UNLV University of Nevada, Las Vegas

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1 UNLV University of Nevada, Las Vegas The Department of Mathematical Sciences Information Regarding Math 14 Final Exam Revised While all material covered in the syllabus is essential for success in the course, the following material will be stressed on the final exam. Chapter/Section taken from the class text: College Algebra (custom 5th edition) by Beecher, Penna and Bittinger. The Final Exam consists of a random selection of 5 out of the following 1 questions. Some objectives have more than one sample problem, as indicated by a c. Questions are phrased similar to the actual exam question. In some cases, options are indicated in [[brackets]]. Chapter 1 1. Objective: Given the endpoints of a line segment, find the length of the segment and its midpoint. Material: Chapter 1, Section 1 Corresponding Textbook Exercises: 1.1 (41-56, 61-74) Sample Problem: Find the distance between P 1 =(-4,9) and P =(5,11), then find the midpoint of the segment joining them.. Objective: Find the domain of a function including rational expressions, square roots, or their composition. Material: Chapters 1, and 4, Sections and 6, and 6 (respectively) Corresponding Textbook Exercises: 1. (, 5-6, 81, 8, 97-98), 1.6 (17-),. (7-4), and 4.6 (95, 96) Sample Problems: Find the domains for the given functions: a) y x b) y 5 x c) y x x s 5s1 d) f() s s 5s 4s x 5 e) y x 7 x x f) y x 4 x 5x6 g) y x 5x 4. Objective: Graph a line given its equation (equation may or may not be in slope intercept form). Material: Chapter 1, Sections and 4 Corresponding Textbook Exercises: 1. (6-70), 1.4 (7-6 and 1-4) Sample Problem: Put the following equation for a line into slope intercept form, and graph the line (choose and label and appropriate scale): 7x y 14 Final Exam Hints, Page 1 of 6

2 4. Objective: Find the equation of a line given two points. Material: Chapter 1, Section 4 Corresponding Textbook Exercises: 1.4 (19-6) Sample Problem: Find the equation of the line between the two given points: (,7) and (,5) 5. Objective: Find the equation of a line that is parallel [[or perpendicular]] to another through a given point. Material: Chapter 1, Section 4 Corresponding Textbook Exercises: 1.4 (4-50, 7) Sample Problem: Find the equation of the line that goes through the given point and is perpendicular [[or parallel]] to the given line (state in slope-intercept form): x 4y 1, (4, ) 6. Objective: Solve a linear inequality (problem may be algebraic only, or given in the context of an application problem). Material: Chapter 1, Section 6 Corresponding Textbook Exercises: 1.6 (1-5) Sample Problem: a) Solve for x, show solution in interval notation. 45x 7 b) Jessica can be paid one of two ways for selling insurance policies: Plan A: $750 per month, plus 10% of sales. Plan B: $1000 per month, plus 8% of sales in excess of $000. For what amount of monthly sales is Plan A better for Jessica? Chapter 7. Objective: Evaluate a piecewise function for given inputs Material: Chapter, Section 1 Corresponding Textbook Exercises:.1 (5-48) Sample Problem: Evaluate g( 4), g( ) and g() for the function x x gx ( ) x 7x x 8. Objective: Find the composition of two or more functions, along with its domain. Material: Chapter, Section Corresponding Textbook Exercises:. (17-8) Sample Problem: Given the following functions, find f ( g( x)), or ( f g)( x) and its domain: f x ( ) x 5, gx ( ) 5 x 9. Objective: Identify a given function is even, odd or neither Material: Chapter, Section 4 Corresponding Textbook Exercises:.4 (9-48) Sample Problem: Classify the following function as even, odd or neither by finding and simplifying f( x): f ( x) x x 14 Final Exam Hints, Page of 6

3 Chapter 10. Objective: Find the roots of a quadratic equation. Material: Chapter, Section Corresponding Textbook Exercises:. (1-16, 9-56, 6-78) Sample Problem: Find the roots of the given quadratic equation by using the quadratic formula: x 5 4x 11. Objective: Solve equations that are (or easily become) quadratic in form questions. Type 1, a quadratic Material: Chapter, Section Corresponding Textbook Exercises:. (79-94) 4 Sample Problem: Solve for x: ( x4) 5( x4) 6 Type, quadratic in form Material: Chapter 5, Section 5 Corresponding Textbook Exercises: 5.5 (5, 6, 9, 0, 61) Sample Problems: Solve for x: x x a) e e 4 5 b) x 4 x 1. Objective: Determine the characteristics of the graph of a quadratic (direction of opening, axis of symmetry, vertex, roots, y intercept) and use this information to graph Material: Chapter, Section Corresponding Textbook Exercises:. (-16) Sample Problem: Graph the function. Label the vertex and intercepts. y x 8x0 1. Objective: Find the maximum or minimum values given a quadratic application problem. Material: Chapter, Section Corresponding Textbook Exercises:. (41-5) Sample Problem: A ball is thrown upward with an initial velocity of 0 ft/sec from a height of six feet. The function st ( ) 16t 0t6 gives the height of the ball t seconds after release. Determine the time when the ball is at maximum height, and find that height 14. Objective: Solve rational equations. Material: Chapter, Section 4 Corresponding Textbook Exercises:.4 (1-0) Sample Problems: Solve for x: 5 1 a) 0 x x 6 8 b) 1 8x 1 x Objective: Solve radical equations. Material: Chapter, Section 4 Textbook Exercises:.4 (1-76, 97) Sample Problems: Solve for x: a) x 1 b) x1 x Final Exam Hints, Page of 6

4 16. Objective: Given a formula, solve for a specific variable. Material: Chapter, Section 4 Corresponding Textbook Exercises:.4 (81-90) Sample Problem: Given the following formula, solve for w: A lw hl hw 17. Objective: Solve linear inequalities with absolute value. Material: Chapter, Section 5 Corresponding Textbook Exercises:.5 (-64) Sample Problem: Solve for x: 16x 5 Chapter Objective: Determine what happens to a given polynomial as the independent variable tends to positive and/or negative infinity (a.k.a. end behavior). Material: Chapter 4, Section 1 Corresponding Textbook Exercises: 4.1 (11-18) Sample Problem: What does the following function tend to as x tends to positive [[or negative]] infinity: gx ( ) x17x Objective: Use long or synthetic division to find the result of a polynomial divided by x c. Material: Chapter 4, Section Corresponding Textbook Exercises: 4. (11-) 4 4x x 5 Sample Problem: Use synthetic division to find the result of the given expression x 0. Objective: Solve a polynomial inequality. Material: Chapter 4, Section 6 Corresponding Textbook Exercises: 4.6 (5-5) Sample Problem: Solve the following for x, and put the solution in interval notation: x 65x x 1. Objective: Solve a rational inequality. Material: Chapter 4, Section 6 Corresponding Textbook Exercises: 4.6 (5-76) Sample Problem: Solve the following for x, and put the solution in interval notation: 4 x 9 x 5 Chapter 5. Objective: Find the inverse of a given function or relation. Material: Chapter 5, Section 1 Corresponding Textbook Exercises: 5.1 (45-60, 79-86) Sample Problem: Given the following function, find f 1 ( x) and its domain: f( x) ( x5) 14 Final Exam Hints, Page 4 of 6

5 . Objective: Convert an exponential equation to its equivalent logarithmic form, or visa-versa. Material: Chapter 5, Section Corresponding Textbook Exercises: 5. (5-54) Sample Problems: x 1 a) Restate as an equivalent logarithmic equation. e 5 b) Restate as an equivalent exponential equation. log 7(5 x) 4. Objective: Solve an exponential equation. Material: Chapter 5, Section 5 Corresponding Textbook Exercises: 5.5 (1-8) Sample Problem: Solve for x: 5 a) 7 x 49 x 1 b) 4 x 5. Objective: Solve a log equation. Material: Chapter 5, Section 5 Corresponding Textbook Exercises: 5.5 (1-56) Sample Problem: Solve for x: a) log x log ( x 8) b) log xlog( x 4) log1 6. Objective: Find half life or doubling time given context of model. Material: Chapter 5, Section 6 Corresponding Textbook Exercises: 5.6 (c, 6c, 7c, 16c) Sample Problem: 5. The number of bacteria cells doubles [[or halves]] every 11 minutes. Find the t value b in the equation Pt ( ) k b, where P measures number of cells for any time t in minutes. 7. Objective: Given equation, find half life or doubling time. Material: Chapter 5, Section 6 Corresponding Textbook Exercises: None Sample Problems: The number of bacteria cells at any time, t, can be expressed by the given equation. Find the half-life or doubling time, whichever is appropriate. ln t a) Pt ( ) Pe 0 Ans: half-life is 0.5t ln b) Pt ( ) 00 e Ans: double time of 0.5 c) 0.7t ln Pt ( ) 00 e Ans: half life is Final Exam Hints, Page 5 of 6

6 Chapter 6 8. Objective: Solve a system of two [[or three]] linear equations with two [[or three]] unknowns. Material: Chapter 6, Sections 1 and Corresponding Textbook Exercises: 6.1 (17-44), 6. (1-16) Sample Problem: Solve the given system: x y a) 4x y xyz 4 b) x yz 0 xy5z 1 9. Objective: Identify the solution(s) for an augmented matrix in row-echelon form. Material: Chapter 6, Section Corresponding Textbook Exercises: None Sample Problems: Write out the solution (x, y, z) for the given reduced matrix, if it does not exist explain why: a) Ans: ( xyz,, ) (4,7,) b) Ans: No solution, this is an inconsistent system c) Ans: ( x, yz, ) (4,7 zz, ) Chapter 7 0. Objective: Solve a nonlinear system of equations. Material: Chapter 7, Section 4 Corresponding Textbook Exercises: 7.4 (7-54) Sample Problem: Solve the given system (find only real valued solutions): 4yx7 y xy 5 Chapter 8 1. Objective: Write the terms of a recursive sequence given as a formula. Material: Chapter 8, Section 1 Corresponding Textbook Exercises: 8.1 (61-66) 1 Sample Problem: For the given recursive sequence, find b : b1, bn 1 b n 14 Final Exam Hints, Page 6 of 6