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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) |
| 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) |
| |
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) |
| 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) |
| |
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.) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| |
12. |
Recognize the graph, equation, and properties, of any of the basic
functions in the Library of Functions
(except Greatest-Integer). (Sec 2.3) |
| |
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) |
| 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) |
| 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) |
| |
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) |
| 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) |
| 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) |
| 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.) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| |
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) |
| |
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) |
| 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) |
| 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) |
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