Unit 12 Topics in Algebra
  

Learning Objectives
Rational Equations and Functions
1
    Ratio and Proportion
  • Solve proportions
  • Use proportions to solve real-life problems
2
    Percents
  • Use equations to solve percent problems
  • Use percents in real-life problems
3
    Direct and Inverse Variations
  • Use direct and inverse variation
  • Use direct and inverse variation to model real-life situations
4
    Simplifying Rational Expressions
  • Simplify a rational expression
  • Use rational expressions to find geometric probability
5
    Multiplying and Dividing rational Expressions
  • Multiply and divide rational expressions
  • Use rational expressions to find geometric probability.
6
    Adding and Subtracting Rational Expressions
  • Add and subtract rational expressions that have like denominators
  • Add and subtract rational expressions that have unlike denominators
7
    Dividing Polynomials
  • Divide polynomials by a binomial or by a binomial factor
  • Use polynomial long division
8
    Rational Equations and Functions
  • Solve rational equations
  • Graph rational functions
Learning Objectives
Radicals and Connections to Geometry
1
    Functions Involving Square Roots
  • Evaluate and graph square root functions
  • Use square root functions to model real-life problems
2
    Operations with Radical Expressions
  • Add, subtract, multiply and divide radical expressions
  • Use radical expressions in real-life situations
3
    Solving Radical Expressions
  • Solve radical equations
  • Use radical equations to solve real-world problems
4
    Completing the Square
  • Solve a quadratic equation by completing the square
  • Choose a method for solving a quadratic equation
5
    The Pythagorean Theorem and Its Converse
  • Use the Pythagorean Theorem and its converse
  • Use the Pythagorean Theorem and its converse in real-life problems
6
    The Distance and Midpoint Formulas
  • Find the distance between two points in a coordinate plane
  • Find the midpoint between two points in a coordinate plane
7
    Trigonometric Ratios: Exploring Data and Statistics
  • Use the sine, cosine, and tangle of an angle
  • Use trigonometric ratios in real-life problems
8
    Logical Reasoning: Proof
  • Use logical reasoning and proof to prove a statement is true
  • Prove that a statement is false
Unit 12 Key Concepts
Concept:1. c1
Concept:2. c2
Concept:3. c3
Concept:4. c4
Concept:5. c5
Concept:6. c6

Skills Quizzes : Properties of Real Numbers

Quiz Name Skill Assessed Practice File Passing Grade Notes
Graphing Solve systems of equations by graphing; check the solution See homework assignments for practice problems 3 out of 4
Substitution Solve systems of equations using the substitution method; check the solution. See homework assignments for practice problems 3 out of 4  
Linear Combinations Solve systems of equations using linear combinations; this includes adding, subtracting, multiplication, division; check the solution. See homework assignments for practice problems 3 out of 4  
Writing Systems of Equations Write a system of equations to model a problem; then solve the system and check the solution. 5 out of 6
Writing Systems of Equations Write a system of equations to model a problem; then solve the system and check the solution.
Sample: The difference of George's age and Madison's age is 9 years. The sum of 6 times George's age and 5 times Madison's age is 153. How old is each? 		Practice problem sets (PDF) 3 out of 3 Practice problem set solutions (PDF)
Sample Word Problems For each of these word problems, students should be able to:
  • Write a system of equations that models the propblem
  • Choose an appropriate method for solving the system - graphing, substitution, linear combinations
  • Solve the system (for all variables)
  • Check the solution (in all equations) algebraically

Samantha has $3.40 in dimes and quarters. The number of dimes is 8 less than the number of quarters. How many coins of each type does she have? A piggy bank has $4.30 in dimes and quarters. If the number of dimes is 7 more than 2 times the number of quarters, how many coins of each type are in the piggy bank?
George's age is 5 times Kendell's age. The sum of their ages is 48. Find the age of each. The difference of Jimmy's age and Linda's age is 10 years. The sum of 5 times Jimmy's age and 4 times Linda's age is 104. How old is each?
There were 235 people at a movie to raise funds for the drama club. Admision was $8.00 for each adult and $4.00 for each student. The total receipts for all tickets was $1504.00. How many adults and how many students attended? The length of a rectangle is 11 m less than 5 times the width. The perimeter is 434 m. Find the length and width of the rectangle.
George scored 13 more points than twice as many as Roy did. Their combined score was 40 points. How many points did each score? The difference of Jen's age and Mark's age is 6 years. The sum of 4 times Jen's age and 3 times Mark's age is 108. How old is each?