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Algebra review for midterm

Algebra review for midterm. Fall 2013. Chapter 1: Foundations for Algebra. Variables and Expressions Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers Powers and Exponents Roots and Real Numbers Order of Operations Simplifying Expressions Introduction to Functions.

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Algebra review for midterm

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  1. Algebra review for midterm Fall 2013

  2. Chapter 1: Foundations for Algebra • Variables and Expressions • Adding and Subtracting Real Numbers • Multiplying and Dividing Real Numbers • Powers and Exponents • Roots and Real Numbers • Order of Operations • Simplifying Expressions • Introduction to Functions

  3. Chapter 1: Can you… • Translate between words and algebra? • Evaluate algebraic expressions? (plug it in, plug it in) • Add and subtract real numbers? (positive, negative, fractions, decimals) “Same signs, add and keep…” • Multiply and divide real numbers? (Positive, negative, fractions, decimals) • Evaluate expressions containing exponents? (-6)2 vs. -62 • Evaluate expressions containing square roots? • Classify numbers in the real number system? (rational, irrational, natural, whole, integer) • Use the order of operations to simplify expressions? • Use the Commutative, Associative, and especially the Distributive Properties to simplify expressions? • Combine like terms? (need this later in Chapter 2 as well) • Graph ordered pairs in the coordinate plane? • Graph functions from ordered pairs?

  4. Chapter 2: Equations • Solving Equations by Adding or Subtracting • Solving Equations by Multiplying or Dividing • Solving Two-Step and Multi-Step Equations • Solving Equations with Variables on Both Sides • Solving for a Variable • Solving Absolute-Value Equations • Rates, Ratios, and Proportions • Application of Proportions • Percents • Application of Percents • Percent Increase and Decrease

  5. Chapter 2: Can you… • Solve one-step equations using addition or subtraction? (with fractions, decimals, and all integers) • Solve one-step equations using multiplication or division? (with fractions, decimals, and all integers) • Combine terms that are alike? (this was not in the book but is a skill you need to have mastered) • Solve two-step and multi-step equations? (with fractions, decimals, and all integers) • Solve equations with variables on both sides? (with fractions, decimals and all integers) • Explain the difference between identities and contradictions? • Solve a formula for a given variable? • Solve an equation in two or more variables for a given variable? • Solve equations in one variable that contain absolute value expressions? • Write an equation based on a situation? (any situation…could require any type of equation!) • Interpret the solutions to equations? • Use ratios, rates, and unit rates? (convert between units, use scale, • Write and solve proportions? (to solve similar figure problems, measure objects indirectly, draw conclusions about scale factor) • Solve problems involving percents? (use a proportion, tax, tip, discount, commission, interest) • Find percent increase and percent decrease?

  6. Chapter 3: Inequalities • Graphing and Writing Inequalities • Solving Inequalities by Adding or Subtracting • Solving Inequalities by Multiplying or Dividing • Solving Two-Step and Multi-Step Inequalities • Solving Inequalities with Variables on Both Sides • Solving Compound Inequalities • Solving Absolute Value Inequalities

  7. Chapter 3: Can you… • Identify solutions of inequalities with one variable? • Write and graph inequalities with one variable? • Solve one-step inequalities by using addition? • Solve one-step inequalities by using subtraction? • Solve one-step inequalities by using multiplication and division? (only if you multiply by a negative number….) • Solve two-step and multi-step inequalities? • Solve inequalities that contain variables on both sides? • Interpret the answers for any inequality problem? • Solve compound inequalities? (AND- less than, island / OR- greater than, oar) • Solve absolute value inequalities? (rewrite as a compound inequality)

  8. Chapter 4: functions • Graphing Relationships • Relations and Functions • Writing Functions • Graphing Functions • Scatter Plots and Trend Lines • Arithmetic Sequences

  9. Chapter 4: Can you… • Match a simple graph with a situation? • Graph a situation (no ordered pairs, just generally up or down and at certain rates)? • Tell when a graph should be continuous or discrete? • Identify a function given a graph or a set of ordered pairs? • Find the domain and range of relations and functions? • Identify independent and dependent variables? • Write an equation in function notation and then evaluate the function for given input values? • Graph functions given a limited domain AND a domain of all real numbers? (can you plug in values to a function and create ordered pairs to graph? can you choose your own input values and plug them into an equation?) • Can you create and also interpret a scatter plot? • Can you create a trend line and use it to make predictions? • Can you recognize and also extend an arithmetic sequence? • Can you use the formula to find a given term of an arithmetic sequence? an = a1 + (n– 1)d

  10. Chapter 5: Linear functions • Identifying Linear Functions • Using Intercepts • Rate of Change and Slope • The Slope Formula • The Distance and Midpoint Formula • Direct Variation • Slope-Intercept Form • Point-Slope Form • Slopes of Parallel and Perpendicular Lines • Transforming Linear Functions

  11. Chapter 5: Can you… • Identify a linear function by looking at a graph, table, or equation? • Find the x- and y-intercepts of a graph and explain what they mean? • Use those x- and y-intercepts to graph lines? • Find the Rate of Change in a table? • Differentiate between Rate of Change & CONSTANT Rate of Change (aka Slope)? • Find the slope using the slope formula and explain what the slope means? • Know when to use and then appropriately use the midpoint and distance formulas? • Identify, write, and also graph direct variation? • Write a linear equation in slope-intercept form? • Graph a line using slope- intercept form? • Graph a line and write a linear equation using point-slope form? • Write a linear equation given two points? • Transform point-slope form into slope-intercept form? • Identify and graph parallel and perpendicular lines? • Write equations to describe lines parallel or perpendicular to a given line? • Describe how changing the slope and y-intercept affect the graph of a linear function?

  12. Formulas from chapter 5 y = kx y = mx + b

  13. algebra’s Geometry • All Area Formulas: Square, Rectangle, Trapezoid, Parallelogram, Triangle • Circumference and Area of Circles • Surface Area of Figures (prisms, pyramids, spheres) • Volume of Figures (prisms, pyramids, spheres)

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