Algebra I: High School

About the Course

This Algebra I course is a foundation in algebraic principles and problem-solving skills. Students will learn how to understand and solve mathematical problems involving variables, ratios, inequalities and exponents. They will gain practice in simplifying expressions and choosing the best method for solving complex equations. The course is aligned to Common Core State Standards and it is designed to prepare students for advanced algebra and geometry.

Course Topics

• Word Problems - Interpreting and solving simple and multi-step word problems
• Percent Notation - Converting between percent notation and both decimal and fraction notation
• Ratios, Proportions & Calculations - Solving problems including ratios, money, percents, combinations and permutations
• Real Numbers - Understanding the different types of numbers and an introduction to inequalities and absolute value
• Exponents and Exponential Expressions - Solving equations involving exponential expressions, including multiplying, dividing, rational exponents and negative exponents
• Radical Expressions - Understanding square roots, simplifying radical expressions and mathematical operations involving radical expressions
• Algebraic Expressions & Equations - Working with algebraic expressions and solving algebraic equations including linear, quadratic and polynomial equations
• Algebraic Distribution - Distributing constants, variables and signs in algebraic expressions
• Functions - Understanding functions, including domain, range, inverse functions and function operations
• Inequalities - Understanding inequalities, including absolute value inequalities, and graphing 1- and 2-variable inequalities
• Linear Equations - Working with linear equations, including graphing, interpreting slope and solving systems of equations
• Factoring - Factoring involving numbers and variables, prime factorization and least common multiplies
• Quadratic Equations - Solving quadratic equations using the quadratic formula and solving quadratic inequalities
• Factoring & Graphing Quadratic Equations - Using FOIL, the area method and completing the square; graphing parabolas in standard, intercept and vertex form
• Polynomials - Operations with polynomials, including adding, subtracting, multiplying and dividing using both long and synthetic division
• Rational Expressions - Operations with rational expressions, including adding, subtracting, multiplying and dividing
• Matrices & Absolute Value - Understanding matrices and finding the determinant; solving and graphing absolute value equations
• Statistics & Probability - Calculating mean, median, mode and range; calculating probability with independent and dependent events; interpreting tables, schedules, bar graphs and pie charts

Assignments

Algebraic Expressions

• The temperature outside has dropped 13 degrees in the last two hours. If the temperature right now at 7:00 p.m. is 78 degrees, what was the temperature at 5:00 p.m?
• Tom builds tree houses for a living, but in the last three years, the cost of building a tree house has gone up 15% due to material costs rising. If three years ago, the cost of building a tree house was $500, how much will it cost Tom to build four tree houses this year?
• Simplify the following algebraic expression: 4x(x + 5y) - 3(2xy - 1)
• Solve the following equation for x: 8x + 3(4 - 2x) = 10
• Janet gets paid $40 for each time she babysits her neighbor's kids. She's been working hard lately to buy a necklace she's been wanting that costs $215. If she babysits the kids 5 times, will she have enough money to buy the necklace?

Inequalities

• Franco is collecting seashells. Right now, he has 12 seashells in his pocket. If he collects 3 more seashells a day, how many days will he have to collect seashells so he has at least 21 seashells?
• Solve and graph 2x + 6 ≥ 28
• Solve and graph 8 > 4 - x ≥ -1
• Solve and graph the system of inequalities, labeling each equation on the graph: 2y - 3 ≤ 4x + 1; 4y + 8 > -8; x < 1
• Solve and graph y < |x - 3| + 2
• Create your own inequality using a real-world scenario from your life. For example, 'My goal is to make at least $100 by selling Girl Scout cookies at $4 a box. So far, I've sold 10 boxes.' The inequality for this situation would look like: 40 + 4x ≥ 100.

Graphing & Factoring Quadratic Equations

• Identify the vertex of this parabola: y = 3(x + 5)2 - 6
• Rewrite this equation in intercept form: y = 3x2 + 6x - 24
• Use the area method to find the product: (7x + 2)(4x - 4)
• Factor: x2 + 3x - 28
• Factor: 3x3 - 3x2 - 60x
• Factor and solve for p: 4p2 + 23p - 6 = 0
• Factor and solve for x: 3x2 - 8 = -10x
• Rewrite this equation in vertex form: y - 3 = x2 + 6x - 1

Matrices & Absolute Values

• Find the determinant:
• Find the determinant:
• Solve for x: |2x + 7| = 13
• Solve for x: -3|2x - 6| - 1 = -13
• Identify the vertex of this absolute value graph: y = |x + 7|
• Write the equation of the absolute value graph:
• Write the equation of the absolute value graph: