All Units
STOP an easy way to remember how to solve equations
S - Seperate T - Totally Alone Variable O - Opposites (make sure you do to the operation to both sides) to get rid of P - Please Check your work - plug the answer back in to see if it is correct
Rectangular Prism Surface Area (SA)
SA = 2lw + 2lh + 2wh * remember you decide what is the l = length, w =width, h = height. Some pictures may not label this for you. As long as you label the picture with w, h and l your answers will work!
Combining Like Terms
Step #1 - Organize your like terms. * you can use a highligther, underline or rewrite in a particular organized order Step #2 - Combine the coefficients that have same variable exponent level (remember exponents can not be added unless they are the same) examples: 2y + y 3y 2y2 + y note these variable exponent levels are different and thus can not be joined.
Discount (Proportional)
The amount by which the regular price of an item is reduced.
Volume (V)
The amount of space an object takes up *This is what is in the inside of an object and is the size it takes up.
Base
The number that is going to be raised to a power.
Exponent
The power to which a given number or expression is to be raised.
Slope (m) = Rise Run
The rise is up and down the y - axis the run is left to right on the x - axis Example y = 2/3x + 2
Simiarity Statement
The statement tells you how to match up angles and sides to each other.
Congruent Symbol
The symbol used to show that the sides in a shape are equal
Bar Graph (Histogram)
a bar graph presents data so that comparisons of different items can be made. * it is used to compare the frequency of data. * use a bar graph when you want to compare 2 or more sets of data.
Constant
a constant is a lone number that only represents itself example: 3x + 2 , the lone number is 2 and represent adding of 2 4c - 5, the lone number is 5 and represent the subtraction of 5
Parellogram
a quadrilateral with both pairs of opposite sides parallel
Tax (Proportional)
a required payment to a local, state, or national government. Tax is money that is added to the buyers cost of an item or service.
Cylinder
a solid bounded by a cylindrical (sides of the can) surface and two circle bases (top and bottom) * remember circle can be made up a diameter line going across the circle but ... we need to be using radius when determining volume or surface area. * a radius is the diameter / 2.
Rectangular Prism
a solid figure in which all six faces are rectangles
Operation
addition, subtraction, multiplication, division * this is the verb (action) for my math statement * it tells you what needs to happen Example: x - y tells you the action is to subtract in this expression statement
#21 Proportions Unit #2
an equation of ratios that two different ratios are equivalent See picture for example example: I have 1 candy bar for 3 people 1:3 is that the same as having 2 candy bars for 6 people 2:6?
Multiplicative Inverse Property
reciprocal - another name for Inverse States that the product of a number and its inverse is one . example 3/4 x = 12 Solve by multiplying by its reciprocal 4/3 * 3/4 x = 12 x 4/3 the 4/3 * 3/4 cancel each other out and leave you with just he x (variable) 12 x 4 /3 equals 12 so the answer will be x = 12
What is Slope (m)
slope is the rate of change between 2 points and can be written as an linear equation y = mx + b; m is the slope
Distributive Property ("Superman")
states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum. This is useful especially when dealing with the unknown # (the "variable:)
Corresponding Angles & Sides
the angles that occupy the same position in the shape, the corresponding angles are equal.
Term
the term is the pieces/steps of the math statement (expression) Can include the following: * lone number (constant) * variable * coefficient with a variable example: in the statement 3x + 2 - y there are 3 steps/terms 3x (coefficient with variable) and 2 (constant) and -y (variable)
Reading & Writing Expressions (Key words are a helpful hint on what to do)
* Addition - add, sum, in all, both, total, all together, plus, increase by * Subtraction - subtract, difference, left, take away, how many/much more, how many less, minus, decrease by, less * Multiplication - product, times, twice, multiply factor, double, triple * Division - quotient, divide, share, dividend ex - the product of 6 and h plus 8 6h + 8
≥ Greater to equal to
* Greater than or equal to, the minimum, at least the value to be true, cannot be smaller * closed circle means it includes that number on the number line ex: x ≥ 2
#23 Cross Multiplying aka "The Butterfly Method/Effect"
* Product of the numerator of one ratio and the denominator of the other ratio.
Line Graph
* a line graph presents data so that changes and trends over time can be identified and a comparisons can be made. *use when you have ongoing data * used when you want to show changes over time.
Line Plot
* a line plot shows the frequency of data values. The range determines the # of lines. The x's represent the data value. * useful when finding the range (value points) * Mode, mean, median set of data. * easy to identify outliers and clusters. * an outlier is a piece of data that is set far apart from the rest of the data. * a cluster is where data tends to group together. * best to use when you have a small range.
Inequality Unit #9
* a math statement that shows two expressions that are not equal to one answer! (it can have a range of answers that make it correct) * we can have answers ranging all the way to -∞, ∞ * No equal sign = we will use the symbols >, ≥, <, ≤ * always put the variable on the left side of the Inequality and let the symbol indicate what direction it will go in. example X < 3 see the picture for more examples
Pictograph
* a pictograph presents data using pictures or symbols * each picture or symbol represents and assigned amount of data * Use when you only have 2-6 categories * the key tells the # that each picture or symbol represents. Use when you have large amounts of data that is to big for a bar graph.
Pie Graph
* a pie graph shows how parts are related to the whole. * use when you want to show how a total amount of data is divided into parts. *can be used to show % * use when you have 3-7 categories
Stem-and-Leaf plot (stemplot)
* a special talbe where each data value is split into a "stem" and a "leaf" plot. * the "stem" is the first digit and the leaf is the last digit in a value. * useful when organizing numerical data * in the picture 72 for a grade would be represented with the stem being 7 (which represents 70) and the leaf part would be 2. * in the example there is a grade of 72, 72, 74, 75, 76, 79 that is represented on the first row of the stemplot
> Greater than
* greater than, more than, larger than, above * open circle means it does not include that number on the number line ex: x > 2
Solution Set
* it is a range ( meaning more than 1 answer( of numbers that satisfies the inequality X ≥ 15 the solution set {15, ∞} that means and number starting at 15 and going on forever would be true answer
≤ Less than equal to
* less than equal to , the maximum, at most, not greater than * closed circle means it includes that number on the number line ex: x ≤ 2
< Less than
* less than, smaller than, BELOW * open circle mean it does not include the number on the number line ex: x < 1
Special Rules for a Inequality "Rule Breaker"
*I flip my sign when . . . when multiplying or dividing by a negative number. * the sign will flip from < to > when this rule is in effect.
What is a Histogram?
*a graph that provides a visual interpretation of data indicating the # of pts, that lie within a range of valued (called the "CLASS"). * the frequency of the data falls in each class is depicted by the use of the bar. * a frequency distribution shows how often an item, a # of range occurs.
Histogram
*a histogram is a form of a bar graph in which categories are consectutive and equal intervals. * the lenght or height of each bar is determined by the frequency falling into that particular interval.
5.72 × 10⁹
5,720,000,000
5.72 × 10²
572
Plotting points on coordinate plane
A (4, 4) Quad 1 B (-3, -3) Quad III C (3, -6) Quad IV D (-5, 2) Quad II
Rhombus
A parallelogram with four congruent sides
square
A parallelogram with four congruent sides and four right angles.
rectangle
A parallelogram with four right angles and opposite sides equal
Trapezoid
A quadrilateral with exactly one pair of parallel sides
#20 Ratios Unit #2
A ratio is a comparison of two quantities; you can write a ratio in a variety of ways In words 3 to 5 with a ratio sign 3:5 as a fraction 3/5
Slope between two points
(y₂- y₁) / (x₂- x₁) First Thing to DO is label your ordered pairs (x₁, y₁) (x₂, y₂) -4 - 2 (1, 2) (5, - 4) 5 - 1 m = -6/4 simplify -3/2
3 × 10¹
30
3.05 x 10²
305
Types of Slope "Disco Hands"
4 different types of slope Positive Slope Negative Slope 0 Slope - flat line on the horizon Undefined - straight up and down
4.386 x 10⁷
43,860,000
5.3 × 10⁻⁶
0.0000053
4 × 10⁻⁴
0.0004
5.72 × 10⁻⁴
0.000572
7.8 × 10⁻³
0.0078
5.3 × 10⁻²
0.053
5.72 × 10⁻¹
0.572
7.8 × 10⁻¹
0.78
Histogram Set up "the Steps"
1) Organize & Collect Data into a table 2) Create Columns using data range - intervals - Frequency Picture shown is an example - example of favorite juices - data range (0-12), Intervals (skipping by 2s), frequency is the amount of students that picked.
300
3 × 10²
How Do I Combine Like Terms
1. Organize your like terms. You can use a highlighter, underline or rewrite in a particular order by term types. 2. Combine the coefficients that have the same Variable exponent levels examples 2y + y they are the same variable type and can have their coefficients added remember even if the 1 is not shown it is implied its there answer will be 3y
Solving Equations
1. the goal is to isolate the variable 2. the method is to do the same thing to both sides of the equation, using inverse operations * See the example in picture
2.4 x 10⁴
24,000
2.4327 × 10⁴
24,327
2.4327 × 10⁷
24,327,000
Cylinder Surface Area
2πrh+2πr² * the radius is the half line across the circle * the h = height which is the length of the side
Tip (Proportional)
Also known as a gratuity, it is a small amount of money in return for a service.
Scientific Notation
An easier way to write a very large or very small number.
two-step equation
An equation that contains two operations
Congruent Figures Unit #3
Congruent means has the same shape and same size. Their corresponding angles have the same measurement and their corresponding sides have the same measurement.
Similar Figure Symbol
Indicates the shape is the same but the size is different
Coefficient
Is a number in front of a variable (letter) to represent how many of that variable there is examples: 3x + 2 the coefficient is the 3 the statement means 3 times x plus adding 2 to your answer 4c -5 the coefficient is 4 the statement means 4 times c minus 5. * notice the picture circles the coefficient - you will be doing this in your statement to indicicate a coefficient
Example of Experimental Probability
Is acutally what happens when we test/experiment I flip a coin 10 times and get heads 4 times and tails 6 times. My experimental probability for heads is 4/10 = 2/5 my experimental probability for tails is 6/10 = 3/5 However, my theoretical probability would have been 5/10 for either heads or tails.
Coordinate Plane
Origin (0, 0) use as your starting point Ordered Pair - (x , y) (left to right, up and down) Quadrants - Split up in four make a C in counterclockwise order - I (+,+), II (-,+), III (-,-), IV (+,-)
Order of Operations (PEMDAS)
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction * this is the order that we do the verb (actions) in a math statement
#22 Ratio Boxes
Parts = Parts Whole Whole Example: 3 pieces 6 pieces 1 candy bar = 2 candy bar
Theoretical Probability
Probability based on comparing the number of possible favorable outcomes to the number of total possible outcomes
Experimental Probability
Probability that is based on repeated trials of an experiment. The ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed.
Surface Area (SA)
The total area of the surface (touchable) of a 3D object. * example - what wrapping paper would actually touch * touchable parts * remember area simple means the size of an object
Sale Price or Final Total Cost
This is the acutal cost paid either the total cost which is adding tip and tax or the sale price taking the original price minus the discount.
#24 Broken Butterfly
This is used when you have an unknown answer to solve for - set up the same way as the butterfly method (24 x 12) = 96 note 96 is the missing piece 3
Example of Theoretical Probability
Using a Dice what is the theoretical Probability of rolling a 4 - 1/6 Possible = 1 out of 6 possible answers if using a deck of cards with 52 cards in it possibility of getting the 6 cards (their are 4 in the deck) = 4/52 put in simplest form that is 1/13
Rectangular Prism Volume
V= lwh the volume is the area of its base x height x width * in this example I labeled the w, h and l for you, but that will not always be the case.
STOP
We can still use STOP to do the problem but now we will have two calculate lines/steps - remember to get rid of the annoying neighbor (constant) First to get the married couple (coefficient & variable) by themselves.
percent proportion
compares part of a quantity to the whole quantity using a percent.
Similar figures
figures that have the same shape but not the necessarily the same size. The corresponding angles have the same angle measurement and their corresponding sides are proportional. *** Use the butterfly Method to solve.***
Histogram Terms
frequency - the amount of occurences you have and is represented by a bar. interval - the increments that your titles represent on the x & y - axis mean -the average, obtained by adding the scores and then dividing by the number of scores median - the middle score; half the scores are above it and half are below it mode - most frequently occurring score class - range of values
Expressions
is a math statement that contains numbers, variables, and at least one operation. *It will not have an = (equal sign) in it. *the statement part of a math sentence
Variable
is a symbol that represents an unknown quantity. Such as x or y. * I love to use x but I could use anything I want, like m or k or j . . . * we will be using subsitition for a number for the letter in expressions
#25 Scale Factor
is the ratio of the size of an object in comparison to the actual size of the object For example - when using a map you might have 1 inch on the map of your neighborhood actually equal 4 miles. Your scale factor is a 1 to 4.
Markup
is when a store increases the price of of an item from what they actually paid the manufacture to what they sell if for to the customers.
Negatives when dealing with variables
when you are left with a negative variable and an answer you can simply swap their signs Example: - x = 5 this is the same as swap their signs x = -5
Equations
written mathematical statements in which two quantities are equal! Example: x + 5 = 8 * solution to an equation is the value that makes it a true statement in the equation above 3 would be the solution for x to make it true 3 + 5 = 8
Good Math for single variables
y really equal 1y - y really equals -1y good math does not need to show the 1 value as a coefficient mathematicians consider it redundant to have it there it can be assumed!!!
slope intercept
y=mx+b, where m is the slope and b is the y-intercept of the line. y-intercept is where is crosses over the y-axis!!! ordered pair will always be (x, 0)
Cylinder Volume
πr²h