2.1 Algebraic Expressions and Combining like Terms

Transcription

1 2.1 Algebraic Expressions and Combining like Terms Evaluate the following algebraic expressions for the given values of the variables Simplify the following algebraic expressions by combining like terms, if possible W.D. has determined that his average monthly cost of playing tennis can be represented by the algebraic expression. In this expression, represents the number of cans of balls and represents the number of pairs of shoes he uses each month. Determine the monthly cost if he uses cans of balls and pair of shoes. Revised Page 1 of 36

2 2.2 The additive Property of Equality MATH 0308 Solve the following linear equations and check your solutions [ ] 87. [ ] 90. [ ] [ ] Revised Page 2 of 36

3 2.3 The Multiplicative Property of Equality Solve the following linear equations and check your solutions Betsy and Charlie live between Los Angeles and San Francisco. If they live twice as far from San Francisco as they do from Los Angeles and it is miles between the two cities, how far do they live from Los Angeles? 102. Dora s Discount Auto World sells new cars at a price that is of the manufacturer s suggested retail price (MSRP). Dora s price on a new Junebug is. What is the MSRP of a Junebug? Revised Page 3 of 36

4 2.4 Combining Properties to Solve Linear Equations Solve the following equations [ ] 60. [ ] 6 [ ] 6 [ ] 6 Revised Page 4 of 36

5 2.7 Applications of Linear Equations MATH 0308 In problems 1-20 convert each phrase to an algebraic expression. Let be the variable. Use equations to find the solutions of the following problems Revised Page 5 of 36

6 60. Revised Page 6 of 36

7 2.9 Linear Inequalities Find the solutions of the following inequalities and graph the solution sets on a number line Revised Page 7 of 36

8 1 Natural Number Exponents MATH 0308 Name the base and the exponent in each of the following expressions. Rewrite each of the following expressions using exponents. Evaluate each of the following expressions Using the laws of exponents, simplify the following expressions, if possible [] ] [ ] [ ] Revised Page 8 of 36

9 2 Integer Exponents Evaluate each of the following. [ ] [ ] 3 3 Simplify each of the following. (Remember to write your answers with only positive exponents.) Revised Page 9 of 36

10 3 Adding and Subtracting Polynomials Simplify each of the following polynomials by combining like terms, if possible. After simplifying, state the degree and specify which are monomials, binomials, and trinomials. Simplify each of the following polynomials by combining like terms, if possible. After simplifying, write the polynomial in standard form and determine the leading coefficient Perform the indicated operations, and simplify your answer by combing like terms. ( ) Revised Page 10 of 36

11 MATH Revised Page 11 of 36

12 4 Multiplying Polynomials Multiply the following polynomials. ( ) Revised Page 12 of 36

13 5 The FOIL Method and Special Products of Binomials Perform the indicated multiplications [ ][ ] 6 [ ][ ] Revised Page 13 of 36

14 6 Dividing Polynomials Perform the indicated divisions Revised Page 14 of 36

15 4.1 The Greatest Common Factor MATH 0308 Find the prime factored form for each of the following numbers. Find the greatest common factor for each of the following groups of numbers. Find the greatest common factor for each of the following groups of monomials. 3 3 Completely factor the following polynomials Revised Page 15 of 36

16 4.2 Factoring the Difference of two Perfect Squares and perfect Square Trinomials Completely factor the following polynomials Revised Page 16 of 36

17 4.3 Factoring Trinomials with Leading Coefficient of 1 Completely factor the following trinomials Revised Page 17 of 36

18 4.4 Factoring General Trinomials Completely factor the following trinomials. MATH Revised Page 18 of 36

19 4.5 Factoring by Grouping Completely factor the following polynomials Completely factor the following trinomials Revised Page 19 of 36

20 4.6 Factoring the Sum and Difference of Two Perfect Cubes Completely factor the following binomials Revised Page 20 of 36

21 4.7 Factoring Summary Completely factor the following polynomials Revised Page 21 of 36

22 4.8 Solving Quadratic Equations by Factoring Find the solutions of the following equations; also check your solutions Revised Page 22 of 36

23 4.9 Applications of Quadratic Equations Solve the following problems. Revised Page 23 of 36

24 5.1 Reducing to Lowest Terms MATH 0308 Reduce the following rational expressions to lowest terms Revised Page 24 of 36

25 5.2 Multiplying and Dividing Rational Expressions Perform the indicated operations, and reduce the answers to lowest terms Revised Page 25 of 36

26 5.3 Adding and Subtracting Rational Expressions with a Common Denominator Perform the indicated additions and subtractions Revised Page 26 of 36

27 5.4 Adding and Subtracting Rational Expressions with Different Denominators Perform the indicated additions and subtractions Revised Page 27 of 36

28 5.6 Fractional Equations Solve the following equations Revised Page 28 of 36

29 1 Solutions of Linear Equations in two Variables For each equation, determine whether the given ordered pair is a solution. Find solutions for each equation using the indicated values for x or y Solve each equation for y, then find solutions using the indicated values for x Solve each equation for x, then find solutions using the indicated values for y Revised Page 29 of 36

30 2 The Cartesian Coordinate System MATH Identify the coordinates of each point in Figure 2.10 For each point in Figure 2.11 state whether each coordinate is positive, negative, or zero. Plot the points indicated in each of the following sets. { } { } { } Revised Page 30 of 36

31 3 Graphing Linear Equations Graph the following equations. MATH 0308 Find the x- and y-intercepts, and use them to graph each equation Solve each equation for y, then use the new equation to find ordered pair solutions. Also, graph the equations Revised Page 31 of 36

32 4 The Slope of the Line Find the slope of the line passing through each of the following pairs of points. Find the slopes of the lines whose equations are given. Graph the lines satisfying the following conditions. Revised Page 32 of 36

33 5 Equations of Lines Find the equations of the following lines. Write the answers in slope-intercept form. Find the slopes and y-intercept of the following lines. Find the equations of the following lines. Write the answers in slope intercept form, when possible. Find the equations of the lines passing through the given points. Write the answers in slopeintercept form, when possible. Find the equations of the lines passing through the given points parallel to the given lines. Write the answers in slope-intercept form, when possible. Revised Page 33 of 36

34 5 Equations of Lines Continued MATH 0308 Find the equations of the lines passing through the given points perpendicular to the given lines. Write the answers in slope-intercept form, when possible. 57. Revised Page 34 of 36

35 7.2 The Substitution Method MATH 0308 Using the substitution method or addition elimination method to determine the solution(s) of the following linear systems of equations. If there are no solutions, write inconsistent. If there are infinitely many solutions, write dependent. Revised Page 35 of 36

36 7.3 The Addition Elimination Method MATH 0308 Using the elimination method or substitution method to determine the solution(s) of the following linear systems of equations. If there are no solutions, write inconsistent. If there are infinitely many solutions, write dependent. Revised Page 36 of 36

37 7.4 Applications of Linear Systems MATH 0308 Use a linear system of equations to solve each of the following problems. Revised Page 37 of 36