Final Exam Outline
Intermediate Algebra, MAT1033
| Chapter 1 | |
| (1.1) | Understand how to graph sets of real numbers (e.g. #101-111, p. 14). |
| Chapter 2 | |
| (2.5) | Solve and graph a linear inequality with three parts. Write the solution set in interval notation ( e.g., #1-7, 41-52, pp. 100-102) |
| (2.6) | Understand the definition of intersection and union of two sets. See pp. 104-109. (pp. 109-111, #1-5, 17-62). |
| (2.7) | Understand the concept of absolute value and be able to solve absolute value equations (pp. 119-120, #5-19, 59-63, 64, 71-83). See pp. 113-117. |
| Chapter 3 | |
| (3.1) | Given the equation of a line, find the line's x- and/or y-intercepts and use them to graph the line. Determine the midpoint of a line segment when given the coordinates of the end points. Refer to pp. 145-149, #3-9, 13-27, 31, 33-49, 69-75. |
| (3.2) | Given information about a line, determine the line's slope. Also, based on the equations of two lines, be able to identify which are parallel, which are perpendicular, and which are neither (i.e., intersecting but not at right angles). pp. 157-159, See #5-60. |
| (3.3) | Given information about a line, write its equation. Are you comfortable with the assorted forms of linear equations (slope-intercept, point-slope, and standard form) and how to apply them to problems? See #1-67, pp. 172-174. |
| (3.4) | Sketch the graph of a compound inequality (e.g., #7-34, pp. 182-183). Do you understand the difference(s) between "and" versus "or"? |
| (3.5) |
Understand the definition of a
relation and a function. From a graph, be able to distinguish between
relations that are functions and relations that are not functions. Understand function notation (e.g., #5-37, 41-73, pp. 194-196). |
| Chapter 4 | |
| (4.1) | Solve a system of linear equations. This section discusses the substitution and elimination methods for doing this. See pp. 232-234, #1-53 |
| (4.3) | Write a system of two equations in two unknowns for an application problem (pp. 254-258, see #3, 5, 11, 17-23, 31, 33). |
| Chapter 5 | |
| (5.5) | Use long division to divide two polynomials (e.g., #5-37, 41, pp. 324-325) |
| Chapter 6 | |
| (6.1-6.3) | Understand the assortment of factoring techniques discussed this term, including factoring by grouping, binomial factoring (both trial-and-error and splitting the middle term), difference of squares, sum/difference of cubes, and, of course, gcf-type factoring. Refer to the wide array of problems on pp. 342-343, pp. 349-350, & pp. 354-355. |
| (6.4) | Factor a sum/difference of two cubes. See pp. 359 and associated homework problems scattered through the rest of chapter 6. |
| (6.5) | Solve problems that require the zero-factor property (pp. 366-367, #3-39, 54, 55, 59, 61, &65) |
| Chapter 7 | |
| (7.1) | Reduce a rational expression to its lowest terms. Refer to Examples 2-3 (pp. 382-383) and #1-21, 25-57, 61-87 (pp. 386-389). |
| (7.2) | Add/subtract rational expressions (e.g., #7-17, #21-77, pp. 396-397). Understand the difference between a rational expression and a rational equation. |
| (7.3) | Simplify a complex fraction (e.g., #3-20, p. 404). Recall the two methods for these. |
| (7.4) | Determine the domain of a rational expression. Solve an equation involving rational expressions (pp. 410-411, #1-39). |
| (7.5) |
Solve an equation/formula for the indicated variable (e.g., #1-19, 31, 33, 39, 41-51, pp. 422-426). |
| Chapter 8 | |
| (8.1) |
Simplify an algebraic radical expression (p. 442). Understand the differences between square roots, cube roots, fourth roots, etcetera (pp. 446-447, #1-35, 45-57. |
| (8.2) |
Simplify an algebraic expression involving fractional exponents (e.g., #1-89, pp. 455-456). |
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| (8.3-8.4) |
Simplify two radical expressions. Be comfortable with products and with sums/differences. Find the distance between two points. You will increase the likelihood of your remembering it if you know upon what geometry theorem this formula is based. See p. 462 (e.g., #15-17, #23-57, #61-91, 109, 111, #119-125, pp.465-469 & #1-45, 49, 59, 61, pp. 473-474). |
| (8.5) |
Rationalize the denominator of a radical expression (e.g., #1-39, #43-81, #85-99, 103-109, pp. 481-483). Do you understand the differences between square roots and higher-index radicals? |
| (8.6) |
Solve two radical equations (a la #1-55, 63, 67, 69, pp. 490-492). Refer to pp. 486-489 for illustrations. Make sure you understand the differences in approaching those with one radical versus those with two. |
| (8.7) |
Simplify approximately three complex number expressions. Practice with problems like #1-37, 41-67, 73-81, etc. pp. 499-501 |
| Chapter 9 | |
| (9.1) |
Understand how to use the even-root property to solve equations . Know how to complete the square to form a perfect square trinomial. Know how to solve quadratic equations in general. Recall the other methods for solving these (factoring, the even-root property, completing-the-square, using the quadratic formula). Problems #5-23, 29-65 pp525-527 should provide you with ample practice. |
| (9.2) |
Know the quadratic formula and how to apply it to solve quadratic equations. See pp. 534-535, #5-35. |
| (9.3-9.4) | Know how to: solve equations with fractions by writing them in quadratic form, use quadratic equations to solve applied problems and solve formulas for variables involving squares and square roots. See pp. 543-545, #1-23, 27-55, 77 & pp. 552-554, 1-31. |