Integrated Math Midterm Review Team One Team Two Team Three Team Four 1 2 3 4

Integrated Math Midterm Review Turn In: Linear Part Two Packet & Linear Part Two Study Guide Get Out: Midterm Study Guide Pick Up: Calculator Team One Team Two Team Three Team Four 1 2 3 4

Memorize All & Use Know Pieces, Use Recognize Format

Question One - Create a table of x & y values -Plug in x, evaluate for y - Plot ordered pairs (𝑥,𝑦) Question One

Question Two Function Types Linear - Create a table of x & y values Quadratic Exponential Absolute Value - Create a table of x & y values -Plug in x, evaluate for y - Plot ordered pairs (𝑥,𝑦) Question Two

Question Three Function Shapes Linear: Straight Line Quadratic: Double Curve Exponential: Single Curve Absolute Value: V - Create a table of x & y values -Plug in x, evaluate for y - Plot ordered pairs (𝑥,𝑦) Question Three

Question Four Function Characteristics Linear: 𝑦=𝑚𝑥+𝑏 Quadratic: 2 in the exponent Exponential: 𝑥 in the exponent Absolute Value: straight line brackets - Create a table of x & y values -Plug in x, evaluate for y - Plot ordered pairs (𝑥,𝑦) Question Four

Function X values can’t repeat Y values don’t matter Question Five

Question Six Function: 𝑥 values can’t repeat Ordered pairs are in the form (𝑥,𝑦)

Question Seven Plug in 7 for 𝑥 in parentheses 𝑓 𝑥 means 𝑦 or the value of the function

Question Eight Isolate the variable Work backwards from PEMDAS Use inverse operations to move terms across the equal sign Question Eight

Question Nine Isolate the variable Work backwards from PEMDAS Use inverse operations to move terms across the equal sign Question Nine Undo the fraction in pieces: -multiply by denominator -divide by numerator

Question Ten Isolate the variable Work backwards from PEMDAS Use inverse operations to move terms across the equal sign Question Ten Combine like terms (same variable or just numbers)

Question Eleven Isolate the variable Work backwards from PEMDAS Use inverse operations to move terms across the equal sign Question Eleven Move variable to one side and all numbers to the other!

Question Twelve Isolate the variable Work backwards from PEMDAS Use inverse operations to move numbers across the equal sign Question Twelve Distribute to both terms in the parentheses using multiplication

Question Thirteen Combine like terms (same variable or just numbers) Move variable to one side and all numbers to the other! Number of Solutions 𝑥=# one False statement zero True statement infinite

Question Fourteen Identify variable (unknown value) Identify coefficients and operations Identify total (after equal sign) Question Fourteen

Question Fifteen Isolate the variable Work backwards from PEMDAS Use inverse operations to move numbers across the inequality sign Question Fifteen If you divide or multiply by a negative number as an inverse operation, you must flip your inequality sign! Graphing Inequalties <, > open endpoint ≤ , ≥ closed endpoint < , ≤ less than to negatives > , ≥ greater than to positives

Distribute to both terms in the parentheses using multiplication Question Sixteen Isolate the variable Work backwards from PEMDAS Use inverse operations to move numbers across the inequality sign Graphing Inequalties <, > open endpoint ≤ , ≥ closed endpoint < , ≤ less than to negatives > , ≥ greater than to positives

Question Seventeen Identify variable (unknown value) Identify coefficients and operations Identify total (after inequality sign) Question Seventeen Inequality Signs total is a maximum total > inequality total is a minimum total < inequality total can be reached include equal to line

Question Eighteen AND: connected Inequalities - Split inequality into two pieces to solve Middle section goes with both Graph both solutions on the same line Shaded in between Question Eighteen

Question Nineteen OR: Disconnected Inequalities - Solve each inequality separately Graph both solutions on the same line Shaded outside Question Nineteen

Question Eighteen Writing Inequalities <, > open endpoint value ≤ , ≥ closed endpoint value < , ≤ less than to negatives > , ≥ greater than to positives Question Eighteen OR: Disconnected Inequalities Shaded outside Written as two separate inequalities

Question Twenty One Writing Inequalities <, > open endpoint value ≤ , ≥ closed endpoint value < , ≤ less than to negatives > , ≥ greater than to positives Question Twenty One AND: connected Inequalities Shaded inbetween Lesser endpoint value on the left Greater endpoint value on the right # <𝑥<#

Question Twenty Two Forms of Linear Equations 𝑦=𝑚𝑥+𝑏 Slope Intercept 𝐴𝑥+𝐵𝑦=𝐶 Standard Question Twenty Two Linear Equation Outlaws 𝑥𝑦 multiplied variables 1 𝑥 variables in denominator 𝑥 variables under radicals 𝑥 absolute value brackets 𝑥 2 exponents besides one

Question Twenty Three Pick any value for 𝑥 Plug in chosen value for 𝑥 in parentheses Evaluate for the value of 𝑦 Follow PEMDAS Write the 𝑥 & 𝑦 values as an ordered pair (𝑥,𝑦) Question Twenty Three

Question Twenty Four Linear Table Characteristics - 𝑥 and 𝑦 must change by a constant amount - Change must use addition or subtraction Question Twenty Four

Finding Slope in Equations Must be in slope intercept form 𝑦=𝑚𝑥+𝑏 Isolate 𝑦 completely using inverse operations Slope is the coefficient of 𝑥 once 𝑦 is alone Question Twenty Five

Finding Slope from Two Points Use the slope formula: 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Label points and watch out for negatives! Or graph both points and use rise/run Question Twenty Six

Question Twenty Seven Vertical Lines 𝑥=# equation Goes through the 𝑥−axis Slope = # 0 Question Twenty Seven Horizontal Lines 𝑦=# equation Goes through the y−axis Slope = 0 #

Question Twenty Eight Domain: 𝑥 values Range: 𝑦 or 𝑓 𝑥 values - Order from least to greatest Question Twenty Eight

Question Twenty Nine Domain: 𝑥 values Range: 𝑦 or 𝑓 𝑥 values Plug in domain values one at a time for 𝑥, Solve for 𝑓(𝑥) values for range Question Twenty Nine

Question Thirty Domain: 𝑥 axis boundaries from left to right Range: 𝑦 axis boundaries from top to bottom -arrows mean it keeps on going: no boundary here! Question Thirty No boundaries: All real numbers Two boundaries: D #<𝑥<# R #<𝑦<# One Boundary: D 𝑥># or 𝑥<# R 𝑦>#, or 𝑦<#

Writing Linear Equations Write in slope intercept form 𝑦=𝑚𝑥+𝑏 𝑦-intercept 𝑏 is where line crosses 𝑦 axis Slope 𝑚 is 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 from point to point Question Thirty One

Question Thirty Two 8 Write in slope intercept form 𝑦=𝑚𝑥+𝑏 𝑦-intercept 𝑏 is where the 𝑥-value equals 0 Slope 𝑚 is 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 Question Thirty Two 8

Question Thirty Three Write in slope intercept form 𝑦=𝑚𝑥+𝑏 𝑦-intercept 𝑏 is a one time value What you start with, only happens once Slope 𝑚 is a repeating value Key words each, every, per Question Thirty Three

Question Thirty Four Write in slope intercept form 𝑦=𝑚𝑥+𝑏 Slope 𝑚 is the coefficient of 𝑥 𝑦-intercept 𝑏 is when the 𝑥−value equals zero Plug in 𝑥=0 to equation, solve for 𝑦 𝑥-intercept is when the y−value equals zero Plug in y=0 to equation, solve for 𝑥 Interpret meaning of intercepts & slope with variables! Question Thirty Four

Question Thirty Five Look at the number in parentheses Increasing #>1 Decreasing #<1 Find the rate by subtracting that number by 1 #−1=r Change decimal rate to percent with D2P Question Thirty Five

Question Thirty Six Look at the number in parentheses Increasing #>1 Decreasing #<1 Find the rate by subtracting that number by 1 #−1=r Change decimal rate to percent with D2P Question Thirty Six

Evaluating Exponentials Identify what the variable 𝑥 stands for Plug in given value for 𝑥 into exponent Follow PEMDAS to evaluate for 𝑦 or 𝑓(𝑥) Question Thirty Seven

Question Thirty Eight - Create a table of 𝑥 & 𝑦 values -Plug in input 𝑥, evaluate for output 𝑦 - Plot ordered pairs (𝑥,𝑦) Question Thirty Eight

Question Thirty Nine Exponential Formula Key Words Increasing, Growing: Growth 𝑦=𝑎 1+𝑟 𝑡 Decreasing, Shrinking: Decay 𝑦=𝑎 1−𝑟 𝑡 Compounded: Compound Interest 𝐴=𝑃 1+ 𝑟 𝑛 𝑛∗𝑡 Question Thirty Nine Writing Exponential Formulas 𝑦 : final amount 𝑎 or 𝑃 : original amount 𝑟 : rate as a decimal 𝑡 : time 𝑛 : number of times compounded per year

Question Forty Exponential Formula Key Words Decreasing, Shrinking: Decay 𝑦=𝑎 1−𝑟 𝑡 Question Forty Writing Exponential Formulas 𝑦 : final amount 𝑎 : original amount 𝑟 : rate as a decimal 𝑡 : time Evaluating Exponentials Identify what time variable 𝑡 stands for Plug in given value for 𝑡 into exponent Follow PEMDAS to evaluate for final amount

Exponential Formula Key Words Increasing, Growing: Growth 𝑦=𝑎 1+𝑟 𝑡 Question Forty One Writing Exponentials 𝑦 : final amount 𝑎 : original amount 𝑟 : rate as a decimal 𝑡 : time Finding 𝑡 for When Identify desired final amount Type exponential function into 𝑦= View table to find desired final amount under 𝑦 Corresponding 𝑥 value represents 𝑡

Question Forty Two - Create a table of n & 𝑎 𝑛 values -Plug in input 𝑛, evaluate for output 𝑎 𝑛 - Plot ordered pairs (𝑛, 𝑎 𝑛 ) Question Forty Two

Question Forty Three - Create a table of n & 𝑔 𝑛 values -Plug in input 𝑛, evaluate for output 𝑔 𝑛 - Plot ordered pairs (𝑛, 𝑔 𝑛 ) Question Forty Three

Question Forty Four Examining Sequences Arithmetic : Adds or Subtracts between values Subtract numbers to find difference Increasing : positive 𝑑 Decreasing: negative 𝑑 Geometric: Multiplies or Divides between values Divide numbers to find ratio Increasing: whole number 𝑟 Decreasing: fraction 1 𝑟 Question Forty Four Finding the Next Term Apply the common ratio or difference to the last number given in the sequence

Question Forty Five Examining Sequences Arithmetic : Adds or Subtracts between values Subtract numbers to find difference Increasing : positive 𝑑 Decreasing: negative 𝑑 Geometric: Multiplies or Divides between values Divide numbers to find ratio Increasing: whole number 𝑟 Decreasing: fraction 1 𝑟 Question Forty Five Finding the Next Term Apply the common ratio or difference to the last number given in the sequence

Question Forty Six Explicit Rules Arithmetic : Adds or Subtracts between values 𝑎 𝑛 = 𝑎 1 +𝑑(𝑛−1) Geometric: Multiplies or Divides between values Divide numbers to find ratio 𝑔 𝑛 = 𝑔 1 ∙ 𝑟 𝑛−1 Question Forty Six 𝑎 1 and 𝑔 1 mean the value of the first term Finding Difference & Ratios Arithmetic : Subtract numbers to find difference Increasing : positive 𝑑 Decreasing: negative 𝑑 Geometric: Divide numbers to find ratio Increasing: whole number 𝑟 Decreasing: fraction 1 𝑟

Question Forty Seven Explicit Rules Arithmetic : Adds or Subtracts between values 𝑎 𝑛 = 𝑎 1 +𝑑(𝑛−1) Geometric: Multiplies or Divides between values Divide numbers to find ratio 𝑔 𝑛 = 𝑔 1 ∙ 𝑟 𝑛−1 Question Forty Seven 𝑎 1 and 𝑔 1 mean the value of the first term Finding Difference & Ratios Arithmetic : Subtract numbers to find difference Increasing : positive 𝑑 Decreasing: negative 𝑑 Geometric: Divide numbers to find ratio Increasing: whole number 𝑟 Decreasing: fraction 1 𝑟

Evaluate for the value of the 15th term 𝑎 15 𝑛 means term number Plug in 𝑛=15 Evaluate for the value of the 15th term 𝑎 15 Question Forty Eight

Question Forty Nine - Make a table of values - Identify the constant pattern - Apply it to the last term of 160 until you reach day 6. Question Forty Nine

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