where each number is the previous number multiplied by a certain constant. This constant varies for each series but remains constant within one series.
A geometric sequence is formed by multiplying each term after the 1st term by a constant, to determine the next term.
The constant is the common ratio, r , of any term after the first, to the preceding term.
The General Term:
We actually have a formula that we can use to help us calculate the general term, or nth term, of any geometric sequence. It is x sub n equals a times r to the n – 1 power.
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In this formula, x sub n stands for the particular number in that sequence. So x sub 4 stands for the fourth term in our sequence. The n stands for the term that we are looking at.
Exercise:
My geometric sequence is 4, 12, 36, 108, 324,……
Part 1 : Find 
Know- 
Part 2: Find 
b. 3.4 Developing and Applying the Quadratic Formula
Q:Why it is important?
A:A quadratic equation is any polynomial equation of degree 2, or any equation in the form 
, or any equation that can be expressed in that form.
The quadratic formula is a formula for solving any quadratic equation by using the general form 
, treating a, b, and c as constants.
Exercise:
c. 3.5 Interpreting the Discriminant
Q:Why it is important?
A:The discriminant is the part of the quadratic formula under the square root.
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A positive discriminant indicates that the quadratic has two distinct real number solutions.
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A discriminant of zero indicates that the quadratic has a repeated real number solution.
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A negative discriminant indicates that neither of the solutions are real numbers.
Exercise:
Find out the number of solutions the given equation has, by using its discriminant. Check whether the solutions are real or imaginary.
36x2 + 132x + 121 = 0
Choices:
A. 1 real and 1 imaginary solution
B. 2 real solutions
C. 2 imaginary solutions
D. None of the above
Correct Answer: D
Solution:
Step 1: 36x2 + 132x + 121 = 0
Step 2: Compare the equation with the standard form ax2 + bx + c = 0 to get the values of a, b and c.
Step 3: b2 – 4ac = (132)2 – 4(36)(121) [Substitute the values.]
Step 4: = 17424 – 17424 = 0 [Simplify.]
Step 5: Since the discriminant is zero, the quadratic equation has one real solution.
d. 5.5 Solving System of Equations Algebraically
Q:Why it is important?
A: Solving systems of equations with algebraic methods makes life easier .
There are essentially there different methods to solve systems of equations algebraically. They are listed and described briefly below.
The Graphing Method:When there is one variable solved in both equations, it is easy to use a graphing calculator. In this case, the calculator can be used to graph both equations. The intersection of the two lines will represent the solution to the system of equations.
The Substitution Method: There are two different types of systems of equations where substitution is the easiest method.
Type 1: One variable is by itself or isolated in one of the equations. The system is solved by substituting the equation with the isolated term into the other equation:
x + 2y = 7
y = x – 5
Type 2: One variable can be easily isolated. The systems are solved by solving for one variable in one of the equations, then substituting that equation into the second equation. Solve for a in the second equation, then substitute the second equation into the first.
2a + 3b = 2
a – 2b = 8
The Elimination Method: Both equations are in standard form: Ax + By = C. The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y,then solve for x.
8x + 11y = 37
2x – 11y = -7
Any of the other methods can be used to check your answer, or you can plug in the x and y values to insure that both equations give you true statements.
Exercise: Solving Systems of Equations Algebraically by Elimination
Follow the steps to solve this system of equations.
8x + 11y = 37
2x – 11y = -7
Step 1: Add the two equations.
Step 2: Solve for x.
Step 3: To find the y-value, substitute in 3 for x in one of the equations.
Step 4: Solve for y.
Step 5: Identify the solution as an ordered pair.
e.6.4 The Sine Law
Q:Why it is important?
A:We can use it to solve triangles that are not rectangles.
Exercise– Calculate side c