ALGEBRA SUGGESTED HOMEWORK AND COURSE OBJECTIVES
Sec | Obj | Suggested Homework and Course Objectives for each Section |
A5 | Hwk | 1-11 odd |
1. | Rational Expressions a. Equivalent Rational Expressions. (Class Examples) b. Multiply or divide rational expressions; simplify. (Sec A5: Example 2) c. Add or subtract rational expressions; simplify. (Sec A5: Examples 3-6) d. Simplify mixed quotient. (Sec A5: Example 7) |
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A6 | Hwk | 37, 39, 41, 43, 47, 57, 61, 63, 65 |
2. | Understand the meaning of rational exponents; simplify numbers
raised to rational exponents. (Sec A6: Example 7) |
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3. | Special Factoring Techniques a. Factor by grouping. (refer to your class notes; may also refer to Sec A3: Example 3f) b. Factor and simplify an expression containing rational exponents. (Sec A6: Example 10) c. Factor and simplify an expression containing rational exponents and a common binomial factor. (Class Examples) |
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CN | Hwk | Sec 1.3 1-51 every other odd; Sec 1.5 1-15 and 31-53 every other odd |
4. | Solving Equations a. Solve linear equations. (Refer to your class notes; may also refer to Sec A1: Examples 12) b. Solve quadratic equations (including Quadratic Formula). (Refer to your class notes; may also refer to Sec 1.3: Algebraic solution of Example 6; Sec A2: Example 3) c. Solve rational equations. (Class Examples) d. Solve higher order equations. Understand the existence of real number roots. (refer to your class notes; may also refer to Sec A1: Example 13a) e. Solve equations that contain even- or odd-root radicals. (Refer to your class notes; may also refer to Sec 1.3: Algebraic Solutions of Example 10) |
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5. | Inequalities a. Solve linear inequality. and express the solution in interval notation. (Refer to your class notes; may also refer to Sec.1.5: Examples 7, 8) b. Express the solution to inequalities in interval notation. (Refer to your class notes; may also refer to Sec.1.5: Example 1) c. Express the solution to inequalities in interval notation and understanding the terms “or” and “and”. (Refer to your class notes.) |
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1.1 | Hwk | 1, 21, 23, 31, 33, 49, 55, 57 |
6. | Rectangular Coordinate System a. Understand plotting points on the Rectangular Coordinate Sytem. (Sec 1.1: Figure 2, 3) b. Recall and use the distance formula. (Sec 1.1: Example 2) c. Recall and use the midpoint formula. (Sec 1.1: Example 5) |
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1.2 | Hwk | Recall and use the midpoint formula. (Sec 1.1: Example 5) 1.2 Hwk 3, 7, 9; For 11, 19, 25, 27: sketch the graph by hand by making a table of values, find any intercepts; 31, 33, 37, 41, 47, 49, 51, 53, 54, 57, 59, 61, 63; For 65, 67, 69, 71, 73: find the intercepts, test for symmetry, you do not need to graph. |
7. | General Graphing Principles a. Understand what it means for a point (a,b) to be on the graph of an equation. (Sec 1.2: Example 1,2,9,10) b. Identify intercepts from a graph or from an equation. (Sec 1.2: Example 4,5) c. Symmetry Determine symmetry with respect to the x-axis, y-axis, or origin from a graph (Sec 1.2: Figure 27) Given a point on a graph, give the coordinates of a point that must also be on the graph if the graph is symmetric with respect to the x-axis, y-axis, or origin. (Sec 1.2: Example 7) Algebraically determine if the graph of an equation has any symmetry. (Sec 1.2: Example 8) |
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1.6 | Hwk | 1-75 odd, 85, 87, 89 |
8. | Linear Equations a. Calculate and interpret slope. (Sec 1.6: Example 1) b. Graph lines by hand by obtaining the x- and y- intercepts or any two points. (Sec 1.6: Example 2, 3) c. Identify the slope and y-intercept from the equation of a line. (Sec 1.6: Example 7) d. Write the equation of a horizontal or vertical line. (Sec 1.6: Example 3, 5) Write the equation of a line given two points on the line or given a point and the slope. (Sec 1.6: Ex. 4) e. Write the equation for a linear relationship described in an applications problem. (Class Examples) f. Write the equation of a line that goes through a given point that is parallel or perpendicular to a given line. (Sec 1.6: Example 9, 10, 11) |
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1.7 | Hwk | For 5, 7, 9, 11: Just write the standard form; 15, 17 (You will not
be asked to complete the square and obtain the general form of the equation of a circle.) |
9. | Identify the center and radius and graph a circle when given the
equation in standard (center-radius) form. (Sec 1.7: Examples 1,2) |
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2.1 | Hwk | 1, 3, 5, 9, For 13, 15, 17, 19: add g) find f(3a); 21-32 all, 33,
35(omit c), 37-45 odd, 46, 47, 49-62 all, 67, 69 |
10. | Functions a. Identify the graph of a function; determine whether a relation represents a function. (Sec 2.1: Examples 1,2,7) b. Find value of a function. (Sec 2.1: Example 4) c. Find the domain and range of a function from a graph. (Sec 2.1: Example 8) Find the domain of a function from the equation of the function. (Sec 2.1: Example 6) d. Obtain information from and about the graph of a function. (Sec 2.1: Examples 8,9) |
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2.3 | Hwk | 1-7 odd, 9, 11, 13, 15, 19, 25, 31, 33, 37, 39, 41-49 odd, 55, 63, 65, 71 |
11. | Properties of Functions a. From a graph, identify intervals where a function is increasing, decreasing, or constant. (Sec 2.3: Example 3) b. From a graph, identify local maximums or local minimums and where they occur. (Sec 2.3: Figure 24) c. Find the average rate of change of a function. (Sec 2.3: Example 2) d. Find the slope of the secant line containing (x, f(x)) and (x + h, f(x + h)) on the graph of a function y = f(x). (Sec 2.3) e. Determine, from a graph or from an equation, whether a function is even or odd. (Sec 2.3: Example 5,6) |
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12. | Recognize the graph, equation, and properties, of any of the basic
functions in the Library of Functions (except Greatest-Integer). (Sec 2.3) |
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13. | Functions defined Piecewise a. Evaluate a function defined piecewise. (Sec 2.3: Example 7) b. Graph a function defined piecewise. (Sec 2.3: Example 7) |
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2.4 | Hwk | 1-23 odd, 29-43 odd, 59, 61, 63, |
14. | Graphing with Reflections, Compressions/Stretching, Translations a. Identify reflections about the x- or y-axis; graph a function reflected about either axis. Understand the affect of a reflection about a coordinate axis on the coordinates of a point on a graph or on the domain or range of the function. (Sec 2.4: Figure 46) b. Identify compressing or stretching factors from an equation; graph a function with these. Understand the affect of a compressing or stretching factor on the coordinates of a point on a graph or on the domain or range of the function. (Sec 2.4: Example 3) c. Identify vertical or horizontal translations from an equation; graph a function with these. (Sec 2.4: Example 1,2) |
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2.5 | Hwk | 1-9 odd, 13-27 odd, 31, 33, 37, 47, 49, 51 |
15. | Form the sum, difference, product, or quotient of two functions;
evaluate; give the domain of the new function. (Sec 2.5: Example 1) |
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16. | Function Composition a. Form the composite of two functions; evaluate a composite function. (Sec 2.5: Examples 2, 4) b. Find the domain of a composite function. (Sec 2.5: Example 3) |
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2.6 | Hwk | 1a, 3a |
17. | Construct and analyze functions and math models. (Sec 2.6: Examples 1-5) | |
3.1 | Hwk | 1-7 odd, 13-21 odd, 25, 29, 35, 37, 39, 41, 43, 43, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 75 abc |
18. | Quadratic Functions a. Given a quadratic function in the form y = ax^2 +bx + c, find the vertex, all intercepts, and sketch the graph by hand. (Sec 3.1: Examples 1 – 5) b. Given a quadratic function in the form y = a(x – h)^2 + k, find the vertex, all intercepts, and sketch the graph by hand. (Apply graphing translations from Sec 2.4) c. Obtain the quadratic function needed to solve an applications problem; find the maximum or minimum value of a quadratic function. (Sec 3.1: Example 7-10) |
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3.2 | Hwk | Figure 19 and 20 |
19. | Power Functions a. Graph a power function by hand; give domain and range and identify intervals where increasing or decreasing. (Sec 3.2: Figure 19, 20) |
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3.8 | Hwk | Solve algebraically. 1, 3, 9, 11 17, 25, 27, 33, 39, 41, 45, 47, 49, 53 |
20. | Polynomial and Rational Inequalities a. Solve a polynomial inequality algebraically. (Sec 3.8: Example 1, 2) b. Solve a rational inequality algebraically. (Sec 3.8: Example 3) c. Given a rational inequality, find the number of partitioning values needed to solve. (Class Examples.) |
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4.1 | Hwk | 1, 3, 5, 9, 11, 15, 17, 19; For 21, 25, 27: verify and graph.; For
29: just verify; 33, 35, 37, 39, 41; For 47, 49, 53: just find the inverse |
21. | Inverse Functions a. Determine whether a function is one-to-one by looking at a graph or set of ordered pairs. (Sec 4.1: Example 2) b. Given the graph of a one-to-one function, draw the graph of the inverse function. (Sec 4.1: Example 4) c. Use composition to determine if two functions are inverses. (Sec 4.1: Example 6) d. Given an equation of a function, find an equation of the inverse function, f-1. (Sec 4.1: Example 6, 7) |
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4.2 | Hwk | For 11-18 omit D, H, G, do 11,
12, 15-17; For 19-24 omit F, do 19, 21-24; 25, 27, 37, 39, 41; and 4.5: 19,31 |
22. | Exponential Functions a. Given an exponential function, give the domain, range, intervals where increasing or decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.2: Example 2, 3) b. Given an exponential function with a translation, give the domain, range, intervals where increasing or decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.2: Example 4,5) c. Use a calculator to evaluate exponential expressions, including applications problems. (Sec 4.2: Example 1) d. Solve exponential equations by obtaining the same base. (Sec 4.5, Example 4) |
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4.3 | Hwk | 1-21 every other odd, 25-49 odd,
For 53-60 omit D, G, H, do 53, 54, 57-59; For 61-66 omit E, F, do 61, 63, 65, 66; 67-73 odd, |
23. | Logarithmic Functions a. Evaluate logarithmic functions exactly. Identify when logarithmic functions are defined and when not defined. (Sec 4.3: Example 4) b. Given a logarithmic function, give the domain, range, intervals where increasing or decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.3: Figure 25) c. Given a logarithmic function with a translation, give the domain, range, intervals where increasing or decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.3: Example 6, 7) d. Find the domain of a logarithmic function. (Sec 4.3: Example 5) |
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4.4 | Hwk | 1-31 odd, 35,41 |
24. | Properties of Logarithms a. Understand when and how to apply basic logarithm properties. (Sec 4.4: Examples 1,2) b. Understand the inverse function relationship between exponential and logarithmic functions. Simplify expressions using this relationship. (Sec 4.4: Example 2) c. Write a logarithmic expression as a sum or difference of logarithms. (Sec 4.4: Example 3, 4, 5) Write a logarithmic expression as a single logarithm. (Sec 4.4: Example 6) |
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4.5 | Hwk | 1-11 odd, 15-23 odd, 31-39 odd, 45-53 odd |
25. | Solve Exponential Equations a. Solve exponential equations algebraically. (Sec 4.5: Example 7,8,9) b. Solve exponential equations algebraically when base is e or 10. (Class Examples) |
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26. | Solve Logarithmic Equations a. Solve logarithmic equations algebraically. (Sec 4.5: Example 2) b. Solve logarithmic equations algebraically using the definition of logarithms. (Sec 4.5: Example 1, 3) |
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27. | Solve other kinds of equations involving exponential functions. (Class Examples) | |
28. | Solve other kinds of equations involving logarithmic functions. (Class Examples) | |
4.6 | Hwk | 1, 13, 29, 31, 33, 37 |
29. | Compound Interest a. Future Value or Present Value with quarterly or monthly compounding. (Sec 4.6: Examples 1,3, 4, 5) b. Future Value or Present Value with continuous compounding. (Sec 4.6: Examples 3, 4, 5) c. Determine time required to double or triple an amount of money. (Sec 4.6: Example 7) |
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10.1 | Hwk | 3, 11, 15, 17, 21, 25 |
30. | Solve, algebraically, 2 linear
equations in 2 unknowns; interpret the solution graphically. (Sec 10.1: Example 4-9) |
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10.7 | Hwk | 1, 5, 11 |
31. | Solve, algebraically, a system of nonlinear equations in two unknowns. (Sec 10.7: Examples 1,2) | |
10.8 | Hwk | 1, 3, 9, 11, 13, 21, 23 |
32. | Linear Inequalities a. Graph a linear inequality. (Sec 10.8: Examples 1, 3) b. Graph a system of linear inequalities. (Sec 10.8: Examples 4,6-9) |