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Questions and Answers
What word indicates to use parenthesis when translating a verbal sentence into an algebraic one?
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?
What letter represents the domain? Range? Output? Input? Independent variable? Dependent variable?
What is the PERCENT of change formula?
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.
Describe how to write an algebraic proof when solving an equation. Name the properties of equality.
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Definition of a relation.
Definition of a relation.
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Definition of a function.
Definition of a function.
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What's the shortcut for recognizing a function in ordered pair form?
What's the shortcut for recognizing a function in ordered pair form?
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How do you use the vertical line test to tell if a graph is a function?
How do you use the vertical line test to tell if a graph is a function?
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How can you tell if a graph, table, or equation is showing a linear model?
How can you tell if a graph, table, or equation is showing a linear model?
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What is the slope formula?
What is the slope formula?
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What is the slope of a vertical line?
What is the slope of a vertical line?
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What is the slope of a horizontal line?
What is the slope of a horizontal line?
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What is the rate of change formula?
What is the rate of change formula?
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What is the direct variation formula?
What is the direct variation formula?
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How do you find 'k'?
How do you find 'k'?
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What is the slope-intercept form of a line?
What is the slope-intercept form of a line?
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What does m and b stand for?
What does m and b stand for?
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What is the standard form of a line?
What is the standard form of a line?
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What are the 3 rules for standard form?
What are the 3 rules for standard form?
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How do you find the x and y-intercepts of an equation?
How do you find the x and y-intercepts of an equation?
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What is true about the slopes of parallel lines? Their y-intercepts?
What is true about the slopes of parallel lines? Their y-intercepts?
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What is true about the slopes of perpendicular lines? Their y-intercepts?
What is true about the slopes of perpendicular lines? Their y-intercepts?
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What is residual?
What is residual?
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What is the difference between correlation and causation?
What is the difference between correlation and causation?
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What must you do if you multiply or divide both sides of an inequality by a negative number?
What must you do if you multiply or divide both sides of an inequality by a negative number?
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If an absolute value equation is equal to a negative, what is the answer?
If an absolute value equation is equal to a negative, what is the answer?
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What are some ways to solve a system?
What are some ways to solve a system?
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What should the answer to a system look like?
What should the answer to a system look like?
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When will a system have no solution?
When will a system have no solution?
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When will a system have infinitely many solutions?
When will a system have infinitely many solutions?
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What is the rule of multiplying two powers with the same base?
What is the rule of multiplying two powers with the same base?
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What is the rule of dividing two powers with the same base?
What is the rule of dividing two powers with the same base?
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What is the rule for taking a power to a power?
What is the rule for taking a power to a power?
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What is the rule for changing a negative exponent into a positive?
What is the rule for changing a negative exponent into a positive?
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Any (nonzero) number to the zero power is equal to what?
Any (nonzero) number to the zero power is equal to what?
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What is the Pythagorean Theorem formula?
What is the Pythagorean Theorem formula?
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Explain how to find the distance between two points on a coordinate plane using the Pythagorean Theorem.
Explain how to find the distance between two points on a coordinate plane using the Pythagorean Theorem.
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What is an outlier?
What is an outlier?
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What is the formula for finding the nth term of an arithmetic sequence?
What is the formula for finding the nth term of an arithmetic sequence?
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What is the formula for finding the nth term of a geometric sequence?
What is the formula for finding the nth term of a geometric sequence?
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What is the midpoint formula?
What is the midpoint formula?
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What is the distance formula?
What is the distance formula?
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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.
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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.