Algebra 1B Final Exam Study Set

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Questions and Answers

What is the slope formula?

(Y2-Y1)/(X2-X1)

What is the slope-intercept form?

y=mx+b

What is the standard form of a linear equation?

Ax + By = C

What is the point slope form?

y - y1 = m(x - x1) Signup and view all the answers

What is the vertex form of a quadratic function?

y = a(x-h) + k Signup and view all the answers

What is the slope of the line that passes through the points (-4,6) and (8,-2)?

1 Signup and view all the answers

What is the slope of the line that passes through the points (2,5) and (4,6)?

1/2 Signup and view all the answers

What is the slope of a vertical line?

undefined Signup and view all the answers

How is the equation for a vertical line written?

X = <constant> Signup and view all the answers

What is the slope of a horizontal line?

0 Signup and view all the answers

How is the equation for a horizontal line written?

Y = <constant> Signup and view all the answers

What is the slope of a line parallel to y = 1/2x - 3?

1/2 Signup and view all the answers

What is the slope of a line perpendicular to y = 1/2x - 3?

-2 Signup and view all the answers

What is the y-intercept for the line y = -4x + 6?

6 Signup and view all the answers

What is the slope for the line y = -4x + 6?

-4 Signup and view all the answers

What is the y-intercept for the line 6x + 3y = 12?

4 Signup and view all the answers

What is the x-intercept for the line 6x + 3y = 12?

2 Signup and view all the answers

What does the solution of a system of equations mean?

Where two lines intersect/cross; a point that two lines share Signup and view all the answers

What does it mean if a system of equations does not have a solution?

The lines are parallel; they never intersect Signup and view all the answers

What does it mean if a system of equations has an infinite amount of solutions?

They are the same line Signup and view all the answers

If you are writing a system of equations to represent the number of tickets sold at a concert, what will your two systems represent?

The number of tickets and the price of tickets Signup and view all the answers

How do you write 'The length is 3 less than 5 times the width' as a mathematical expression?

L = 5W - 3 Signup and view all the answers

How do you write 'The length is 2 less than 1/2 the width' as a mathematical expression?

L = 1/2W - 2 Signup and view all the answers

What is the equation for the perimeter of a rectangle with a perimeter of 25 in. and the length is 3 less than 4 times the width?

25 = 2W + 2(4W - 3) Signup and view all the answers

What is the equation for the perimeter of a rectangle with a perimeter of 15 in. and the length is 1 less than 1/3 the width?

15 = 2W + 2(1/3W - 1) Signup and view all the answers

Describe what standard form is in regards to polynomials.

A polynomial written in the order of highest degree to lowest degree. Signup and view all the answers

What is the term for a polynomial with a degree of 1?

Linear Signup and view all the answers

What is the term for a polynomial with a degree of 2?

Quadratic Signup and view all the answers

What is the term for a polynomial with a degree of 3?

Cubic Signup and view all the answers

What is the term for a polynomial with a degree of 4?

Quartic Signup and view all the answers

What is the term for a polynomial with one term?

Monomial Signup and view all the answers

What is the term for a polynomial with two terms?

Binomial Signup and view all the answers

What is the term for a polynomial with three terms?

Trinomial Signup and view all the answers

What is the equation for the area of a rectangle?

Length x Width Signup and view all the answers

What is the greatest common factor of 16x - 12?

4 Signup and view all the answers

What is the greatest common factor of 15xyz + 10xy - 25xz?

5x Signup and view all the answers

Would you shade above or below the line to represent possible solutions for Y > 3x?

Above Signup and view all the answers

Study Notes

Key Algebra Concepts

Slope Formula: The slope of a line defined as ( \frac{Y2 - Y1}{X2 - X1} ).
Slope Intercept Form: A linear equation represented as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
Standard Form: Linear equations written in the format ( Ax + By = C ).
Point Slope Form: Equation of a line expressed as ( y - y1 = m(x - x1) ).
Vertex Form: Quadratic functions shown in the format ( y = a(x - h) + k ).

Slope Calculations

Slope of Line through points (-4,6) and (8,-2): Calculated to be 1.
Slope of Line through points (2,5) and (4,6): Slope equals ( \frac{1}{2} ).
Vertical Line Slope: The slope is undefined; its equation is of the form ( x = \text{constant} ).
Horizontal Line Slope: The slope equals 0; its equation is of the form ( y = \text{constant} ).

Line Relationships

Parallel Lines: Lines with the same slope (e.g., slope of ( y = \frac{1}{2}x - 3 ) is ( \frac{1}{2} )).
Perpendicular Lines: Lines that have slopes that are negative reciprocals (e.g., perpendicular slope to ( y = \frac{1}{2}x - 3 ) is -2).
Y-Intercept Calculation: For ( y = -4x + 6 ), the y-intercept is 6.
Slope Calculation: For ( y = -4x + 6 ), the slope is -4.

Systems of Equations

Intersection Point Meaning: The point where two lines intersect represents the solution of a system of equations.
No Solution Scenario: When lines are parallel, indicated by their slopes being equal, they do not intersect.
Infinite Solutions Scenario: Occurs when both lines are identical, represented by the same equation.

Mathematical Expressions

Ticket Sales Representation: Two equations can model ticket count and pricing for a concert.
Length vs. Width Expressions:
- "Length is 3 less than 5 times the width": ( L = 5W - 3 )
- "Length is 2 less than ( \frac{1}{2} ) of the width": ( L = \frac{1}{2}W - 2 )

Perimeter Equations

Perimeter Equation for Rectangle (P = 25 in., L = 3 less than 4W): ( 25 = 2W + 2(4W - 3) ).
Perimeter Equation for Rectangle (P = 15 in., L = 1 less than ( \frac{1}{3} )W): ( 15 = 2W + 2(\frac{1}{3}W - 1) ).

Polynomial Terminology

Standard Form in Polynomials: Arrangement from highest to lowest degree.
Degrees of Polynomials:
- Degree 1: Linear
- Degree 2: Quadratic
- Degree 3: Cubic
- Degree 4: Quartic
Types of Polynomials:
- One-term: Monomial
- Two-terms: Binomial
- Three-terms: Trinomial

Areas and Common Factors

Area of Rectangle: Given by the formula ( \text{Length} \times \text{Width} ).
Greatest Common Factor:
- For ( 16x - 12 ): GCF is 4.
- For ( 15xyz + 10xy - 25xz ): GCF is ( 5x ).

Graphing Solutions

Shading Regions:
- For ( Y > 3x ): Shade above the line to represent feasible solutions.
- Other inequalities will similarly dictate where to shade based on their respective boundaries.

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Description

Prepare for your Algebra 1B final exam with this comprehensive study set of flashcards. Each card covers key formulas and definitions, including slope formulas and various line forms to solidify your understanding of essential concepts. Test your knowledge and ensure you're ready for the exam.