Algebra Units 1-4

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Algebra Units 1-8 Key Concepts and Instructions

Unit 1: Expressions and Variables
- Evaluate algebraic expressions by substituting values for variables
- Combine like terms
- Use distributive property

Unit 2: Solving Linear Equations
- Solve one-step and multi-step equations
- Equations with variables on both sides
- Basic form:

Unit 3: Linear Inequalities
- Solve and graph inequalities on a number line
- Compound inequalities (AND/OR)
- Basic form:

Unit 4: Functions
- Function notation f(x)
- Domain and range
- Linear functions:
- Graph functions and identify key features

Unit 5: Linear Systems
- Solve systems by substitution and elimination
- Graph systems of equations
- Basic form:

Unit 6: Exponents and Exponential Functions
- Laws of exponents
- Exponential growth/decay:
- Scientific notation

Unit 7: Polynomials
- Add, subtract, multiply polynomials
- Factor polynomials
- FOIL method for binomials

Unit 8: Quadratic Functions
- Solve quadratic equations by factoring
- Quadratic formula:

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Timothy & Tya

United States

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Algebra Units 1-4


Froggy Jumps Algebra Units 1-4Online version Algebra Units 1-8 Key Concepts and Instructions Unit 1: Expressions and Variables - Evaluate algebraic expressions by substituting values for variables - Combine like terms - Use distributive property Unit 2: Solving Linear Equations - Solve one-step and multi-step equations - Equations with variables on both sides - Basic form: Unit 3: Linear Inequalities - Solve and graph inequalities on a number line - Compound inequalities (AND/OR) - Basic form: Unit 4: Functions - Function notation f(x) - Domain and range - Linear functions: - Graph functions and identify key features Unit 5: Linear Systems - Solve systems by substitution and elimination - Graph systems of equations - Basic form: Unit 6: Exponents and Exponential Functions - Laws of exponents - Exponential growth/decay: - Scientific notation Unit 7: Polynomials - Add, subtract, multiply polynomials - Factor polynomials - FOIL method for binomials Unit 8: Quadratic Functions - Solve quadratic equations by factoring - Quadratic formula: by Timothy & Tya 1 x a x = 5 b x = 4 c x = 3 2 Simplify: 3(a + 4) - 2a a a - 12 b 5a + 4 c a + 12 3 Combine like terms: 6x - 2x + 3 a 4x + 3 b 8x c 4x - 3 4 Solve for x: 5x - 7 = 2x + 9 a x = 8 b x = 2 c x = -2 5 What is the slope of the line y = 3x + 4? a 1/3 b 4 c 3 6 Convert to equation: y = 2x - 5, solve for y when x = 3 a y = 11 b y = -1 c y = 1 7 Solve: (x - 2) + 3x = 12 a x = 3 b x = 4 c x = 2 8 Distribute: 4(a - 3) = 20 a a = 8 b a = 5 c a = -2 9 Solve for x: 1/2 x = 7 a x = 14 b x = 21 c x = 7 10 If 2x + 3 = 0, what is x? a x = -2 b x = -3/2 c x = 3/2 11 What is the slope-intercept form of a line? a ax + by = c b y = mx + b c y = x^2 + c 12 Given y ≤ 2x + 1 and y ≥ -x + 4, which point lies in the intersection? a (4, 0) b (2, 5) c (0, 0) 13 A rational number can be written as what? a a/b with integers a, b ≠ 0 b a^2 + b^2 = 1 c √(a/b) with integers a, b 14 Which is an irrational number? a √2 b 0.25 c 1/3 15 A quadratic equation is written in which standard form? a a^2x + b^2x + c^2 = 0 b ax^2 + bx + c = 0 c y = ax^2 + bx + c 16 What is the vertex form of a quadratic? a y = a(x - h)^2 + k b y = ax^2 + b c y = (x/h)^2 + k 17 Solve x^2 - 5x + 6 = 0. What are the roots? a x = 2 or x = 3 b x = -2 or x = -3 c x = 1 and x = 5 18 If f(x) = 3x + 4, what is f(2)? a 14 b 10 c 8 19 What describes the feasible region in a system of inequalities? a All plane points b Only boundary lines c Points satisfying all inequalities 20 Discriminant b^2 - 4ac tells how many real roots a quadratic has. If it is negative, how many real roots are there? a None b One c Two

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Algebra Units 1-4

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Algebra Units 1-4Online version

by Timothy & Tya

x

Simplify: 3(a + 4) - 2a

Combine like terms: 6x - 2x + 3

Solve for x: 5x - 7 = 2x + 9

What is the slope of the line y = 3x + 4?

Convert to equation: y = 2x - 5, solve for y when x = 3

Solve: (x - 2) + 3x = 12

Distribute: 4(a - 3) = 20

Solve for x: 1/2 x = 7

If 2x + 3 = 0, what is x?

What is the slope-intercept form of a line?

Given y ≤ 2x + 1 and y ≥ -x + 4, which point lies in the intersection?

A rational number can be written as what?

Which is an irrational number?

A quadratic equation is written in which standard form?

What is the vertex form of a quadratic?

Solve x^2 - 5x + 6 = 0. What are the roots?

If f(x) = 3x + 4, what is f(2)?

What describes the feasible region in a system of inequalities?

Discriminant b^2 - 4ac tells how many real roots a quadratic has. If it is negative, how many real roots are there?