Algebra Placement Test Flashcards

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Questions and Answers

What are the properties of exponents covered in Lesson 1?

Product of Powers Property

Quotient of Powers Property

Power of a Power Property

All of the above (correct)

What is the product of powers property?

When multiplying two powers with the same base, add the exponents.

What is the quotient of powers property?

When dividing two powers with the same base, subtract the exponents.

What is the power of a power property?

To raise a power to another power, multiply the exponents. Signup and view all the answers

What is the power of a product property?

To raise a product to a power, raise each factor to the power. Signup and view all the answers

What is the power of a quotient property?

To raise a quotient to a power, raise both the numerator and the denominator to the power. Signup and view all the answers

What is the effect of a zero exponent on a number?

Any non-zero number raised to the zero exponent equals one. Signup and view all the answers

What happens when a number is raised to a negative exponent?

It equals the reciprocal of the number raised to the positive exponent. Signup and view all the answers

What is a rational exponent?

An exponent that is a fraction, representing both a root and a power. Signup and view all the answers

What is the formula for exponential growth?

y = initial amount(1 + rate)^time Signup and view all the answers

What is the formula for exponential decay?

y = initial amount(1 - rate)^time Signup and view all the answers

What is the Distributive Property of addition?

a(b + c) = ab + ac Signup and view all the answers

What is the Associative Property of Addition?

(a + b) + c = a + (b + c) Signup and view all the answers

What is the Associative Property of Multiplication?

(a * b) * c = a * (b * c) Signup and view all the answers

What is the Addition Property of Zero?

a + 0 = a Signup and view all the answers

What is the Distributive Property of subtraction?

a(b - c) = ab - ac Signup and view all the answers

What does a line graph represent?

A line graph displays data points connected by straight lines. Signup and view all the answers

What is a bar graph?

A bar graph uses rectangular bars to represent data quantities. Signup and view all the answers

What is a pictograph?

A pictograph uses images or icons to represent data values. Signup and view all the answers

What is a pie chart?

A pie chart shows parts of a whole as slices of a circular graph. Signup and view all the answers

What is a stem and leaf plot?

A stem-and-leaf plot is a method for displaying quantitative data in order. Signup and view all the answers

What is the rate of change?

Change in y/change in x or (y2 - y1)/(x2 - x1) Signup and view all the answers

What is a linear graph?

A linear graph represents a straight-line relationship between variables. Signup and view all the answers

What is an exponential graph?

An exponential graph shows a rapid increase or decrease, forming a curve. Signup and view all the answers

What is a quadratic graph?

A quadratic graph forms a parabola and represents second-degree relationships. Signup and view all the answers

What is the equation of a line?

y = mx + b; where m is the slope and b is the y-intercept. Signup and view all the answers

What is slope-intercept form?

The slope-intercept form is a linear equation represented as y = mx + b. Signup and view all the answers

What is point-slope form?

Point-slope form is represented as y - y1 = m(x - x1). Signup and view all the answers

What is factoring?

Factoring is breaking down a polynomial into simpler components. Signup and view all the answers

What is the quadratic formula to solve ax^2 + bx + c?

x = (-b ± √(b^2 - 4ac)) / (2a) Signup and view all the answers

What is a perfect square trinomial?

A perfect square trinomial is represented as a^2 ± 2ab + b^2. Signup and view all the answers

What is the difference of two square patterns?

a^2 - b^2 = (a + b)(a - b) Signup and view all the answers

What is graphing quadratic functions?

Graphing quadratic functions involves plotting a curve to represent their equations. Signup and view all the answers

Study Notes

Properties of Exponents

Product of Powers Property: When multiplying two powers with the same base, add their exponents: ( a^m \cdot a^n = a^{m+n} ).
Quotient of Powers Property: When dividing two powers with the same base, subtract the exponents: ( \frac{a^m}{a^n} = a^{m-n} ).
Power of a Power Property: To raise a power to another power, multiply the exponents: ( (a^m)^n = a^{mn} ).
Power of a Product Property: Distribute the exponent to each factor in the product: ( (ab)^n = a^n \cdot b^n ).
Power of a Quotient Property: Distribute the exponent to both the numerator and the denominator: ( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} ).
Zero Exponent: Any non-zero base raised to the power of zero equals one: ( a^0 = 1 ) (where ( a \neq 0 )).
Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: ( a^{-n} = \frac{1}{a^n} ).
Rational Exponent: An exponent that is a fraction indicates roots: ( a^{\frac{m}{n}} = \sqrt[n]{a^m} ).

Exponential Growth and Decay

Exponential Growth Model: Represented by the formula ( y = \text{initial amount} \cdot (1 + \text{rate})^{\text{time}} ).
Exponential Decay Model: Represented by the formula ( y = \text{initial amount} \cdot (1 - \text{rate})^{\text{time}} ).

Algebraic Manipulation

Distributive Property of Addition: Shows how to distribute a multiplier across a sum: ( a(b + c) = ab + ac ).
Associative Property of Addition: The way numbers are grouped does not affect the sum: ( (a+b) + c = a + (b+c) ).
Associative Property of Multiplication: The grouping of numbers does not affect the product: ( (a \cdot b) \cdot c = a \cdot (b \cdot c) ).
Addition Property of Zero: Adding zero to any number leaves it unchanged: ( a + 0 = a ).
Distributive Property of Subtraction: Distributes across a difference: ( a(b - c) = ab - ac ).

Graphing and Data Interpretation

Line Graph: Displays data changes over time with points connected by lines.
Bar Graph: Uses rectangular bars to represent discrete categories or values.
Pictograph: Uses pictures or symbols to visually represent data quantities.
Pie Chart: Circular chart divided into slices to illustrate numerical proportions.
Stem and Leaf Plot: Displays quantitative data in a graphical format, preserving original data values.

Rates of Change

Rate of Change Formula: Defined as the change in y over the change in x: ( \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} ).

Comparing Models

Linear Graph: Represents a constant rate of change in a straight line.
Exponential Graph: Shows rapid increases or decreases, generally curved.
Quadratic Graph: Takes the shape of a parabola, representing squared relationships.

Writing Equations of a Line

Equation Format: ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

Graphing Lines

Slope-Intercept Form: Focused on the slope and y-intercept for graphing linear equations.
Point-Slope Form: Expresses the equation of a line in relation to a specific point on the graph.

Solving Quadratic Equations

Factoring Approach: Represents a quadratic in the form ( ax^2 + bx + c ); ( b ) represents the sum of roots, and ( c ) represents the product of roots.
Quadratic Formula: Used to find solutions for ( ax^2 + bx + c = 0 ).
Perfect Square Trinomial: Format ( a^2 + 2ab + b^2 = (a+b)^2 ) or ( a^2 - 2ab + b^2 = (a-b)^2 ).
Difference of Two Squares: Expresses as ( a^2 - b^2 = (a + b)(a - b) ).

Graphing Quadratic Functions

Focuses on graphing parabolas and identifying key features such as vertex and axis of symmetry.

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Description

Test your knowledge of exponents with these flashcards covering key properties such as the product of powers and power of a product. Each card presents a fundamental concept necessary for mastering algebra. Ideal for students preparing for an algebra placement test.