Brain Dump - Period 1

GROUP 1

Irrational numbers Integers● Pi is the most famous irrational number ● Integers are numbers and their opposites● Irrational numbers don’t have a pattern ● Real numbers is the set of rational and irrational● To find perfect and imperfect square roots you use a square numbers root number line ● 0 is not considered a counting numberRational numbers Number Sense Number systems● Fractions are rational numbers ● Natural numbers consist of all numbers not Including 0● Any repeating decimal must have 9 as a denominator ● Real numbers are any and all numbers depending on the amount of numbers.● The set of integers does not include decimals or fractions ● Whole numbers are the set of counting numbers plus zero (0,1,2,3….) ● Rational numbers have a constant pattern and predictable outcomes.

Integers Estimating Imperfect Square Roots● An integer consists of both positive and negative numbers. ● When Trying to Estimate Imperfect square root:● Integers can be negative or positive whole numbers ● first see what perfect square roots it falls between● Integers with negatives or have a Zero can be subtracted ● then You’ll add the middle integer (ex. 3.5) ● To see if the square root less than the number given and from any other number and get an integer result● Positive integers or whole numbers and zero are neutral see if the square root is closer to The one Less than the other or greater than the Imperfect Square Root .Rational and Irrational Numbers Number Sense ● Rational numbers are numbers that can be expressed as theratio of two integers ● Rational numbers can have decimals that either terminate when they repeat they have a bar notation on top. ● Irrational Numbers are when you don’t know what the next 3

Integers Repeating Decimals● Irrational numbers do not repeat or terminate (nickname ● If you have a repeating decimal then you place that is crazy). number over 9.● Repeating decimals have a bar over the numbers that are ● How ever many numbers are at the top thats how many 9ś being repeated. will be needed at the bottom of the fraction, when doing a repeating fraction or decimal.● When finding the square root of a number you multiply the number by itself to get the square root.Fractions Number Sense● To convert a fraction to a decimal you divide the numerator ● Number Sense-essentially refers to a student's “fluidity by the denominator. and flexibility with numbers”.● To simplify a fraction to its lowest terms you find what number both the numerator and the denominator can be divided by.

Steps for solving equations by hand Scientific Notation1.Draw a line through the middle ● When writing a Number In Scientific Notation You need2.Distribute as needed ( If you have a Fraction you should multiply to have:everything by the fraction’s denominator) ● a base between 1 and 103.Combine Like terms ● Times 10 to a power4.Choose sides ● Example: 2.3*10^75.Use Inverse Operations to get the numbers and Variables on theright sidesSteps for Solving Equations using a Expressions LAws Of ExponentsCalculator and Equations1.Press Y= ● Exponential form- Exponent of a power indicates how2.Insert the left side of the equation into Y1= many times the base multiplies itself3.Insert the Right side of the Equation into Y2=4.Press 2nd, Trace,5, enter, Enter, Enter ● Multiply powers-If you are multiplying powers with the same base, keep the base and add the exponents

● When you write out an equation you use an equal sign and ● When you are using perfect squares and square roots youWhen you write out an expression you do not have to draw you number line and place your numbers● When you have two exponents with the same base you add the ● When you are finding the area of a number, you have toexponents and keep the base find the cubed root or square root of that number.● When you are dividing two exponents with the same base youkeep the bases but subtract the exponents Expressions and Equations● When you are multiplying a power by a power you multiply ● The negative sign in front of the exponent tells you thatthe exponents but keep the base. it is not happy and is telling you to move me and the● If you have a negative exponents then you turn that exponent to a fraction. (Ex. ⅕^2) exponent becomes positive

Algebraic expression● An algebraic expression is a mathematical phrase that can ● Scientific notation, mall to homecontain ordinary numbers, variables and operators like ● When multiplying scientific Notation you have toadd,subtract multiply the coefficients and add their exponents● When multiplying exponents with the same base keep the base ● WHen dividing Scientific Notation you have to divide theand add the exponents. coefficients and subtract their exponents.● When dividing exponents with the the same base keep the base ● With a calculator you have to put you problem in andand subtract the exponents. follow the steps above. SLOPE Expressions solutions and EquationsSlope: Solutions: ● X=3: one solution ● Slope “pers” like a cat

● Exponential Form ( Example) - x^n= x*x*x...X*X*X*x Multiple X, N- times (Another Example: 5^3= 5*5*5)●Solving equations steps Expressions and Equations● Product Law Of Exponents Example: P ○ (ab)^2=a^2 B^2 ○ (xy)^n= X^2 Y^2

Linear vs nonlinear functions (calculator)● non- linear functions have an exponent other than 1 & 0. 1. Stat● Linear functions are those whose graph is a straight line. 2. Edit● Linear functions in a equation have an exponent of 0 or 1. 3. Type x into l1 & y into l2 4. Stat 5. Calc 6. 4 7. Enter (3x) Functions● A function has a relation where each “x” value is paired with exactly one “y” value● Y values can be matched with more than one x● Vertical line test - if you can draw a line going up & down,

The four ways to be seen How to find the m and the bThere are four ways a function can be seen: 1. Graph- use rise/run to find the m, use the point where the graph touches the y-axis to find the 1. Graph 2. y=Mx+B 2. y=mx+b- use the number beside the x which is the m and the 3. Table number that stands alone is the b 4. Word form 3. Table- to put this in the calculator you press Stat, then you go to edit, x’s goes with L1, and y’s goes with L2, then press STAT again then slide over to CALC and push 4 calculate. 4. Word form- slope always pers and you can always turn it into a chart, the b will stand by itself and the m will always be beside the variable Functions Linear and Nonlinear Functions

System of Equations Graphing Functions● When you have more than one equation you know that it is ● When graphing a function you have to put the coordinatesa system of equations. in the right place, which will form a straight line.● You can make a slope or a graph with systems of equations. Functions

Formulas for Volume Formulas for area● The volume of A sphere is 4/3*pi*r cubed ● The area of a triangle is ½ bh● The volume of a cylinder is Pi*r squared* h ● The Area of a circle is Pi*R squared● The volume of a cone is ⅓ *Pi*r Squared*H ● THe area of a square is S^2● The Volume of a cube is S^2 ● The area of a rectangle is Length * Width● The Volume of a rectangular prism is L*W*H ● Volume is always cubed. Geometry Pythagorean Theorem● Every 2d figure ends with The unit of measurement^2 ● Pythagorean Theorem● Every 3d Figure Ends With He Unit of Measurement^3 ● a^2+b^2=C^2● You must put 3 as an exponent when cubing a shape. ● A = leg ,B =leg ,C = hypotenuse● You must put 2 as an exponent when squaring a shape. ● Must be a right triangle. ● When you are missing one of the legs, you subtract the hypotenuse and the other leg, then find the square root of

TransformationIN Translation problems The Shape with only letters are the ● Translations- slides but shape and size stays the sameoriginals. ● Rotations - turns in 90 degree increments but the sizeThe Shapes with (‘) Are Called Prime.Flip The Shape And its Reflected . and shape stays the sameTurn The Shape and its rotated. ● Reflections-a mirror image but the size and shape stays theSlide the shape and its translated same ● Dilations-get bigger or smaller but stays the same shapetips/reminders Geometry● Congruent means same shape & size. ● Rotations move clockwise or Counter Clockwise in 90● Similar means same shape different size degree increments● The original shape is always labeled with letters● Unoriginal shapes are labeled with primes ● When You move clockwise you move to the right● Prime is shown as ‘ beside the variable ● When you move counter clockwise you move to the left ● Complementary angles are 90 degrees

Angle relationships ● Angle relationships can deal with vertical angles and corresponding angles, supplementary angles and complementary angles, acute angles, right angles, obtuse anglesVerticalSupplementary angles Geometry Complementary angles● Supplementary - 180 degrees. ● Complementary - 90 degrees.● 180 is a straight line going vertical, Horizontal, Diagonal ● 90 degrees is a right angle, as in a corner of a square

Vertical angles Acute angles/ right angles ● Vertical angles- are going straight up and down ● Acute- Angle is when it is smaller than a right angle ● Right angle is when you have a letter “l”. Obtuse angles Geometry Corresponding anglesA obtuse angle is and angle greater than 90 degrees but less than A corresponding angle is when you have a line intersecting 2180 degrees. lines.

Scatter plotser ● Positive Correlation is when the number is getting bigger as it moves upward ● Negative Correlation is when the number decreases as it goes downward ● No correlation/Association is when the dots are everywhere And there is no Association between the dots Statistics Percentages from Table● When using scatterplots you have to make sure that the ● You have to add the percent total to the table. points/dots are almost equally separated on the slope/line. ● You can’t choose the percent of column for the table and● If there is an uneven numbers of points on one side of the the percent of rows. scatterplot it is not a strong correlation.● An Outlier is a point in a scatterplot that is away from all of the other points on the scatter plot.● Strong correlation means the dots are tighter to the line.

you must learn what a percentage is first and how to use/explain them ● Percentage- for every 100 (out of 100) ● Percents can be written as decimals,and fractions ● Percent also means per 100Statistics Percentages from Table● You have to divide the number by the total then multiply by ● 100.●