2021 Year End Algebra Review

Questions and Answers

What word indicates to use parenthesis when translating a verbal sentence into an algebraic one?

Quantity

What letter represents the domain? Range? Output? Input? Independent variable? Dependent variable?

Both A and B (correct)

Z=Parameter

X=Domain, Input, Independent Variable

Y=Range, Output, Dependent Variable

What is the PERCENT of change formula?

difference/original = %/100

Describe how to write an algebraic proof when solving an equation. Name the properties of equality.

Make a two column chart with statements and reasons. The properties of equality include Addition, Subtraction, Multiplication, and Division. Signup and view all the answers

Definition of a relation.

Any set of ordered pairs Signup and view all the answers

Definition of a function.

A relation where each x is paired with exactly one y Signup and view all the answers

What's the shortcut for recognizing a function in ordered pair form?

If you notice that there is an x value repeated with a different answer for the y value Signup and view all the answers

How do you use the vertical line test to tell if a graph is a function?

As the vertical line passes over the graph, it can only intersect the graph one time. Signup and view all the answers

How can you tell if a graph, table, or equation is showing a linear model?

The graph shows a line; the table shows consistent numbering for the x values, and the equation can be written in slope-intercept form. Signup and view all the answers

What is the slope formula?

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?

Zero Signup and view all the answers

What is the rate of change formula?

Difference in the dependent variable/Difference in the independent variable Signup and view all the answers

What is the direct variation formula?

y = kx; k is the constant of variation Signup and view all the answers

How do you find 'k'?

y divided by x Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b Signup and view all the answers

What does m and b stand for?

m=slope, b=y-intercept Signup and view all the answers

What is the standard form of a line?

Ax + By = C Signup and view all the answers

What are the 3 rules for standard form?

A is non-negative; A, B, & C are integers; A, B, C have a GCF of 1 Signup and view all the answers

How do you find the x and y-intercepts of an equation?

Substitute 0 for y and solve for x. Substitute 0 for x and solve for y. Signup and view all the answers

What is true about the slopes of parallel lines? Their y-intercepts?

Parallel lines have the same slopes, but different y-intercepts. Signup and view all the answers

What is true about the slopes of perpendicular lines? Their y-intercepts?

Perpendicular lines have slopes that are opposite and reciprocal. Signup and view all the answers

What is residual?

The difference between the observed value and the predicted value. Signup and view all the answers

What is the difference between correlation and causation?

Correlation is the relationship between two variables; causation is when one variable directly causes the other. Signup and view all the answers

What must you do if you multiply or divide both sides of an inequality by a negative number?

Change the inequality sign. Signup and view all the answers

If an absolute value equation is equal to a negative, what is the answer?

No solution Signup and view all the answers

What are some ways to solve a system?

Graphing, Substitution, and Elimination Signup and view all the answers

What should the answer to a system look like?

An ordered pair (intersection point) Signup and view all the answers

When will a system have no solution?

Parallel lines Signup and view all the answers

When will a system have infinitely many solutions?

Same line (coinciding lines) Signup and view all the answers

What is the rule of multiplying two powers with the same base?

Keep the base, add the exponents Signup and view all the answers

What is the rule of dividing two powers with the same base?

Keep the base, subtract the exponents Signup and view all the answers

What is the rule for taking a power to a power?

Keep the base, multiply the exponents Signup and view all the answers

What is the rule for changing a negative exponent into a positive?

Move it to the opposite location of the fraction bar and make the exponent positive Signup and view all the answers

Any (nonzero) number to the zero power is equal to what?

1 Signup and view all the answers

What is the Pythagorean Theorem formula?

a^2 + b^2 = c^2 Signup and view all the answers

Explain how to find the distance between two points on a coordinate plane using the Pythagorean Theorem.

Draw the vertical and horizontal distance to form a right triangle and then use the Pythagorean Theorem. Signup and view all the answers

What is an outlier?

A value in a data set that is much less or much greater than the rest of the data. Signup and view all the answers

What is the formula for finding the nth term of an arithmetic sequence?

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

What is the formula for finding the nth term of a geometric sequence?

an = a1 * r^(n-1) Signup and view all the answers

What is the midpoint formula?

(x1+x2)/2, (y1+y2)/2 Signup and view all the answers

What is the distance formula?

sqrt((x2 - x1)^2 + (y2 - y1)^2) Signup and view all the answers

Study Notes

Algebraic Concepts and Definitions

Quantity: Indicates the use of parentheses when translating verbal sentences into algebraic form.
Domain and Range: Domain (X) represents input and independent variable; Range (Y) represents output and dependent variable.
Percent of Change Formula: Calculated as difference/original = %/100.
Algebraic Proof: Utilize a two-column chart with statements and reasons. Properties of equality include addition, subtraction, multiplication, and division.
Relation: Defined as any set of ordered pairs.
Function: A specific type of relation where each x is paired with exactly one y.
Vertical Line Test: A function graph intersects a vertical line only once.

Line Equations and Properties

Linear Model Indicators: Identified by a straight graph, consistent x-values in tables, and equations in slope-intercept form (y = mx + b).
Slope: Defined as the ratio of rise to run; slope formula is (\frac{y_2-y_1}{x_2-x_1}).
Undefined and Zero Slopes: Vertical lines have an undefined slope; horizontal lines have a zero slope.
Direct Variation Formula: Expressed as (y = kx), where k is the constant of variation.
Standard Form of a Line: Represented as (Ax + By = C) with specific rules for A, B, and C.

Systems of Equations

Solving Systems: Possible methods include graphing, substitution, and elimination. Solution represented as an ordered pair.
No Solution: Occurs when the system consists of parallel lines.
Infinitely Many Solutions: Arises from coinciding lines.

Exponents and Radicals

Exponent Rules: Include keeping the base when multiplying or dividing (add or subtract exponents respectively) and changing negative exponents by moving them across the fraction line.
Simplifying Radicals: Ensures no perfect square factors under the radical and adheres to rules of simplification.
Extraneous Solutions: Values that do not satisfy the original equation resulting from transformations.

Quadratics and Polynomials

Standard Quadratic Form: Expressed as (y = ax^2 + bx + c). The characteristics of "a" determine the direction and width of the parabola.
Methods for Solving Quadratics: Include graphing, square roots, factoring, and using the quadratic formula.
Discriminant: (b^2 - 4ac) determines the nature of solutions (real roots vs. no solutions).

Sequences and Series

Arithmetic vs. Geometric Sequences: Arithmetic sequences use addition of a constant, while geometric sequences utilize multiplication of a constant.
Nth Term Formulas: Arithmetic: (a_n = a_1 + d(n - 1)); Geometric: (a_n = a_1 \cdot r^{n-1}).

Data Representation and Analysis

Box and Whisker Plot: Visual representation showing quartiles, median, and interquartile range.
Probability Concepts: Compound probability calculated through multiplication of independent events.
Outliers: Values that significantly deviate from the rest of the data, determined through interquartile range calculations.

Statistical Measures

Mean Absolute Deviation: Measures how far each data point is from the mean.
Standard Deviation: Indicates the variation from the mean within a dataset.

Additional Topics

Distance Formula: (\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}) used to determine the distance between two points.
Midpoint Formula: ((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})) calculates the center point between two coordinates.
Pythagorean Theorem: (a^2 + b^2 = c^2) applicable to right-angled triangles.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz provides a comprehensive review of key algebra concepts from the year 2021. It includes questions on translating verbal sentences, understanding domain and range, and calculating percent change. Perfect for students preparing for exams or reinforcing their algebraic knowledge.