Questions and Answers
What is a Box and Whisker Plot?
What does the Interquartile Range (IQR) represent?
The difference between Q3 and Q1.
What is a Histogram?
Like a bar graph, but no space between bars, with data organized into intervals.
What is the formula for the area of a circle?
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What is the formula for the circumference of a circle?
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What does the equation 5 = 0 imply about its solutions?
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What does the equation 5 = 5 imply about its solutions?
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What is the Commutative Property?
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What is the Associative Property?
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Are polynomials closed under addition, subtraction, and multiplication?
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Are polynomials closed under division?
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What is the coefficient of the term 7ab?
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Define 'set'.
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What does 'domain' refer to?
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What does 'range' refer to?
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What is an independent variable?
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What is a dependent variable?
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What determines if a relation is NOT a function?
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How can you tell if a graph is a function?
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In function notation, how is y typically expressed?
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How are consecutive integers represented?
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How are consecutive even or odd integers represented?
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What are the two cases to consider when solving absolute value equations?
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What is notable about proportions?
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How do you solve a proportion?
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How would you write '3% of x' algebraically?
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How would you write '3% more than x' algebraically?
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What does a linear function produce when graphed?
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What is the value of y at the x-intercept?
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What value of x do you use to find the y-intercept?
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What is the parent function of a linear equation?
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What does the parent function of a linear equation look like when graphed?
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What are zeros, roots, or solutions of equations also known as?
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What does 'change in y over the change in x' refer to?
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How can you find the slope of a line using two points?
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What is the slope of a vertical line?
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What is the slope of a horizontal line?
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What would the graph of y = 3 look like?
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How many x-intercepts does the line x = 6 have?
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What do arithmetic sequences have?
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What is the common difference (d) of this arithmetic sequence: 33, 29, 25, 21, 17?
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How do you find the 'nth term' of an arithmetic sequence?
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What is the equation used for a line in slope-intercept form?
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In the equation y = mx + b, what does b represent?
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Write the equation for a line passing through (4, 2) and (-2, -4).
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What do parallel lines have in common?
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What is the slope of a line perpendicular to y = 5x + 2?
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When does a scatterplot show positive correlation?
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When does a scatterplot show negative correlation?
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When does a scatterplot show no correlation?
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What is a correlation coefficient?
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What is an inverse relation?
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What type of dot is used for '<' or '>' when graphing inequalities?
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What type of dot would you use for 'greater than or equal to' and 'less than or equal to'?
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When solving an inequality, when do you flip the inequality symbol?
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When graphing systems of inequalities, what type of line is used for inequalities like '<' or '>'?
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When graphing systems of inequalities, what type of line is used for 'greater than or equal to' and 'less than or equal to'?
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How do you solve the compound inequality -2 < x - 3 < 4?
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How can you verify that you have graphed and shaded a system of inequalities correctly?
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What relationships can systems of equations result in?
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How would you solve the system of equations: y = 4x - 6 and 5x + 3y = -1?
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How would you solve the system of equations: 4x + 6y = 32 and 3x - 6y = 3?
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After solving the system of equations y = 2x and y = 6 - x, how can you ensure your answer is correct?
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How would you simplify b^3 times b^6?
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How would you simplify (4b^7)^2?
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When simplifying x^7/x^5, what is the rule for the exponents?
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How do you handle a negative exponent in an expression?
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How do you raise a fraction to a power?
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What is the standard form of the number 6.32 x 10^9?
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What is the standard form of the number 4 x 10^-7?
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What is the scientific notation of the number 201,000,000?
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What is the equation for exponential growth?
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What is the equation for exponential decay?
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What distinguishes geometric sequences?
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What formula do you use to find the 'nth term' of a geometric sequence?
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What is the degree of the polynomial 5y - 9 - 2y^4 - 6y^3?
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What is the leading coefficient of the polynomial 8 - 2x + 4x^5 - 3x^2?
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-4^2 = ?
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(-4)^2 = ?
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What is 5x^2 when x = 2?
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What does foil mean?
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What is the result of multiplying (6x + 5)(2x^2 - 3x - 5)?
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Use the zero product property to solve (x - 8)(x + 7) = 0.
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Factor out the GCF from -4a^2b - 8ab^2 + 2ab.
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What are the roots of the equation x^2 + 6x = 27?
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Study Notes
Box and Whisker Plots
- Utilizes five-number summary to visualize data spread: minimum value, lower quartile (Q1), median, upper quartile (Q3), and maximum value.
Interquartile Range (IQR)
- Represents the difference between the upper quartile (Q3) and lower quartile (Q1), indicating the range of the middle 50% of data.
Histogram
- A type of bar graph without gaps between bars, organizing data into intervals.
Area of a Circle
- Calculated using the formula ( A = \pi r^2 ), where r is the radius. Permits squaring of the radius before multiplying by ( \pi ).
Circumference of a Circle
- Calculated using the formula ( C = \pi d ), where d is the diameter.
Solving Equations
- If an equation simplifies to ( 5 = 0 ), it indicates no solutions.
- If it results in ( 5 = 5 ), all real numbers are solutions.
Properties of Operations
- Commutative Property allows for changing the order of addends or factors without changing the sum or product.
- Associative Property allows for regrouping of addends or factors without changing the sum or product.
Polynomials
- Closed under addition, subtraction, and multiplication, meaning the results are always polynomials.
- Not closed under division.
Coefficient of a Term
- The numerical factor in a term; for example, in the term ( 7ab ), 7 is the coefficient.
Set and Elements
- A collection of objects or numbers shown in braces, e.g., {3, 5, 7, 9}. Each number is termed an "element".
Variables
- Domain refers to x-values, and range refers to y-values.
- Independent variable corresponds to x, while the dependent variable corresponds to y.
Function Relationships
- A "mapping" shows the relationship between elements of the domain and range. It's not a function if one x-value maps to multiple y-values.
Function Graphing
- Use the vertical line test: If a vertical line intersects the graph more than once, the graph is not a function.
- In function notation, y is typically expressed as ( f(x) ).
Consecutive Integers
- Represented as ( x, x+1, x+2 ). To find three consecutive integers that sum up to a specific value, set up the equation accordingly.
Absolute Value Equations
- Analyze two cases: the expression is either positive/zero or negative.
Proportions
- Cross products are always equal. To solve a proportion, set the cross products equal to each other.
Percentages
- "3% of x" translates to ( 0.03x ), while "3% more than x" translates to ( 1.03x ).
Linear Functions
- Graphically represented as a line. The x-intercept is found by setting y to 0, and the y-intercept is found by setting x to 0. The parent function is ( f(x) = x ).
Slope and Intercepts
- Slope is defined as "change in y over change in x".
- A vertical line has an undefined slope and a horizontal line has a slope of 0.
Arithmetic Sequences
- Defined by a common difference, e.g., 3, 5, 7 (difference of 2).
- To find the nth term, use ( a_n = a_1 + d(n-1) ).
Polynomial Properties
- The highest degree of a polynomial indicates its degree, and the leading coefficient is the coefficient of the term with the highest degree.
Scientific Notation
- Example: ( 6.32 \times 10^9 ) equals ( 6,320,000,000 ) in standard form.
Exponential Functions
- Growth model: ( y = a(1 + r)^t ) and decay model: ( y = a(1 - r)^t ).
Geometric Sequences
- Defined by a common ratio as opposed to a common difference, e.g., increasing by a factor of 4.
Factoring and Solving Equations
- Use the zero product property to solve ( (x - 8)(x + 7) = 0 ).
- Factor quadratics by removing the greatest common factor first.
Simplifying Expressions
- Apply rules for exponents, such as adding exponents when multiplying like bases and subtracting exponents when dividing.
Inequalities
- Represent solutions on a number line with open dots for "<" and ">", and closed dots for "≥" and "≤".
- Flip the inequality sign when multiplying or dividing both sides by a negative number.
Systems of Equations
- Can yield one solution, infinitely many solutions, or no solutions based on their graphical representations.
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Description
This quiz focuses on key concepts in Algebra 1, including Box and Whisker Plots, Interquartile Range, and Histograms. Prepare for the FSA with flashcards that cover essential definitions and statistics used in data analysis. Enhance your understanding of how to interpret and represent data effectively.