2023 Algebra 1 SOL Vocabulary & Strategy Guide

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Aarthi Vadhanam
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Aarthi Vadhanam
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Aarthi Vadhanam
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Question Answer
Translating Expressions Translate from left to right unless you see a... turn-around phrase
Translating Expressions Examples of turn-around phrases are... less than subtracted from reduced by fewer than decreased by lower than
Translating Expressions Sum of, difference of, product of all mean we should use... parentheses
Translating Expressions Translate the following: Two times the sum of a number and four 2(x + 4)
Translating Expressions Translate the following: Five less than a number squared x² - 5
Translating Expressions Write an expression for The square root of a number divided by 3
Evaluating Expressions In Desmos, how do you make... √ 1) Type "sqrt" or 2) find the symbol on the Desmos keypad
Evaluating Expressions In Desmos, how do you make... ∛ 1) Type "cbrt" or 2) open the Desmos keypad -> click functions -> scroll to bottom
Evaluating Expressions In Desmos, how do you make... absolute value bars (| |) Open the Desmos keypad and look for
Evaluating Expressions In Desmos, how do you make... an exponent 1) Keyboard: shift and 6 (to get ^) 2) Desmos keypad: click the button
Evaluating Expressions In Desmos, how do you make... a big fraction Click the divide key on the Desmos keypad or click / on your keyboard
Evaluating Expressions What letters can you make into sliders? Any letter except x or y
Evaluating Expressions What if you need to set the letter equal to 15 and you can't slide it that far? Click into the number and change it
Square Roots What does simplest form mean? smallest number/coefficient INSIDE the radical
Square Roots Which is simpler? Why? √32 or 4√2 4√2 because 2 is smaller than 32
Square Roots Simplify: √150
Square Roots TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD
Cube Roots & Radical Operations How do you create a cube root? 1) Type "cbrt" or 2) open the Desmos keypad -> click functions -> scroll to bottom
Cube Roots & Radical Operations After he typed 4, CLICK OUT of the radical before typing - 6
Cube Roots & Radical Operations TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD
Equations & Word Problems How do you use Desmos to solve an equation? First...type the equation into Desmos Then...look for the vertical line Finally...click the point on the line. x= that number
Equations & Word Problems The solution is also the... x-intercept
Equations & Word Problems Which letter must you use for the variable? only x
Equations & Word Problems Solve: 3(x + 1) = 5 + x
Equations & Word Problems Write an equation: Jaycin went bowling recently with her friends. Shoe rental was $2.50 and games were $1.75 each. If she spent $7.75 on shoe rental and games, how many games did she bowl? x = games 2.50 + 1.75x = 7.75 3 games
Literal Equations TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD Solve for x: 180 = 2x + y
Systems of Equations The solution to two or more equations is where the lines... intersect/cross/meet
Systems of Equations How many solutions? One solution
Systems of Equations How many solutions? No solutions, parallel lines
Systems of Equations How many solutions? Infinite solutions, same line
Systems of Equations The solution is represented as an _____________________ that satisfies both equations. ordered pair
Systems of Equations TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD a + b = 7 2a + 3b = 10 Type into Desmos using x and y! x + y = 7 2x + 3y = 10 Solution is (11,-4)
Systems of Equations Word Problems Dashawn paid $54 for 3 large candles and 4 small candles. Niya paid $60 for 1 large candle and 8 small candles. How much did each small candle cost?
Systems of Equations Word Problems Aaliyah sold a total of 10 baked goods. Each cookie costs $1.25 and each brownie costs $2.50. Aaliyah made $20 at the bake sale. How many cookies did Aaliyah sell?
One-Variable Inequalities Graph an inequality in Desmos using the variable... x
One-Variable Inequalities Write the inequality for the graph x > 8
One-Variable Inequalities Write the inequality for the graph x < 8
A.5a One-Variable Inequalities Write the inequality for the graph x ≤ 8
One-Variable Inequalities Write the inequality for the graph x ≥ 8
One-Variable Inequalities TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD Find the answer to the inequality -4(x - 7) + 1 ≤ -3 Type in Desmos! x ≥ 8
One-Variable Inequalities Graph the solution on the number line.
Inequality Word Problems What words represent Less than < fewer than below under
Inequality Word Problems What words represent Greater than > more than over above exceeds
Inequality Word Problems What words represent Less than or equal to ≤ no more than not above at most limit does not exceed not over maximum total
Inequality Word Problems What words represent Greater than or equal to ≥ at least no fewer no less not under not below minimum
Inequality Word Problems The owner of a new restaurant is designing its floor plan. His goal is to have a seating capacity of at least 368 customers. The small tables can seat 2 customers, while the large tables can seat 5 customers.
Two-Variable Inequalities Is the point a solution? YES it's in the shaded region
Two-Variable Inequalities Is the point a solution? NO it's on a dotted line
Two-Variable Inequalities Is the point a solution? YES it's on a solid line
Two-Variable Inequalities Is the point a solution? YES it's on solid lines near the darkest area
Two-Variable Inequalities Is the point a solution? NO it's on a dashed line
Two-Variable Inequalities Is the point a solution? NO it's not in the darkest area
Two-Variable Inequalities Is the point a solution? NO it's not in the shaded area
Two-Variable Inequalities Is the point a solution? NO it's not in the darkest area
Two-Variable Inequalities Is the point a solution? YES it's on a solid line in the darkest area
Slope Slope is always... in front of the x when the equation says y=
Slope What is the slope formula? m =
Slope Substitute into the slope formula (3, -5) and (-4, -7)
Slope Slope is also ______/________ and ___________ of ___________ rise/run and rate of change
Slope Find the slope
Slope Which equations represents the line that passes through the points (-4, 4) and (8, -2)?
Slope
Linear Equations Parallel looks like... never intersecting, same slope and different y-intercepts
Linear Equations Equations of perpendicular lines have... opposite reciprocal slope and look like lines intersecting at a 90 degree angle
Linear Transformations Slope number in front of x
Linear Transformations Y-intercept number added or subtracted to x
Linear Transformations
Linear Transformations
Linear Transformations
Linear Transformations
Linear Transformations
Linear Transformations The parent linear function is... f(x) = x
Polynomials TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD
Polynomials 1. Type in the _________ 2. Type in all four answer options 3. Click the _________ on the left to view each graph one by one 1. Type in the PROBLEM 2. Type in all four answer options 3. Click the COLORS on the left to view each graph one by one
Polynomials How do you use Desmos to solve? First... Type in the problem and answers into separate rows
Polynomials How do you use Desmos to solve? Then... put =5 at the end of all rows (or some other number greater than 3)
Polynomials How do you use Desmos to solve? Finally... compare the curves to match the correct answer to the problem!
Polynomials TRY THIS PROBLEM YOURSELF BEFORE YOU FLIP THE CARD
Quadratic Functions All quadratic functions have __________ and they look like a ____________. All quadratic functions have x² and they look like a U.
Quadratic Functions
Quadratic Functions
Quadratic Functions
Quadratic Functions What four words mean the same thing? zero = solution = root = x-intercept
Quadratic Functions They are all looking for where our graph cross the __________ x-axis
Quadratic Functions Find the zeros The graph crosses the x-axis at x = -4 and x = 2
Factors and Zeros Factors and zeros have ___________________ opposite signs
Factors and Zeros x = -3 and x = 1
Factors and Zeros (x - 2)(x - 4)
Factors and Zeros (x + 1)(x - 5) x = -1 and x = 5
Factoring & Quadratic Functions Factors and their functions have common _____________ x-intercepts
Factoring & Quadratic Functions B. (3x + 1) has the same x-intercept as the problem
Functions A function never repeats the ____________________ x-values
Functions Is this a function or not? NO, the x-value of 0 repeats
Functions Is this a function or not? NO, the x-value of 2 repeats
Functions Is this a function or not? YES, no x-value repeats
Functions Is this a function or not? NO, fails the vertical line test. X-values of 1 and 2 repeats
Functions Is this a function or not? YES, passes the vertical line test no x-value repeats
Domain and Range Domain represents... x-values
Domain and Range Range represents... y-values
Domain and Range For domain, scan the graph from... left to right
Domain and Range For range, scan the graph from... bottom to top
Domain and Range Domain is... ℝ= all real numbers (-∞, ∞)
Domain and Range Range is... { y | y ≥ -4 } [-4, ∞)
Exponential Functions Exponential Functions have an ________ in the ________________. x in the exponent
Exponential Functions They look like Curve that approaches the x-axis
Exponential Functions How do you know that a table represents an exponential function? the y-values change by a common multiplier
Function Transformations Shift up or down add or subtract outside x
Function Transformations Stretch or compress multiply or divide
Function Transformations shift up by 4
Function Transformations stretch by a factor of 3
Function Transformations shift down by 4
Function Transformations Compress by a factor of 1/3
Function Transformations Reflect over x-axis negative in front of expression
Matching Tables to Graphs/Equations How do you create a table in Desmos? Type "table" OR click the + button in the top left corner and click table
Matching Tables to Graphs/Equations If you can't see the points in Desmos, what should you do? Click the magnifying glass in the blue column next to your table
Matching Tables to Graphs/Equations When you graph the correct equation, what will it look like with the points? The correct equation will either -go through ALL the points OR -be the best match for the points out of ALL the answer options
Comparing Functions g
Comparing Functions
Comparing Functions
Comparing Functions
Comparing Functions
Scatterplots & Data Cycle What type of pattern do the points follow? Linear
Scatterplots & Data Cycle What type of association do the points have? negative
Scatterplots & Data Cycle How strong of association do the points have? strong
Scatterplots & Data Cycle As age increases, the number of accidents_____ decreases
Scatterplots & Data Cycle How many accidents might be associated with drivers 25 years old? 8
Scatterplots & Data Cycle A data point of 12 accidents per 100 drivers might correlate with which age? 23
Scatterplots & Data Cycle Which question below could a researcher have asked to collect this data? How often are drivers of different ages involved in car accidents?
Line of Best Fit y = ________x + __________ y = -2.14x + -0.4
Curve of Best Fit y = ______x² + ______x + ________ y = 0.98x² + -1.95x + 3.2
Test Taking Skills/Strategies Did I __________each direction & question carefully and ___________? Did I READ each direction & question carefully and COMPLETELY?
Test Taking Skills/Strategies What information do I see? ( _________, graphs, _________ or points) What information do I see? (EQUATIONS, graphs, TABLES or points)
Test Taking Skills/Strategies What are the keywords that I see? (________, highlight, ________ with a different word/synonym) What are the keywords that I see? (CIRCLE, highlight, REPLACE with a different word/synonym)
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