Standard #1: Write an Algebraic Expression from a word problem. Text Section: 1.1

Reminders KEY WORDS Sum, Increased by, More Than, Plus Difference, Less Than, Decreased by Product, Per, Groups of, Times Quotient, Divided by, Ratio

Examples Addition: 4 plus a number 5 more than a number A number increased by 3 The sum of a number and 2 Subtraction: The difference of a and b *** 3 less than a number *** A number decreased by 8 A number less 6 Multiplication: The product of a and b 5 times a number Twice a number Division: The quotient of a and b A number divided by 8 The ratio of x and y

Answers Addition: 4 + x X + 5 X + 3 X + 2 Subtraction: A - b X - 3 X - 8 X - 6 Multiplication: ab 5x 2x Division: a/b x/8 x/y

Standard #2: Combine like terms in an expression. Text Section: 1.7

Reminders Distribute First (if necessary) Combine ONLY if they have the SAME variable AND SAME exponent!

Examples 1. 12x + 30x2. 6.8y 2 – y n + 11n /2x 3 + 3/4x (x + 6) + 3x (x – 4) (-2 – x) + 8

Answers 1. 42x2. 5.8y 2 3.4n + 11n /4x x x x + 14

Standard #3: Evaluate an expression. Text Section: 1.6

Reminders Use Parentheses when you substitute in for a Variable. PEMDAS!!!

Examples 1. 5(1-2) – (3-2) 2. – 9 – (-18) [5- (3 + 2²)] 4. 7x (3 + 2x) for x = -1

Answers

Standard #4: Solve a 1 step equation. Text Section:

Reminders 5 Steps! X + 3 = X = X= = 10

Examples 1. n – 3.2 = x + 7 = 9 3. m = = 4c

Answers 1. n = x = 2 3. m = = c

Standard #5: Solve a 2 step equation. Text Section: 2.3

Reminders D C (no M) S then 8 STEPS! 2x – 3 = x = x = x = 16/2 x = 8 2(8)- 3 = 13

Examples 1. 6x + 3 – 8x = = 6 – (x + 2) 3. 2a + 3 – 8a = (x – 2) + 2x = 40

Answers 1.x= x = a= -5/6 4. x= 8

Standard #6: Solve a Multi-step equation. Text Section: 2.4

Reminders DCMS (YES, in that order!)

Examples 1. 7k = 4k b + 2 = 3b 3. 2(y + 6) = 3y 4. 3 – 5b + 2b = -2 – 2(1 – b)

Answers 1. K = 5 2. B = Y = B = 7/5

Standard #7: Write and solve an equation from a word problem. Text Section:

Reminders Use Key words, write the equation and solve. You may need to use DCMS, 5 steps or 8 steps

Examples A person’s maximum heart rate is the highest rate, in beats per minute that the person’s heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15-year-old.

Answers 15 + x = 220 X = 205

Standard #8: Solve an Absolute Value Equation. Text Section: Ch 2 Extension

Reminders IS IT ALONE???? IS IT NEGATIVE? If an absolute value equation equals a positive number there are two solutions. If an absolute value equation equals 0 there is one solution. If an absolute vale equation equals a negative number there are no solutions.

Examples 1.4|x + 2| = 20 2.|x| - 3 = 4 3.|x + 3| + 4 = = |x + 2| + 8

Answers 1.x = 3, x = x = 7, x = -7 2.x = no solution

Standard #9: Isolate a Variable. Text Section: 2.5

Reminders Use Opposite Operations to get the Letter all by itself.

Examples 1.Given d = rt, solve for t 2. Given A = ½ bh, solve for b 3.Solve m – n = 5 for m 4.Solve m = x for k k

Answers 1.t = d/r 2. B = 2a/h 3.M = 5 + n 4.K = m x

Standard #10: Write an inequality from a word problem. Text Section: 3.1

Reminders <>≤≥≠ A < BA > BA ≤ BA ≥ BA ≠ B A is less than B A is greater than B A is less than or equal to B A is greater than or equal to B A is not equal to B

Examples Write in Words 1.b < r ≥ ≥ w 4. -1/2 < a

Answers 1.All real numbers less than All real numbers greater than or equal to 2 3.All real numbers less than or equal to 5 4. All real numbers less than - 1/2

Standard #11: Solve an inequality by adding and subtracting. Text Section:

Reminders Same 5 Steps as solving an Equation. X + 3 < X < X< 7

Examples 1.x + 9 < d – 3 > ≥ n – ½ ≥ t

Answers 1.x < 6 2. d > n< T < 5 ½

Standard #12: Solve an inequality by multiplying and dividing. Text Section:

Reminders SAME 5 or 8 Steps with 1 TRICK If you Multiply or Divide BY (not into) a Negative- you MUST flip the inequality SIGN!

Examples ≥ 5q ≤ 7x ≥ -x

Answers 1.q≥ x ≥ x ≥ -10

Standard #13: Solve an Absolute Value Inequality. Text Section: Ch 3 Extension

Reminders IS IT ALONE???? Set up TWO inequalities: Flip the sign AND Negative! **Tip: Remember “less thAND”** **Tip: Remember “greatOR”**

Examples 1.|x|-3<12 2. |x-4|+7≤-2 3. |x|-20> |x-8|+5≥11

Answers 1.X No solution 3. X > 7 OR x < X > 14 OR x < 2

Standard #14: Graph an inequality on a number line. Text Section: Chapter 3

Reminders Graph on a Number Line Open Circle when it is Closed Circle when it is Shade Left or Right??? Make sure your solution has the Variable on the left side BEFORE you Graph.

Examples Graph 1.b < r ≥ ≥ w 4. -1/2 < a

Answers

Standard #15: Interpret/Describe solutions of an inequality. Text Section: Chapter 3

Reminders AT LEAST > AT MOST < MORE THAN > LESS THAN <

Examples 1. Give three possible solutions. 5s > Which inequality has the solution shown? d < -3 a. 4 > d + 7c. d – 8 < - 5 b. 9 + d > 6d. 2 < d 3. Which inequality has -2 as a solution? a. 2x > 4b. -2x 4d. -2x > Which statement justifies the given inequality? x ≥ $300 a. You spent more than $300 b. You spent at least $300 c. You spent less than $300 d. You spent at most $300

Answers 1.3,4,5 etc.. 2.A 3.D 4.B

Standard #16: Recognize a function in a variety of ways. Text Section: 4.2

Reminders The x values, MAY NOT REPEAT!!!! Determine if it is a function from: Graph Table Chart Ordered Pairs Mapping Diagram Equation VERTICAL LINE TEST!

Examples Is it a FUNCTION? 1.{(-4,2),(2,3),(0,7),(-4,-1)} xy −25 −

Answers 1.No 2.No 3.Yes 4.yes

Standard #17: Identify inputs and outputs. Text Section: 4.2

Reminders INPUT- X Values OUTPUT- Y Values

Examples 1.List the Inputs 2.List the Outputs {(4,0),(2,-3),(0,-6),(-2,-9)} xy

Answers 1.(5,4,3,2) 2.(0,-3,-6,-9)

Standard #18: Identify domain and range. Text Section: 4.2

Reminders DOMAIN- X Values RANGE- Y VALUES

Example What is the Domain? Range?

Answers Domain: (-2,3,4,10) Range: (-1,0,2,4,6)

Standard #19: Write a rule for a given function. Text Section: 4.3

Reminders ALL rules Start with: Y = Ask yourself: “what do I have to do to x to get y???”

Examples 1. Write an equation (rule) for the following function. 2. A caricature artist charges his clients a $10 setup fee plus $15 for every person in a picture. a. Write a rule for the artist’s fee. b. Write ordered pairs for the artist’s fee when there are 1, 2, 3, and 4 people in the picture. x2468 y−3−113

Answers 1.Y = x – 5 2.A. y = 15x + 10 B. (1,25)(2,40)(3,55)(4, 70)

Standard #20: Evaluate an equation in function notation. Text Section: 4.3

Reminders Substitute in for the given Variable Follow PEMDAS DCMS

Examples

Answers

Standard #21: Graph a linear function. Text Section: 4.4

Reminders LINEAR means LINE Make sure your graph is a LINE!

Examples 1. Graph y = -4x Graph y = 2x – 5 3. Graph y = -x Graph y = 7

Answers

Standard #22: Determine if a Relation is a Linear Function. Text Section: 5.1

Reminders LINEAR Function (linear is the KEY word) DO NOT just look at x values, you have to see if there is a common difference in the x AND the y values! No Absolute Values Exponents Sq Roots Variable in the Denominator

Examples Is it LINEAR (not just a function)! 1. {(-4,3), (-1, 1), (2, -1), (5, -3)} Tell which equation is linear. a.y = x+ 2c. -2y + 5x = 8 b.y = 2x 3 d. y = |x|+ 2 x-3135 y

Answers 1. yes 2. no 3. A

Standard #23: Write a function in Standard Form Text Section: 5.1

Reminders Ax + By = C “A” can NOT be a fraction OR negative. If A is negative- change ALL signs. If there is a fraction, multiply all by the DENOMINATOR!

Examples Write in Standard Form 1. 5x + 3y = x-y = x = 2y y = ½ x – 5

Answers 1.5x + 3y = -2 a = 5, b = 3, c = x – y = 1 a = 1, b = -1, c = 1 3.9x + 2y = 7 a = 9, b = 2, c = 7 4.x – 4y = 10 a= 1, b = -4, c = 10

Standard #24: Identify Values of A,B, and C Text Section: 5.1

Reminders It has to be in Ax + By = C A, B, and C are Real numbers- NOT variables!!

Examples Give values of A,B, and C 1.5x + 3y = -2 2.x – y = x + 2y = 7 4. x – 4y = 10

Answers 1. a = 5, b = 3, c = a = 1, b = -1, c = 1 3. a = 9, b = 2, c = 7 4. a= 1, b = -4, c = 10

Standard #25: Find the x and y-intercept in a given situation. (equation, graph, word prob) Text Section:

Reminders Answer MUST BE an ordered pair! Cover the y, solve for x Cover the x, solve for y

Examples Find the x and y intercepts of the following. 1.2x + 5y = –x + 6y = 18 3.You can earn $12 an hour babysitting and $15 an hour raking leaves. You want to make $360 in one week

Answers 1. (5,0),(0,2) 2. (-18,0)(0,3) 3. (30,0)(0,22)

Standard #26: Interpret Rate of Change (slope in a word problem). Text Section: 5.4

Reminders Rate of Change = SLOPE = y- y x - x

Examples x23578 y The table shows the average temperature for five months. Find the rate of change for EACH time period.

Answers 2-3 = = 7/2 5- 7= = 1

Standard #27: Identify Slope as being: (positive, negative, zero, undefined) Text Section: 5.4

Reminders Positive Negative Zero Undefined

Examples Tell whether the slope of each line is positive, negative, zero, or undefined

Answers 1. positive 2. undefined 3. negative 4. zero

Standard #28: Identify Slope in a given situation (ordered pairs, table, graph) Text Section: 5.4

Reminders Rise Run Up and Over Y-y X-x M=

Examples 1.(-2, -2) and (7, -2) x1234 y

Answers 1.M = 0 2.M = 2/3 3.M = 7/2

Standard #29: Write an Equation in Slope Intercept Form from a given situation Text Section:5.6

Reminders y = mx + b m = slope b = y intercept

Examples Write an equation in SLOPE INTERCEPT FORM 1.m = 4; (-3, 5) 2. (3, -2)(12, 1) 3. 8x – 4y = 16

Answers 1.y = 4x y = 1/3x – 3 3.y = 2x - 4

Standard #30: Graph from Slope Intercept Form Text Section: 5.6

Reminders Change to y = mx + b Plot your b (your beginning point) Up and Over for your slope Y = Horizontal Line x = Vertical Line Y = x Diagonal Line Y = x Diagonal Line

Examples 1.x = 2 2. y = - x y = 3x 8. y = -3

Answers

Standard #31: Graph from Standard Form Text Section: 5.2

Reminders Change to y = mx + b Plot your b (your beginning point) Up and Over for your slope Y = Horizontal Line x = Vertical Line Y = x Diagonal Line Y = x Diagonal Line

Examples 1.6x + 3y = x + 12y = -24

Answers 1. 2.

Standard #32: Write an Equation to a Line Parallel Text Section: 5.8

Reminders Parallel Lines= SAME Slope 1.Slope 2.Pt Slope 3.Slope intercept

Examples Give all 3 Answers for Each. PARALLEL 1. y = 3x + 4; (2, -5) 2. 5x -10y = 20; (-4,2)

Answers 1.m = 3 y + 5 = 3(x -2) y = 3x m = ½ y – 2 = ½ (x + 4) y = ½ x + 4

Standard #33: Write an Equation to a Line Perpendicular Text Section: 5.8

Reminders Perpendicular Lines= Opposite Inverse Slopes 1.Slope 2.Pt Slope 3.Slope intercept

Examples Give all 3 Answers for Each. PERPENDICULAR 1. y = 3x + 4; (9, -5) 2. 5x -y = 12; (-10,2)

Answers 1.m = -1/3 y + 5 = -1/3(x -9) y = -1/3x m = -1/5 y – 2 = -1/5 (x + 10) y = -1/5 x

Standard #34: Graph a Linear Inequality on a Coordinate Plane Text Section: 6.5

Reminders Dashed or Solid? Shade Above or Below? Positive or Negative?

Examples 1-2 Graph each linear inequality. 1.x ≤ -2 2.y ≥ x + 4 Write a linear inequality for the given graph.

Answers Y > -x + 4

Standard #35: Gather data from a Scatter Plot. Text Section: 4.5

Reminders Do NOT Connect the dots Correlations: Positive, Negative, No Correlation

Examples 1.Describe the correlation 2. Predict typos in 12 chapters

Answers 1.Positive Correlation 2.Approx 14

Standard #36: Model a Scatter Plot Text Section: 4.5

Reminders Dots- don’t connect Titles- x and y axis

Examples Hours Studied Test Grade Graph a scatter plot using the table. Remember to include all aspects of the graph.

Answers Test Grade Hours Studied

Standard #37: Estimate a Line of Best Fit Text Section: 4.5

Reminders y = mx + b Check your slope Check your y intercept *especially on multiple choice!

Examples 1.Estimate the line of best fit 2. Which equation represents the line of best fit for the given scatter plot?

Answers 1.y = -x y = -2x - 1

Standard #38: Find the n th term of a Sequence Text Section: 4.6

Reminders a n = a 1 + (n-1)d The 1 st term in the sequence Term you need to find Common Difference in the sequence

Examples Find the given term of each arithmetic sequence. 1.5,2,-1,-4,…; 23 rd term ,0,1.1,2.2…; 51 st term 3.407,402,397,392…; 17 th term 4. 11,21,31,41,…; 33 rd term

Answers 1. A 23 = A 51 = A 17 = A 33 = 331 Look how the Answers are Written!!

Standard #39: Find the Common Difference in a Sequence Text Section: 4.6

Reminders Common Difference is the d in the formula Look at the sequence, do the numbers go up (+) or down (-), and by what value?

Examples Find the common difference (d) in each arithmetic sequence ,105,103,101,… , 5, 5.15, 5.3, … 3. 3 ½, 2 ¼, 1, -3/4, … 4. 2, 15, 28, 41, …

Answers 1.d= -2 2.d =.15 3.d = - 1 ¼ 4.d = 13

Standard #40: Simplify Exponential Expressions Text Section: 1.4

Reminders WordsMultiplicationPowerValue 3 to the first power to the second power or 3 squared 3 * to the third power, or 3 cubed 3 * 3 * to the fourth power 3 * 3 * 3 * to the fifth power 3 * 3 * 3 * 3 *

Examples 1-3 Simplify each expression 1.(-2) (2/3) 2 Careful with the Parentheses

Answers /9

Standard #41: Write Numbers as a Power of the given base Text Section: 1.4

Reminders Use the given base Then find the exponent for that base to get the given answer.

Examples 4-6 Write each number as a power of the given base. 4. 8; base , base , base 8

Answers or (-5)

Standard #42: Zero and Negative Exponents Text Section: 7.1

Reminders NO NEGATIVE Exponents EVER!!! ANYTHING Raised to the Zero Power is = to 1

Examples 1. m -3 n 2. -3f x -7 y 2 r 3 v x -5 y (g 0 h 0 ) 7

Answers 1. n m f 3 3. v 4 y 2 r 3 x y 6 x

Standard #43: Multiplication of Exponents Text Section: 7.3

Reminders You can only multiply powers that have the same base- if they do you ADD exponents When you raise a power to a power you MULTIPLY the exponents and leave the base the same Check for Negative and Zero Exponents

Examples 1. (f 4 ) 6 g 2. m (h 3 ) 4 (m -2 ) 3 3. (6y 8 ) 2 4. (k 4 ) 2 (m -1 ) -4 NO Negative Exponents!

Answers 1. f 24 g 2. h 12 m y k 8 m 4

Standard #44: Division of Exponents Text Section: 7.4

Reminders When we divide with exponents we subtract the exponents. You can only divide powers with the same base

Examples 3 8 a 5 b 9 y m 5 n (ab) 4 y 4 (m 5 ) 2 n All other Rules still Apply.

Answers = ab y 3 4. n 3 m 5

Standard #45: Standard Form to Scientific Notation Text Section: 7.2

Reminders The Number has to be > 1 but < 10 Be careful where you put your decimal. Is your exponent – or + ?

Examples

Answers x x x x 10 4 Watch your Exponent sign.

Standard #46: Scientific Notation to Standard Form Text Section: 7.2

Reminders Just move the Decimal Negative Exponent- Move Left Positive Exponent- Move Right

Examples X X X X 10 -2

Answers