The Ultimate Math 3 EOC Study Guide by Maddie https://padlet.com/themagicmaddie_12/3zomj4sfg4vc Math 3 made easy my friends en-us 2019-11-25 18:27:06 UTC 2023-12-12 16:26:42 UTC hello@padlet.com Quick Facts themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416316927 There's 17 questions on this one.
It's pretty important, but here's the gist of Math 3 Algebra. 

-Fundamental Theorem of Algebra.
-Identify parts of functions in and out of context. 
-Properties of exponents.
-Remainder Theorem.
-Relationships between functions.
-Rewrite and evaluate rational numbers and functions.
-Graph multi-variable equations.
-Systems of equations.
-Justify your answers using mathematical reasoning.
-Check for extraneous solutions.]]> 2019-11-25 18:31:11 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416316927 Fundamental Theorem of Algebra themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416322299 For math people: any polynomial with degree n will have n amount of roots.

For non-math people: the highest degree of the polynomial  is also the number of roots that equation has.

NOTE: Imaginary (complex) roots come in pairs.

The main purpose of this theorem is to find the number of roots (real or imaginary) an equation has. This normally helps us to solve equations quicker.

Example: 7x^3+210x^2+8
The above equation has three roots, because the highest exponent is raised to the third power.
It has the same amount of roots as
46987698567x^3. The coefficient doesn't matter in this case, just the exponent.

Still need some practice?
https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:polynomials/x9e81a4f98389efdf:fta/v/fundamental-theorem-of-algebra-intro]]> 2019-11-25 18:39:11 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416322299 Identify Parts of Functions in and out of Context themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416329288 Parts of a function include but aren't limited to input, output, domain, range, independent variable, dependent variable, relative maximum, relative minimum, maximum, minimum, intervals of increasing, and intervals of decreasing.

Input- the x-value
Output- the y-value
Domain- the extent to which the x-value can reach
Range- the extent to which the y-value can reach
Independent Variable- the input, or the value that is unaffected by the rest of the function.
Dependent Variable- the output, or the value that is affected by the rest of the function.
Relative Maximum- the highest point a function reaches in relation to a set area of other points.
Relative Minimum- the lowest point  a function reaches in relation to a set area of other points.
Maximum- the highest point a function reaches.
Minimum- the lowest point a function reaches.
Intervals of Increasing- points at which the y-value of a function is approaching positive infinity.
Intervals of Decreasing- points at which the y-value of a function is approaching negative infinity.

How to Identify These Out of Context:
In context, these elements can be found by looking at a graph and making note of each variable in interval notation. Below are links relating to how to work with each.

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/what-is-a-function

https://www.youtube.com/watch?v=G69wMz-eaoM

https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/use-a-graph-to-determine-where-a-function-is-increasing-decreasing-or-constant/

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:maximum-and-minimum-points/v/identifying-relative-and-absolute-maxima-and-minima

How to Identify These In Context:
Use the skills you know how to use from identifying elements of a function out of context, and turn it into just math. My advice to to just turn it into an equation, and solve it from there. 

Practice:
https://www.ixl.com/math/algebra-1/identify-functions

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/e/identify-composite-functions]]> 2019-11-25 18:50:47 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416329288 Properties of Exponents themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416832354 Exponents, like literally everything in math, have a ton of special rules. So here they are.

Quizlet:
https://quizlet.com/4130651/properties-of-exponents-flash-cards/

Chart:]]> 2019-11-26 18:37:05 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416832354 Properties of Exponents (continued) themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416834403 Generally, if there aren't parenthesis you add or subtract, and if there are then you perform the actual operation. Important rules to remember: 
If you have a negative exponent, reverse its place on the fraction (every number is over 1) and the exponent will become positive. 
For example, if you had something raised to the negative second power in the numerator, put it in the denominator and it will become one  over that term squared. 

Practice and Additional Resources: 
https://mcckc.edu/tutoring/docs/bt/exp_rad_log/Exponent_Rules_&_Practice.pdf

https://www.hasdk12.org/cms/lib3/PA01001366/Centricity/Domain/1431/laws_of_exponents_review.pdf

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:exponent-properties-review/e/exponent_rules

https://www.youtube.com/watch?v=kITJ6qH7jS0]]> 2019-11-26 18:39:43 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416834403 Remainder Theorem themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416837670 For Math People: If you divide a polynomial f(x) by (x - h), then the remainder is f(h).
For Non-Math People: If you divide one function by the input value minus the input value of another function, the remainder of the division problem is the value of the other function.
Example: f(4)/(4-2)=g(0)

Other Resources:
https://study.com/academy/lesson/remainder-theorem-and-factor-theorem.html

https://www.purplemath.com/modules/remaindr.htm]]> 2019-11-26 18:44:25 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416837670 Relationships Between Functions themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416843654 These are how functions interact with each other. For example, do functions have the same intercept? What about the same slope? Do they share any characteristics when graphed? 

All of these questions can be answered by graphing functions, and doing function-dependent math to discover defining characteristics. There's more on specific functions in the functions section, but for now there's some links below talking about how to find defining characteristics of specific functions, which can then be compared to discover relationships between them. 

About Functions:
https://courses.lumenlearning.com/waymakercollegealgebra/chapter/characteristics-of-functions-and-their-graphs/

https://www.khanacademy.org/math/algebra-home/alg-functions/alg-comparing-features-of-functions/v/comparing-features-of-functions-2-example-3

https://www.youtube.com/watch?v=I6VtHQ6lNyY

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/v/graphical-relations-and-functions]]> 2019-11-26 18:53:48 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/416843654 Quick Facts themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639343 There's 17 questions, all on functions! Below are the things that you need to know for the test. 

-Trigonometry
-Parent functions
-Function notation
-Compare functions across tables, graphs, and equations
-Inverses
-Logs
-End behavior
-Arc length
-Arc area]]> 2019-12-02 18:12:49 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639343 Quick Facts themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639586 There's 11 questions on geometry. The biggest thing is to know those formulas. 

-Points of concurrency
-Parallelograms
-Area and perimeter formulas
-Circle theorems
-Similar circles
-Pythagorean theorem
-Volume formulas
-Density
-Cross-sections
-Real-life examples (in context)

]]> 2019-12-02 18:13:04 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639586 Quick Facts themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639717 5 questions of the EOC are on stats. The concepts you need to know are right here. 

-Random sampling
-Types of sampling
-Estimation
-Sample variance
-Standard deviation
-Margins of error
-Measures of central tendency
-Interpreting data
-Using graphs]]> 2019-12-02 18:13:14 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418639717 Points of Concurrency themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418643720 In a triangle, a point of concurrency is where three lines, segments, or rays intersect at one point.
There are three main types of points of concurrency, as listed and explained below.

Incenter
-Formed by the intersection of the three angle bisectors.
-The incenter is the center of a circle that will be tangent to the sides of the triangle if drawn.

More Info:
https://www.khanacademy.org/math/geometry-home/triangle-properties/angle-bisectors/v/incenter-and-incircles-of-a-triangle

Practice Problems:
https://www.youtube.com/watch?v=nmQ8kqsnqRU

Circumcenter
-Intersection of the three perpendicular bisectors
-If a circle was drawn around the circumcenter, it would intersect each vertice once.

More Info:
https://www.khanacademy.org/math/geometry-home/triangle-properties/perpendicular-bisectors/v/circumcenter-of-a-triangle

https://www.khanacademy.org/math/geometry-home/triangle-properties/perpendicular-bisectors/v/circumcenter-of-a-right-triangle

Practice Problems:
https://studyres.com/doc/16432886/5.3a-circumcenters-worksheet-%E2%88%86-%E2%88%86

Centroid
-Intersection of the medians of each side. 
-The centroid is the center of gravity for the triangle. 

More Info:
https://www.khanacademy.org/math/geometry-home/triangle-properties/medians-centroids/v/triangle-medians-and-centroids

Practice Problems:
https://www.dummies.com/education/math/geometry/centroids-in-triangles-practice-geometry-questions/

Last But Not Least!
Each of these comes with some fancy rules, and relationships between the chords used to form the points of concurrency. ]]> 2019-12-02 18:18:07 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418643720 Parallelograms themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645549 In math three, you need to know how to find the area of parallelograms. The area is the same as the area of a rectangle, just base times height. 

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/parallelogram-area/v/intuition-for-area-of-a-parallelogram

When you think about it, it actually makes sense. The base is the length, and the height is the width. Instead of finding the area of two triangles, you simply find one and don't split in in half. 

A parallelogram is a quadrilateral with two sets of parallel sides. 

The video above shows everything you need to know to apply the knowledge, but here's some practice to make sure it sticks. 

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/parallelogram-area/e/find-missing-side-when-given-area-of-a-parallelogram]]> 2019-12-02 18:20:30 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645549 Area and Perimeter Formulas themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645686 We've been around it since the very beginning of our math careers. Area and perimeter. The two measures used to calculate dimensions of two-dimensional figures. 
Area- the interior space of an object, what can be colored in or filled. Found by multiplying the length and width.
Perimeter- the exterior space of an object, a fence or an outline. Found by adding all of the side lengths together. ]]> 2019-12-02 18:20:41 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645686 Circle Theorems and More Circles themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645871 This is a padlet made by yours truly previously, with everything you'll need to know about circles. It gives practice resources, so feel free to check those out!]]> 2019-12-02 18:20:55 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418645871 Pythagorean Theorem themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646043 The Pythagorean Theorem can be used to calculate an unknown side value in a right triangle.
Simply, it states that
a^2+b^2=c^2
A is the shortest leg, b is the longest leg, and c is the hypotenuse. 
Example:
If the shorter leg of a triangle has a value of 5, and the hypotenuse has a value of 12, what is the value of b?
5^2+b^2=12^2
25+b^2=144
b^2=119
the square root of 119 will be equivalent to b. B is equal to approximately 10.909. 

Additional Resources:

https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/geo-pythagorean-theorem/v/the-pythagorean-theorem

https://cdn.kutasoftware.com/Worksheets/PreAlg/Pythagorean%20Theorem.pdf

https://www.mathsisfun.com/pythagoras.html]]> 2019-12-02 18:21:09 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646043 Cross-Sections themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646174 Cross-sections are the results of cutting figures through vertical or horizontal planes. 

Horizontal planes will result in the cross-section appearing to be the base of the figure, while vertical planes will result in the cross-section being the height of the figure. ]]> 2019-12-02 18:21:18 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646174 Real-Life Examples themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646945 In order to pass the test and get the correct answers, you have to be able to use real-life examples. Here's some links to real-life examples. 

https://www.mathopolis.com/questions/skills.php?year=G

https://www.khanacademy.org/math/3rd-engage-ny/engage-3rd-module-7


]]> 2019-12-02 18:22:11 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418646945 Volume Formulas themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418657087 Volume is the measure of a the space inside of an object. So, if you were to fill it with water it would be the amount of water it could hold (in cubic units). The chart below shows all the volume and surface area formulas for the most common geometric figures. 

]]> 2019-12-02 18:35:33 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418657087 Volume Formulas (continued) themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418658950 Above, the lateral and curved areas represent sides that aren't straight lines. You don't need to know those for math 3, so don't stress them. However, if the chart above didn't make everything clear, here's some additional practice.

https://quizlet.com/2222771/volume-and-surface-area-formulas-flash-cards/

https://www.youtube.com/watch?v=3wuJJqlr6m0]]> 2019-12-02 18:38:00 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418658950 Area and Perimeter Formulas (continued) themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418664851 The chart above has all of the formulas you'll need to know for math three, most of which just involve using a scale factor. Below, there's some study guides and more information on area and perimeter.

https://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U07_L2_T2_text_final.html

https://quizlet.com/2537530/areaperimeter-formulas-flash-cards/ ]]> 2019-12-02 18:45:42 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418664851 Similar Circles themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418671726 The simple way of putting it is that all circles are similar. The complicated way of putting it is specific chords, lines, arcs, and measures in specific circles are similar, and on the test you'll have to identify similar parts of a circle. The similar chords and theorems about them are shown above, in the circles padlet. However, the facts that circles are similar needs to be proved.

https://mathbitsnotebook.com/Geometry/Circles/CRProveSimilar.html

The proof above explains everything, and the video below goes over it again. 

https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-circle-basics/v/seeing-circle-similarity-through-translation-and-dilation]]> 2019-12-02 18:55:04 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418671726 Sample Tests themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418832955 https://www.act.org/content/dam/act/unsecured/documents/geometry.pdf

https://canvas.dartmouth.edu/courses/4427/pages/practice-exams-math-3

https://www.varsitytutors.com/high_school_math-practice-tests]]> 2019-12-03 01:18:53 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418832955 Rewrite and Evaluate Rational Numbers and Functions themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833198 Rational Numbers- numbers that can be expressed as quotients of fractions. In this case, they're normally expressed as 1 over x.

Rational Equations- rational equations are equations involving rational numbers that leave variables remaining.

Rational equations are used to show relationships between times, and they often have points of discontinuity, and asymptotes.

Points of Discontinuity (holes)- Points where the graph just stopped, and the function cannot exist.

Asymptotes- values that the function approaches but never reaches. They are vertical and horizontal. Horizontal asymptotes are when the denominator equals zero, and vertical asymptotes are when the numerator equals zero.

Rationals are graphed in the first and third quadrants typically, but if negative they'll be flipped to the second and fourth.

More Info:
https://www.math.utah.edu/~wortman/1050-text-rf.pdf

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:rational/x2ec2f6f830c9fb89:rational-graphs/v/another-rational-function-graph-example]]> 2019-12-03 01:19:52 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833198 Graph Multi-Variable Equations themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833452 To solve two-variable and higher systems of equations, you must find a value for each of the variable that makes each equation true. This can be done by substitution, elimination, or graphing. This focuses on graphing. In order to find solutions to multi-variable systems of equations, you must find the place on the graph where they all intersect. 

For example, if the equations all intersect at point (2, 4) then the solution for x is 2 and the solution for y is four. 

For More Information:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:two-variable-linear-equations-intro/v/checking-ordered-pair-solutions-to-equations-1

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:two-variable-linear-equations-intro/v/2-variable-linear-equations-graphs]]> 2019-12-03 01:20:51 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833452 Systems of Equations themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833549 A system of equations is a collection of two or more equations with the same unknown.

They can be solved by graphing, elimination, or substitution.

Graphing
Plug the equations into a calculator, or draw them out on graph paper. By finding the point where the two equations intersect, you find the solution to the system of equations. The y-value will be the solution for y, and the x-value will be the solution for x. 

Example:
https://www.desmos.com/calculator/13z01tmntm

More Help:
https://www.mathplanet.com/education/pre-algebra/graphing-and-functions/solve-systems-of-equations-by-graphing

Elimination:
Elimination uses the least common multiple to add or subtract the equations, and eliminate a variable, thus making the equations have one variable and be easily solved. 

Steps to Solve:

1. Multiply both equations so that a variable value is the same on each equation. They should have the same absolute values, but one should be positive and the other negative.

2. Add or subtract the equation so that the variable value that is equal across equations cancels out.

3. Solve for the remaining variable.

Example: 
2x-5y=8
x-3y=24

-2(x-3y)= -2(24)

     2x-5y=8
+(-2x-3y)= -24

-8y=-16

y=2

Additional Info:
https://www.mathplanet.com/education/algebra-1/systems-of-linear-equations-and-inequalities/the-elimination-method-for-solving-linear-systems

https://www.khanacademy.org/math/algebra-home/alg-system-of-equations/alg-equivalent-systems-of-equations/v/solving-systems-of-equations-by-elimination

Substitution:
In substitution, you plug the equations into each other. For example, if equation one states that y is equal to a value, and equation two states that x is equal to a value, you would plug equation two into the x value of equation one, or plug equation one into the y value of equation two.  

Example: 
y=2x+4
y=3x+5

3x+5=2x+4

x+5=4

x= -1

For More Info:
https://www.purplemath.com/modules/systlin4.htm

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:systems-of-equations/x2f8bb11595b61c86:solving-systems-of-equations-with-substitution/v/practice-using-substitution-for-systems]]> 2019-12-03 01:21:16 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833549 Justify Your Answers Using Mathematical Reasonings themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833632 To justify your answers using mathematical reasoning, cite the problem and the elements of it. Here's some steps for justifying your answers using mathematical reasoning:
1.  Label all your work. 
2. Show all of your work, using known theorems, and concepts. 
3. Explain your answers, and cite your work from steps one and two. 
4. Explain why you chose to use the steps and operations you solved the problems with in steps one and two. 
5. Prove and explain the validity of your answer, again citing known theorems, proofs, and your work in the above steps. 
6. Use another line of logical to prove that the answer you've reached is accurate. 

Here's a video if more help is needed: 
https://study.com/academy/lesson/teaching-reasoning-in-math-types-methods.html]]> 2019-12-03 01:21:33 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833632 Check for Extraneous Solutions themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833742 Extraneous solutions are solutions that result when you solve an equation, but they don't work when you plug them back in.

In Quadratics:
The discriminant (b^2-4ac) can be used to determine how many real roots an equation has. If the discriminant is positive, then the quadratic has two real roots, if it's zero there's one real root, and if it's negative there's no real roots.

Otherwise:
Just remember to plug roots back into the equation.

In Depth:
Here's some more resources about extraneous solutions, and some practice problems with checking for them.

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:eq/x2ec2f6f830c9fb89:extraneous-sol/v/extraneous-solutions

http://clare.glk12.org/mod/book/tool/print/index.php?id=5825]]> 2019-12-03 01:21:52 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/418833742 Random Sampling themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237649 Random sampling is a part of statistics that is used in an attempt to collect truly random, and thus the best (not favoring a specific group) data. The mathematical definition is as follows:

Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected.

Example: 
200 cell phone users are randomly selected and asked if they have pets. 

Good random sampling should sample parties with nothing in common. 
This means all the people sampled cannot be at a football game unless the question must be asked to football fans. It cannot be asked to people at a gym, early risers, or only one set of socio-economic groups. 

More Info: 
https://www.investopedia.com/terms/s/simple-random-sample.asp

]]> 2019-12-03 18:26:22 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237649 Types of Sampling themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237752 First, there's random sampling. That's shown above.

Systematic Sampling
Systematic sampling follows a rule, system, or pattern.

Example:
Every eighth person to walk through a door is surveyed.

Stratified Sampling
The population is divided into groups based on some defining characteristic. This can be age, gender, or job.

Make sure to account for the proportion that a group is of the total population.

This data can then be used to show the overall opinion of the sample set, and the distribution of the data by defining characteristics.

An example could be showing the percent of people in certain age groups at a school or community center.

Cluster Sampling
The entire sample set is split up into multiple groups. Entire groups are then chosen to be surveyed. 

Example: 
100 people are split up into ten groups. Only people from groups 4 and 8 are surveyed.

Convenience Sampling:
Sample data is taken from the people near the person collecting the data. This data is bound to be bias as everyone has something in common.

Example:
Gurnoor asks everyone at a gas station how they feel about soccer.

Additional Resources:

https://www.mathsisfun.com/data/sampling.html

https://www.youtube.com/watch?v=pTuj57uXWlk]]> 2019-12-03 18:26:27 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237752 Estimation themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237830 Estimation is the act of finding an approximate answer that is close to the actual answer. In statistics, there are two types of estimation.

Point Estimation
Point estimation is a parameter that represents all parties, such as the mean. Point estimations should be as follows:

1. Consistent. The larger the sample size, the more accurate the estimation should be, as it represents a larger and more varied scale.

2. Unbiased. The parameter will represent the entire population, and not portions of it.

3. Most Efficient Parameter. The parameter chosen should have the least amount of variation from the rest of the data set.

More Info:
https://www.youtube.com/watch?v=4v41z3HwLaM

https://study.com/academy/lesson/how-to-estimate-in-math-definition-lesson-quiz.html#lesson

Interval Estimation
It's impossible to survey every single person on the planet about every single issue. Because of this, ranges can be created from sample sizes in an attempt to include all members that would be affected by a survey.

Example:
A survey of 25 early college students is taken, asking how many hours of sleep each got. The average is 4 hours. So, to try to represent the students not surveyed, the person conducting the survey would make a range, with 6 as the median. So early college students get 2-6 hours of sleep a night.
In order to check your estimates, you can use the probability theory to determine the confidence interval. One formula is x +/- t(s/square root of n).

More Info:
https://www.statisticshowto.datasciencecentral.com/interval-estimate/

https://www.khanacademy.org/math/statistics-probability/confidence-intervals-one-sample/estimating-population-proportion/v/confidence-interval-example]]> 2019-12-03 18:26:33 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237830 Interpreting Data themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237888 The data collected in statistics can be used to show trends in the population, which in turn help mathematicians to predict what a population will do. In order to interpret statistics, be aware of the margin of error and the standard deviations. This way you can predict with a range what someone in a specific percentage of a population will do. It can also help to look at a line of best fit, as will be mentioned in the "Using Graphs" section.

Another use for statistics can be using outliers to see what results are uncommon, and using the range to see the variation in opinions. Also, the mean shows what the typical sample would do, while the mode shows the most common sample, and the median can be used for reference in the data.

This can be put on a box-and-whisker plot as well, as mentioned in the second link below.

More Info:
https://www.statisticssolutions.com/interpreting-your-data-analysis-how-to-determine-statistical-significance/

https://www.youtube.com/watch?v=8nVFChsPG3g]]> 2019-12-03 18:26:36 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237888 Using Graphs themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237985 Graphs in statistics are box-and-whisker plots, which can be used to show the first and last numbers of a data set, the mean, the median, and the median of the quartiles. There's a link attached above, but here's another one and a visual. 

https://www.youtube.com/watch?v=Ive6_u1-b8o]]> 2019-12-03 18:26:44 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/419237985 Standard Deviation themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420014957 Standard deviation is based on a graph. It's known as the bell curve.

Standard deviation is also the square root of sample variance.

For Math People:
The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

For Non-Math People:
The standard deviation is a measure that's used to show how far each value is from the mean. 

All standard deviation uses the graph below. Each color coded section is plus or minus one deviation. Motion away from the mean to the left is minus a deviation, and motion from the mean to the right is plus a deviation. ]]> 2019-12-05 01:10:56 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420014957 Margins of Error themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420015019 Margin of error is the range of values above and below the sample statistic in a confidence interval.

Confidence Interval: The percent of certainty placed in a set of data. For example, you can be 90 percent sure that your data is accurate.

Example: If you have a 95 percent  confidence interval, and a margin of error of 3, your statistics will be within 3 points of the actual population 95 percent of the time. 

More Info:
https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/margin-of-error/

https://www.statisticssolutions.com/how-does-margin-of-error-work/]]> 2019-12-05 01:11:14 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420015019 Measures of Central Tendency themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420015088 Measures of central tendency are mean, median, mode, outlier, and range.

Mean
The average of the values of the data set. The mean is calculated by adding together the values of the data set and dividing by the number of values.

Example:
If five people all reported making two phone calls a day, then the mean would be found by adding (2+2+2+2+2) and then diving by 5 (number of values in the data set). You would get 2, and that is the mean for this problem.

More Info:
https://www.mathsisfun.com/definitions/mean.html

Median:
The median is the middlemost point in the data set. Meaning, if all the numbers are listed from least to greatest, then the number in the middle of everything would be the median.

Example:
1, 2, 3, 3, 4, 7, 8, 8, 9, 10, 11
7 is the median.

More Info:
https://www.mathgoodies.com/lessons/vol8/median

Mode:
Mode is the more recurrent value in a data set.

Example:
1, 2, 3, 3, 4, 7, 8, 8, 8, 9, 10, 11
The mode is 8.

More Info:
https://www.mathsisfun.com/mode.html

Outlier:
A point that lies outside of the overall pattern of distribution.

Outliers are either much smaller or much larger than the rest of the values in the data set.

Example: 
0, 20, 21, 22, 23, 24, 25, 26, 27

In the data set above, 0 is the outlier.

More Info:
https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/stats-box-whisker-plots/v/judging-outliers-in-a-dataset

Range:
The difference between the highest and lowest values in a data set. This is found by subtracting the lowest number in a data set from the highest number in a data set.
The range is good for getting a comprehensive of all the number you're facing, and how spread out they are.

Example:
0, 1, 4, 4, 6, 7, 8, 15, 15, 21

Range is 21-0
Range is 21

More Info:
https://www.mathsisfun.com/data/range.html]]> 2019-12-05 01:11:34 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/420015088 Sample Variance themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421401381 Sample variance tells us how far away each value is from the mean. It provides an idea of how different the collected samples are from each other, so the viewer knows how accurate the mean comes to representing the entire population. 

The formula for sample variance is show below. 

Sample Variance Example: 
https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/measuring-spread-quantitative/v/sample-variance]]> 2019-12-09 00:30:50 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421401381 Density themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421402306 Density tells us how much mass a substance has per unit cubed. This can be useful for finding whether or not an object can hold the weight of another substance. 

Density is fairly simple, it's mass over volume. These three things can work together in a relationship, as displayed in the the triangle shown below. 

Worked Example: 
https://www.thoughtco.com/how-to-calculate-density-609604]]> 2019-12-09 00:37:12 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421402306 Trigonometry themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421768561 Trigonometry utilizes triangles and the parts of triangles to find unknown values.

Video Explaining Trig:
https://www.youtube.com/watch?v=F21S9Wpi0y8

Basic Trigonometry was a math two concept, but to review what we need for math three (trig ratios) there's a great acronym for it.

S- Sine
O- Opposite
H- Hypotenuse

C- Cosine
A- Adjacent
H- Hypotenuse

T- Tangent
O- Opposite
A- Adjacent

Cosecant is the reciprocal of sine

Cotangent is the reciprocal of tangent

Secant is the reciprocal of cosine

Additional Reading on Ratios:
http://www.softschools.com/math/trigonometry/cotangent_secant_and_cosecant/

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/v/basic-trigonometry

In math three, trig is used to graphically. This means it's used in periods, the amplitude needs to be found, and there's formula. The graphs shown below are the trig graphs, and the formulas are below.

Definitions:

Amplitude- the highest point the graph reaches from the midline.

Period- the time it takes for the cycle to go through everything, before it will repeat itself.

Phase Shift- how far left or right a trig function moves.

Vertical Shift- how far up or down a trig function moves.

Formula:
For F(t) = A f(Bt – C) + D, where f(t) is one of the basic trig functions, we have:


the amplitude is |A|

the period is 2 pi/ B

the phase shift is C/B

the vertical shift is D

More Links:
https://www.purplemath.com/modules/grphtrig.htm

https://www.youtube.com/watch?v=P0iRHgp3--w
]]> 2019-12-09 18:20:11 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421768561 Parent Functions themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421785365
Parent functions all of our favorite kinds of functions, minus any shifts, compresses, or stretches that are applied by manipulating variable values.

If you're ever asked to identify a parent function from the equation, you can look at the highest degree, and if it has an absolute value, piecewise characteristics, or no variables (constant).

Identifying Piecewise Functions:
https://www.youtube.com/watch?v=vzytNmwSehw]]> 2019-12-09 18:44:43 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421785365 Function Notation themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421791014 Function notation is written as the value of a variable. Most common is f(x), pronounced "f of x." If f is replaced with Precious, it would be pronounced "Precious of x." This is just saying that f is a function of x, meaning x is the independent variable, and f is the dependent variable. Function notation is useful for telling the difference between two functions, and referring to them mathematically. 

Function Notation:
https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-functions-and-function-notation/v/understanding-function-notation-example-3]]> 2019-12-09 18:52:37 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421791014 Compare Functions Across Tables, Graphs, and Equations themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421860696 In order to compare functions presented in different mediums, you must be able to gather a set of values from an equation, or an equation from a set of values.

Finding a Set of Values
From the table, it's given. From the graph, you find each y-value that corresponds with an x-value. From the equation, you can plug in values for x, and then find the y-values. This can help you to compare the values outputed by each equation with a specific input value, which helps to compare them.

More Info:
https://www.youtube.com/watch?v=aElUAe7aYEA

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/understanding-function-notation-example-1

Finding an Equation
To find an equation from a set of values, find the first common difference for linears, second common difference for quadratics, and the third common difference for cubics. For absolute value equations, look for the same y-value for x-values that are equidistant from the minimum or maximum of the equation. For radicals, look for y-values that are the square roots of the x-values, and the use the same process (but with cube roots) for cube root equations. Lastly, look for "holes," or asymptotes.

More Info:
https://www.youtube.com/watch?v=dGghismIZfg

https://www.youtube.com/watch?v=plQP_-ol-o8]]> 2019-12-09 20:41:28 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421860696 Using Graphs (continued) themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421870255 Another kind of graph you'll see in statistics is the line of best fit. This line is on a scatterplot. The line of best fit is a line that goes through the mean in a data set, and attempts to connect all the points. The closer the points are to the line, the stronger the correlation is with each factor. ]]> 2019-12-09 21:02:53 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421870255 Inverses themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421893464 Inverses are equations that are opposite of each other. An example of this is a cube root equation and a cubic equation. There are three easy steps for solving an inverse.

Steps:
1. Replace f(x) with y

2. Switch x and y

3. Solve for y

It is possible for an equation to have an inverse that is not a function. To make sure that the inverse is a function, use the vertical line test.

Examples:
Radicals and Quadratics

Cubics and Cube Roots

Logarithms and Exponential

More Info:
https://www.khanacademy.org/math/algebra-home/alg-functions/alg-finding-inverse-functions/a/finding-inverse-functions

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx]]> 2019-12-09 22:05:03 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421893464 Logs themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421896959 Logarithms are equations that ask and answer "how many of one number does it take to get another number?" They do this by using base numbers and exponential equations. A log is most often used to convert an exponential equation into an easily answered form.

Converting to Logs:
Take the exponential base, and make it the base of the log.

Take the answer of the exponential equation, and make it the "of" value of the log.

Take the exponent assigned to the base in the exponential equation, and make it the answer to the log equation.

Converting back from logs is done by finding the inverse, or repeating these steps in the opposite order.

e:
e is for natural logs. It's written as lnex, with x being the variable and e being the base. It is the parent function of logs, and the true inverse for the exponential function. 

More Info on e:
https://www.youtube.com/watch?v=dsySragIVEk

https://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/

More Info on Logs:
https://www.youtube.com/watch?v=Zw5t6BTQYRU

https://www.youtube.com/watch?v=rBnQiLa2TYo

https://www.mathsisfun.com/algebra/logarithms.html]]> 2019-12-09 22:15:41 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421896959 End Behavior themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421901906 End behavior is how a function behaves as it approaches negative infinity, and how a function behaves as it approaches positive infinity. 

End behavior can be determined by following the rules as stated below: 

The value of f(x) as x approaches negative infinity is determined by the degrees of the highest degreed term. If it is even, then as x approaches negative infinity, f(x) approaches positive infinity. If the highest exponent has an odd degree, f(x) will approach negative infinity as x approaches negative infinity. 

In order to find the end behavior as f(x) approaches positive infinity, look at the sign of the highest exponential value. So, if the term used in the paragraph above was negative, then as x approaches positive infinity, f(x) will be opposite of what it is while x approaches negative infinity. If the value of the exponent is positive, then as x approaches positive infinity f(x) will approach the same value (negative or positive infinity) it approached when x was approaching negative infinity. 

Additional Help:
https://www.varsitytutors.com/hotmath/hotmath_help/topics/end-behavior-of-a-function

https://www.youtube.com/watch?v=PbSJHr-fg7I]]> 2019-12-09 22:30:06 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421901906 Arc Length themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421914621 Arc length is a portion of the circumference. While it'll be put in word problems, this value is asked to be solved for frequently. 

Arc length is dependent on the radius and the central angle. Arc length is found by multiplying the radius by the central angle. This is done in radians.

Arc Length:
https://www.omnicalculator.com/math/arc-length#arc-length-formula]]> 2019-12-09 23:14:35 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421914621 Arc Area themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421916716 This is also known as area of a sector. It's used for finding out portions of a circle, and the area of them.

This is done in radians.

The formula is equal to 1/2 r^2  times the central angle.

Arc Area:
https://revisionmaths.com/advanced-level-maths-revision/pure-maths/trigonometry/radians

https://www.mathopenref.com/arcsectorarea.html]]> 2019-12-09 23:22:54 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421916716 Unit Circle themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421922304 2019-12-09 23:44:01 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421922304 Resources for Lessons themagicmaddie_12 https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421923104 https://www.khanacademy.org/math/math3

http://ecfmath.weebly.com/math-3-final-review.html

https://www.youtube.com/playlist?list=PL2O7nE0C-zpuP9ma2DRpCLwyE8xV7H4hI]]> 2019-12-09 23:45:35 UTC https://padlet.com/themagicmaddie_12/3zomj4sfg4vc/wish/421923104