Algebra 1 FSA Study Set

Questions and Answers

What is a Box and Whisker Plot?

A method to display scatter plots.

A way to show the spread in a data set using the five number summary. (correct)

A method to calculate mean.

A type of pie chart.

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?

A=πr^2 Signup and view all the answers

What is the formula for the circumference of a circle?

C=πd Signup and view all the answers

What does the equation 5 = 0 imply about its solutions?

There are no solutions. Signup and view all the answers

What does the equation 5 = 5 imply about its solutions?

All real numbers are solutions. Signup and view all the answers

What is the Commutative Property?

Changing the order of the addends or factors does not change the sum or product. Signup and view all the answers

What is the Associative Property?

Grouping the addends or factors in any way does not change the sum or product. Signup and view all the answers

Are polynomials closed under addition, subtraction, and multiplication?

Yes. Signup and view all the answers

Are polynomials closed under division?

No. Signup and view all the answers

What is the coefficient of the term 7ab?

7 Signup and view all the answers

Define 'set'.

A collection of objects or numbers often shown using braces. Signup and view all the answers

What does 'domain' refer to?

x-values. Signup and view all the answers

What does 'range' refer to?

y-values. Signup and view all the answers

What is an independent variable?

x. Signup and view all the answers

What is a dependent variable?

y. Signup and view all the answers

What determines if a relation is NOT a function?

If one of the x-values is paired with more than one y-value. Signup and view all the answers

How can you tell if a graph is a function?

Use the vertical line test. Signup and view all the answers

In function notation, how is y typically expressed?

f(x). Signup and view all the answers

How are consecutive integers represented?

x, x+1, x+2, etc. Signup and view all the answers

How are consecutive even or odd integers represented?

x, x+2, x+4, etc. Signup and view all the answers

What are the two cases to consider when solving absolute value equations?

(1) The expression inside the absolute value is positive or zero, (2) The expression inside the absolute value is negative. Signup and view all the answers

What is notable about proportions?

Their cross products are always equal. Signup and view all the answers

How do you solve a proportion?

Use cross products and set them equal, then solve. Signup and view all the answers

How would you write '3% of x' algebraically?

0.03x. Signup and view all the answers

How would you write '3% more than x' algebraically?

1.03x. Signup and view all the answers

What does a linear function produce when graphed?

A line. Signup and view all the answers

What is the value of y at the x-intercept?

<ol start="0"> <li></li> </ol> Signup and view all the answers

What value of x do you use to find the y-intercept?

<ol start="0"> <li></li> </ol> Signup and view all the answers

What is the parent function of a linear equation?

f(x) = x. Signup and view all the answers

What does the parent function of a linear equation look like when graphed?

A line with a slope of one passing through the origin. Signup and view all the answers

What are zeros, roots, or solutions of equations also known as?

x-intercepts. Signup and view all the answers

What does 'change in y over the change in x' refer to?

Slope. Signup and view all the answers

How can you find the slope of a line using two points?

m = (y2 - y1)/(x2 - x1). Signup and view all the answers

What is the slope of a vertical line?

Undefined. Signup and view all the answers

What is the slope of a horizontal line?

<ol start="0"> <li></li> </ol> Signup and view all the answers

What would the graph of y = 3 look like?

A horizontal line passing through (0, 3). Signup and view all the answers

How many x-intercepts does the line x = 6 have?

One, at (6,0). Signup and view all the answers

What do arithmetic sequences have?

A common difference. Signup and view all the answers

What is the common difference (d) of this arithmetic sequence: 33, 29, 25, 21, 17?

-4. Signup and view all the answers

How do you find the 'nth term' of an arithmetic sequence?

an = a1 + d(n-1). Signup and view all the answers

What is the equation used for a line in slope-intercept form?

y = mx + b. Signup and view all the answers

In the equation y = mx + b, what does b represent?

The y-intercept. Signup and view all the answers

Write the equation for a line passing through (4, 2) and (-2, -4).

y = x - 2. Signup and view all the answers

What do parallel lines have in common?

Same slope. Signup and view all the answers

What is the slope of a line perpendicular to y = 5x + 2?

-1/5. Signup and view all the answers

When does a scatterplot show positive correlation?

When data trends upward as x increases. Signup and view all the answers

When does a scatterplot show negative correlation?

When data tends to show a negative slope. Signup and view all the answers

When does a scatterplot show no correlation?

When the data appears random. Signup and view all the answers

What is a correlation coefficient?

A number indicating the strength and direction of correlation. Signup and view all the answers

What is an inverse relation?

Changing the x and y coordinates. Signup and view all the answers

What type of dot is used for '<' or '>' when graphing inequalities?

Open dot. Signup and view all the answers

What type of dot would you use for 'greater than or equal to' and 'less than or equal to'?

Closed dot. Signup and view all the answers

When solving an inequality, when do you flip the inequality symbol?

When you multiply or divide by a negative number. Signup and view all the answers

When graphing systems of inequalities, what type of line is used for inequalities like '<' or '>'?

Dashed line. Signup and view all the answers

When graphing systems of inequalities, what type of line is used for 'greater than or equal to' and 'less than or equal to'?

Solid line. Signup and view all the answers

How do you solve the compound inequality -2 < x - 3 < 4?

Write two separate inequalities and solve both. Signup and view all the answers

How can you verify that you have graphed and shaded a system of inequalities correctly?

Choose a test point in the shaded area and substitute into the original inequalities. Signup and view all the answers

What relationships can systems of equations result in?

Exactly one solution, an infinite number of solutions, or no solutions. Signup and view all the answers

How would you solve the system of equations: y = 4x - 6 and 5x + 3y = -1?

Use substitution to solve. Signup and view all the answers

How would you solve the system of equations: 4x + 6y = 32 and 3x - 6y = 3?

Use elimination. Signup and view all the answers

After solving the system of equations y = 2x and y = 6 - x, how can you ensure your answer is correct?

Substitute the values into both equations. Signup and view all the answers

How would you simplify b^3 times b^6?

b^9. Signup and view all the answers

How would you simplify (4b^7)^2?

16b^14. Signup and view all the answers

When simplifying x^7/x^5, what is the rule for the exponents?

Subtract the exponents. Signup and view all the answers

How do you handle a negative exponent in an expression?

Flip the negative power and make it positive. Signup and view all the answers

How do you raise a fraction to a power?

Raise both the numerator and the denominator to that power. Signup and view all the answers

What is the standard form of the number 6.32 x 10^9?

6,320,000,000. Signup and view all the answers

What is the standard form of the number 4 x 10^-7?

0.0000004. Signup and view all the answers

What is the scientific notation of the number 201,000,000?

2.01 x 10^8. Signup and view all the answers

What is the equation for exponential growth?

y = a(1+r)^t. Signup and view all the answers

What is the equation for exponential decay?

y = a(1-r)^t. Signup and view all the answers

What distinguishes geometric sequences?

They have a common factor or ratio. Signup and view all the answers

What formula do you use to find the 'nth term' of a geometric sequence?

an = a1r^(n-1). Signup and view all the answers

What is the degree of the polynomial 5y - 9 - 2y^4 - 6y^3?

<ol start="4"> <li></li> </ol> Signup and view all the answers

What is the leading coefficient of the polynomial 8 - 2x + 4x^5 - 3x^2?

<ol start="4"> <li></li> </ol> Signup and view all the answers

-4^2 = ?

-16. Signup and view all the answers

(-4)^2 = ?

<ol start="16"> <li></li> </ol> Signup and view all the answers

What is 5x^2 when x = 2?

<ol start="20"> <li></li> </ol> Signup and view all the answers

What does foil mean?

First, outside, inside, last - used to multiply binomials. Signup and view all the answers

What is the result of multiplying (6x + 5)(2x^2 - 3x - 5)?

12x^3 - 8x^2 - 45x - 25. Signup and view all the answers

Use the zero product property to solve (x - 8)(x + 7) = 0.

x = 8, x = -7. Signup and view all the answers

Factor out the GCF from -4a^2b - 8ab^2 + 2ab.

2ab(-2a - 4b + 1). Signup and view all the answers

What are the roots of the equation x^2 + 6x = 27?

3 and -9. Signup and view all the answers

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.