Quarter 3 NOtes
Unit 8- Sequences & Series
3/5 & 3/6- Regressions & Average Rate of Change
*Make sure you have STAT DIAGNOSTICS ON in the mode of your calculator.
*Find any regression asked of you by going to STAT and entering 2 lists. Then go back to STAT and CALC the type of regression you want.
*Be careful rounding!
*Average Rate of Change- the slope of the secant line to a non-linear function. (Change of y over the change of x)
*Make sure you have STAT DIAGNOSTICS ON in the mode of your calculator.
*Find any regression asked of you by going to STAT and entering 2 lists. Then go back to STAT and CALC the type of regression you want.
*Be careful rounding!
*Average Rate of Change- the slope of the secant line to a non-linear function. (Change of y over the change of x)
2/28 & 3/1- Geometric Series
*The sum of a geometric sequence is called a geometric series.
*The formula for this is on your reference sheet.
*Be careful to answer the question!!!
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit APLHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
*The sum of a geometric sequence is called a geometric series.
*The formula for this is on your reference sheet.
*Be careful to answer the question!!!
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit APLHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
2/27- Converting Between Explicit & Recursive Formulas
*Determine if the sequence is arithmetic or geometric (is there a common difference or a common ratio).
*Use the reference sheet for explicit formulas.
*To write a recursive arithmetic sequence, it's the first term (an-1) + d. Always state the first term!
*To write a recursive geometric sequence, it's the first term (an-1) *r. Always state the first term!
*Determine if the sequence is arithmetic or geometric (is there a common difference or a common ratio).
*Use the reference sheet for explicit formulas.
*To write a recursive arithmetic sequence, it's the first term (an-1) + d. Always state the first term!
*To write a recursive geometric sequence, it's the first term (an-1) *r. Always state the first term!
2/26- Arithmetic & Geometric Sequences
*Arithmetic Sequences- move from term to term by adding (or subtracting).
*The common difference, d, is the amount you add to get to the next term.
*The formula to find any term of an arithmetic sequence is on your reference sheet!
*Geometric Sequences- move from term to term by multiplying (or dividing).
*The common ration, r, is the amount you multiply by to get to the next term.
*The formula to find any term of a geometric sequence is on your reference sheet.
*Arithmetic Sequences- move from term to term by adding (or subtracting).
*The common difference, d, is the amount you add to get to the next term.
*The formula to find any term of an arithmetic sequence is on your reference sheet!
*Geometric Sequences- move from term to term by multiplying (or dividing).
*The common ration, r, is the amount you multiply by to get to the next term.
*The formula to find any term of a geometric sequence is on your reference sheet.
2/25- Recursive Sequences
*A recursive sequence finds a term by using & knowing the previous term in a formula.
*A recursive sequence formula always has a starting value and is defined by the previous term.
*Be careful when you are substituting and evaluating.
*A recursive sequence finds a term by using & knowing the previous term in a formula.
*A recursive sequence formula always has a starting value and is defined by the previous term.
*Be careful when you are substituting and evaluating.
Unit 7- Trig Graphs
2/13- Tangent Curve, Reciprocal Trig Curves, and Inverse Trig Curves
*Be sure you can determine where all asymptotes occur on tangent, cosecant, secant, and cotangent curves..
*Use your calculator to determine which graph is which (remember reciprocal trig functions do not have calculator keys- how do you type them in?).
*Inverse Trig Functions have restricted domain and ranges so that the curves are actually functions. Your calculator will only draw functions and shows the proper curves of all inverse trig functions.
*Be sure you can determine where all asymptotes occur on tangent, cosecant, secant, and cotangent curves..
*Use your calculator to determine which graph is which (remember reciprocal trig functions do not have calculator keys- how do you type them in?).
*Inverse Trig Functions have restricted domain and ranges so that the curves are actually functions. Your calculator will only draw functions and shows the proper curves of all inverse trig functions.
2/11 & 2/8- Horizontal (Phase) & Vertical Shifts of Sine and Cosine Curves
*Transformation rules follow the same for trig graphs as they do for all other functions.
*Transformation rules follow the same for trig graphs as they do for all other functions.
2/6 & 2/7- Stretching/ Shrinking Sine & Cosine Graphs
*Frequency (b): the number of full cycles over a 2pi interval
*Frequency is always multiplied to the x (or angle)
*Frequency is the "b"- y = asin(bx) or y = acos(bx)
*Frequency (b): the number of full cycles over a 2pi interval
*Frequency is always multiplied to the x (or angle)
*Frequency is the "b"- y = asin(bx) or y = acos(bx)
2/5 & 2/6- Changing the Height of Sine & Cosine Graphs
*Amplitude (a)- half the absolute value of the difference of the max and min.
*Amplitude is always positive.
*Amplitude is the "a"- y = asinx or y = acos x
*Midline- the line of oscillation of a sine or cosine curve.
*Amplitude (a)- half the absolute value of the difference of the max and min.
*Amplitude is always positive.
*Amplitude is the "a"- y = asinx or y = acos x
*Midline- the line of oscillation of a sine or cosine curve.
2/4- Graphing Sine and Cosine
*Sine curve: starts at 0, increases to it's max of 1, decreases to 0, decreases to it's min of -1, and then finishes back at 0.
*Cosine curve: starts at it's max of 1, decreases to 0, continues to decrease to it's min of -1, increases back to 0, and continues increasing to it's max of 1.
*Period- the length of 1 full cycle
*Cycle- a function that starts and stops at the same height after passing through a min and a max.
*Sine curve: starts at 0, increases to it's max of 1, decreases to 0, decreases to it's min of -1, and then finishes back at 0.
*Cosine curve: starts at it's max of 1, decreases to 0, continues to decrease to it's min of -1, increases back to 0, and continues increasing to it's max of 1.
*Period- the length of 1 full cycle
*Cycle- a function that starts and stops at the same height after passing through a min and a max.
3/22 & 3/23- Compound Interest and Exponential Growth and Decay Word Problems
*Recall the A=P(1 +/- r/n)^nt formula from Algebra.
*Recognize that if it is compounding continuously you use the Exponential Growth formula on the Reference Sheet (A = Pe^kt)
*Recall the A=P(1 +/- r/n)^nt formula from Algebra.
*Recognize that if it is compounding continuously you use the Exponential Growth formula on the Reference Sheet (A = Pe^kt)
3/19- The Exponential Function
*e is an irrational number
*y = a(b)^x is an exponential function where b > 0 but doesn't = 1. b must be positive.
*If b is a positive whole number then the function will be increasing. If 0 < b < 1 then the function is decreasing.
*e is an irrational number
*y = a(b)^x is an exponential function where b > 0 but doesn't = 1. b must be positive.
*If b is a positive whole number then the function will be increasing. If 0 < b < 1 then the function is decreasing.
3/16- Solving Log Equations
*Remember, you already know how to convert between exponential and logarithmic form and how to solve exponential equations!
*If you have an equation where log = log (same base) then you can removes the logs and solve. Be sure to use log properties to simplify!!!
*Remember, you already know how to convert between exponential and logarithmic form and how to solve exponential equations!
*If you have an equation where log = log (same base) then you can removes the logs and solve. Be sure to use log properties to simplify!!!
3/15- Converting between Exponential Form and Log Form
*y = b^x is exponential form
*y = log b (x) is log form
*Remember BAE (Base Answer Exponent) when converting: log (Base) Answer = Exponent
*LOGS are EXPONENTS!
*y = b^x is exponential form
*y = log b (x) is log form
*Remember BAE (Base Answer Exponent) when converting: log (Base) Answer = Exponent
*LOGS are EXPONENTS!
3/14- Logarithms as the Inverse of Exponentials
*Logs are EXPONENTS!
*Logarithmic Functions are the inverse of Exponential Functions.
*To get to the correct log key on your calculator, hit ALPHA WINDOW 5.
*To convert, remember log BAE!
*Logs are EXPONENTS!
*Logarithmic Functions are the inverse of Exponential Functions.
*To get to the correct log key on your calculator, hit ALPHA WINDOW 5.
*To convert, remember log BAE!
3/9 & 3/10- Solving Equations Involving Exponents
*If your VARIABLE is the BASE raised to a power, isolate the variable and raise both sides of the equation to the reciprocal exponent.
*If your VARIABLE is the EXPONENT, make sure you have the same base and then set your exponents equal to each other. You will often have to use exponent rules to make the bases match!
*If your VARIABLE is the BASE raised to a power, isolate the variable and raise both sides of the equation to the reciprocal exponent.
*If your VARIABLE is the EXPONENT, make sure you have the same base and then set your exponents equal to each other. You will often have to use exponent rules to make the bases match!
3/8- Fractional Exponents
*Bottom number goes in the crack!
*Doesn't matter if you do the root first and then the power- or if you prefer to complete the power first and then the root.
*Simplify by using all of your exponent rules!
*Bottom number goes in the crack!
*Doesn't matter if you do the root first and then the power- or if you prefer to complete the power first and then the root.
*Simplify by using all of your exponent rules!
3/6- Exponent Rules
*Click on the button below to review the exponent rules you have already learned.
*Click on the button below for the solutions to the 12 examples we did in class.
*Click on the button below to review the exponent rules you have already learned.
*Click on the button below for the solutions to the 12 examples we did in class.
3/23- Arithmetic Series and Sigma Notation
*The sum of any sequence is called a series.
*The sum of an arithmetic sequence is called an arithmetic series.
*There is a formula on the old reference sheet for A2T. There is not one on our Common Core reference sheet.
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit APLHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
*The sum of any sequence is called a series.
*The sum of an arithmetic sequence is called an arithmetic series.
*There is a formula on the old reference sheet for A2T. There is not one on our Common Core reference sheet.
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit APLHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
3/3- Log Properties
*MADS (when you multiply the same base, you add exponents, when you divide the same base, you subtract exponents).
*LOGS ARE EXPONENTS!
*If you are taking the log of a product, then you can separate by adding the logs.
*If you are taking the log of a quotient, then you can separate the logs by subtracting.
*If you are taking the log of something raised to a power, then the power can move out in front and multiply the log.
*MADS (when you multiply the same base, you add exponents, when you divide the same base, you subtract exponents).
*LOGS ARE EXPONENTS!
*If you are taking the log of a product, then you can separate by adding the logs.
*If you are taking the log of a quotient, then you can separate the logs by subtracting.
*If you are taking the log of something raised to a power, then the power can move out in front and multiply the log.