INSTRUCTIONS USEFUL FORMULAS

Transcription

1 MATH 1100 College Algebra Spring 18 Exam 1 February 15, 2018 Name Student ID Instructor Class time INSTRUCTIONS 1. Do not open until you are told to do so. 2. Do not ask questions during the exam. 3. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON. 4. This exam has 7 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions. 5. You will have 60 minutes to complete the exam. No notes or books are allowed. 6. TI-30XS and TI-30XIIS scientific calculators are allowed. NO other calculators are allowed. 7. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam to YOUR instructor. USEFUL FORMULAS y = mx + b A 3 B 3 = (A B)(A 2 + AB + B 2 ) I = P rt y y 1 = m(x x 1 ) A 2 B 2 = (A + B)(A B) A 3 + B 3 = (A + B)(A 2 AB + B 2 ) d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 ( x1 + x 2, y ) 1 + y (x h) 2 + (y k) 2 = r 2 A = P + P rt a 2 + b 2 = c 2 m = y 2 y 1 x 2 x 1

2 Multiple Choice Section: 1. Factor completely: 10a 2 + 2a 15ab 3b. One of the factors is: (a) 2a 3b (b) 5a 1 (c) 2a 1 (d) 5a + 3b (e) a + 3b 2. What is the domain of 2x 2 13x + 42 x 2 7x + 10? (a) x 5, 2 (b) x 5, 2 (c) x 2, 5 (d) x 2, 5 (e) x What is the slope of the following line: 3y + 4x = 2? (a) m = 4 3 (b) m = 3 4 (c) m = 4 3 (d) m = 1 2 (e) m = Determine whether the relation is a function: {( 5, 2), (6, 2), (9, 2), ( 4, 3)}. (a) Yes, it is a function. (b) No, it is not a function. (c) Cannot be determined from the information given. Page 2

3 5. Find the standard equation for a circle having center (6, 7) and radius 1 2. (a) (x 6) 2 + (y + 7) 2 = 1 4 (b) (x 7) 2 + (y + 6) 2 = 1 2 (c) (x + 6) 2 + (y 7) 2 = 1 4 (d) (x + 6) 2 + (y 7) 2 = 1 2 (e) (x 6) 2 + (y + 7) 2 = Solve the following inequality: 1 2 x + 5 < 2. (a) x < 6 (b) x > 6 (c) x < 3 (d) x > 6 (e) x > 3 7. Solve the following: 5 3x + 4 < 7. (a) [ 5, 7) (b) [ 3, 1) (c) [ 4, 4) (d) ( 4, 4] (e) ( 1, 7) 8. What is the y-intercept of the following equation: 16x 4y = 12? (a) (0, 3) (b) (0, 3) (c) (4, 0) (d) ( ) 3 4, 0 (e) (4, 3) Page 3

4 9. Factor completely: x 2 + 2x 15. One of the factors is: (a) x + 5 (b) x 5 (c) x + 3 (d) x 2 (e) x What is the equation of the line that passes through the point (2, 5) and has a slope of 0? (a) x = 2 (b) x = 5 (c) y = 2 (d) y = 5 (e) y = Simplify the following: 6x x(x + 3). (a) x 2 + 4x (b) x 2 + 2x (c) x 2 + 9x (d) x 2 3x (e) x 2 + 3x 12. Which of the following is the x-intercept of 3x 2y = 12? (a) (0, 6) (b) ( 4, 0) (c) (0, 3) (d) (4, 0) (e) (6, 0) Page 4

5 13. What is the equation of the line that passes through (4, 5) and is perpendicular to the line y = 4x + 1. (a) 4x y = 6 (b) x 4y = 20 (c) x + 4y = 24 (d) 4x + y = 5 (e) 4x y = Jessie borrows money at 12% simple interest. After one year, he owes $1400. How much was originally borrowed? (a) $1568 (b) $1200 (c) $1250 (d) $1300 (e) $ Solve for x: 3(x + 15) = 2(2x + 10). (a) x = 15 (b) x = 25 (c) x = 30 (d) x = 45 (e) x = Simplify the following rational expression: 2x 2 8 x 2 + x 6. (a) 2(x + 2) (b) x + 3 (c) (d) 2(x + 2) x + 3 x + 2 2x 4 (e) x2 + 4 x + 2 Page 5

6 17. Given the following graph, find f( 1) f(1). (a) 3 (b) 4 (c) 4 (d) 3 (e) Find the midpoint of the segment with the given points: (7, 5) and (2, 4). (a) (9, 9) ( 5 (b) 2, 1 ) 2 ( 9 (c) 2, 9 ) 2 (d) (5, 4) (e) (3, 3) Workout Section: 19. Find the equation of the circle with center at (2, 2) and passing through ( 4, 6). (a) Find the radius of the circle. (b) Write the equation of the circle. Page 6

7 20. Data on the average household use of electricity, in kilowatt-hours, are listed in the following table. Use any two data points to model the data with a linear function and predict the average annual household electricity use in Year, x Annual Electricity Use (in kw/h) 2009, 0 11, , 1 11, , 2 11, , 3 10,853 (a) A linear function that models the data is: (b) The average annual electricity use in 2019 is: Multiple Choice Workout Total Points: Score: Page 7

8 MATH 1100 College Algebra Spring 2018 Exam 2 March 22, 2018 Name Student ID Instructor Class time 1. Do not open this exam until you are told to do so. INSTRUCTIONS 2. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON. 3. This exam has 7 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions. 4. You will have 60 minutes to complete the exam. No notes or books are allowed. 5. TI-30XS and TI-30XIIS scientific calculators are allowed. NO other calculators are allowed. 6. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam to YOUR instructor. USEFUL FORMULAS y = mx + b y y 1 = m(x x 1 ) ( x1 + x 2, y ) 1 + y (x h) 2 + (y k) 2 = r 2 f(x + h) f(x) h d = rt A 2 B 2 = (A + B)(A B) A 3 + B 3 = (A + B)(A 2 AB + B 2 ) A 3 B 3 = (A B)(A 2 + AB + B 2 ) x = b ± b 2 4ac 2a I = P rt A = P + P rt f(x) = a(x h) 2 + k ( b ( 2a, f b )) 2a i = 1 d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 a 2 + b 2 = c 2 i 2 = 1

9 1. Determine if the function f(x) = x 2 + 8x 15 has a maximum or a minimum. Multiple Choice Section: (a) Maximum. (b) Minimum. (c) Cannot be determined. 2. Describe how the function y = (x 5) 2 4 can be obtained from one of the basic graphs. (a) Start with the graph of y = x 2 and shift the graph left 5 units and up 4 units. (b) Start with the graph of y = x 2 and shift the graph right 4 units and down 5 units. (c) Start with the graph of y = x 2 and shift the graph left 5 units and down 4 units. (d) Start with the graph of y = x 2 and shift the graph right 4 units and up 5 units. (e) Start with the graph of y = x 2 and shift the graph right 5 units and down 4 units. 3. Determine the interval(s) on which the function is increasing. (a) ( 4, 2) (b) ( 8, 4) (c) ( 4, 2) and (6, 8) (d) ( 8, 4) and ( 4, 2) (e) (6, 8) Page 2

10 4. Find the zeros: 2x 2 + 6x + 3 = 0. (a) x = (b) x = and x = and x = (c) x = 3 6 and x = (d) x = 3 3 and x = (e) x = and x = Solve and write your answer in interval notation: 3x 8 > 7. (a) (b) (c) (d) (e) (, 1 ) 3 ( 1 3, 8 ) 3 (, 1 ) ( 8 3 ( 13 ), 5 ) 3, (, 1 ) (5, ) 3 6. Find the axis of symmetry of the function g(x) = x 2 16x 8 (a) x = 5 (b) x = 4 (c) x = 8 (d) x = 8 (e) x = 4 7. Solve and write your answer in interval notation: 4 2x 6. (a) [ 5, 1] (b) [ 1, ) (c) [ 1, 5] (d) [ 5, 1] (e) [1, 5] Page 3

11 8. If we start with the graph of f(x) = x 2 and shift it right 1 unit and then shrink it vertically by 1, what will the 2 resulting graph be? (a) 2x 2 1 (b) 1 (x 1)2 2 (c) 1 (x + 1)2 2 (d) 2(x + 1) 2 (e) 1 2 x2 1 x 9 for x < 3 9. Find h( 3) + h(4), given the function h(x) = 5 for 3 x < 3 2x 12 for x 3 (a) 2 (b) 10 (c) 16 (d) 14 (e) Solve: 2 x 3 = 3 x 4. (a) x = 4 3 (b) x = 1 (c) x = 3 2 (d) x = 2 3 (e) x = Determine whether the function f(x) = x 4 x + 2 is even, odd, or neither. (a) Even (b) Odd (c) Neither Page 4

12 12. Given that f(x) = 2x + 3 and g(x) = x + 3, find (g f)(2). (a) 1 (b) 0 (c) 4 (d) 13 (e) Determine whether the graph of 2 = 3x 3 y 2 is symmetric with respect to the x-axis, y-axis, or the origin. (a) x-axis (b) y-axis (c) x-axis and y-axis (d) Origin (e) x-axis, y axis, and origin 14. Multiply (5 + 7i)(5 7i) (a) 25 49i (b) i (c) 24i (d) 74 (e) Find the vertex of the function g(x) = 3x 2 12x + 7 (a) (2, 43) (b) ( 2, 43) (c) (4, 7) (d) (2, 5) (e) ( 4, 7) Page 5

13 16. Solve: x + 7 x = 5. (a) x = 0, x = 6 (b) x = 0 (c) x = 3, x = 6 (d) x = 3 (e) x = Solve: 11 x + 8 = 4. (a) x = 1 (b) x = 1, x = 8 (c) x = 8, x = 15 (d) x = 1, x = 15 (e) x = Simplify the following complex number: (i) 25 (a) i (b) 1 (c) i (d) 1 (e) 25 Page 6

14 Workout Section: You must show all your work. No work, no credit. 19. Consider the function f(x) = 2x 2 3x + 1. (a) Find f(x + h). (b) Construct and simplify the difference quotient f(x + h) f(x) h for the function f(x) = 2x 2 3x Consider the functions f(x) = 2x 5 and g(x) = x + 5 (a) Find (g f)(3). (b) Find (f g)(x). Multiple Choice Workout Total Points: Score: Page 7

15 MATH College Algebra Spring 2018 Exam 3 April 19, 2018 Name Student ID Instructor Class time INSTRUCTIONS 1. Do not open until you are told to do so. 2. Do not ask questions during the exam. 3. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON. 4. This exam has 9 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions. 5. You will have 60 minutes to complete the exam. No notes or books are allowed. 6. TI-30XS and TI-30XIIS scientific calculators are allowed. NO other calculators are allowed. 7. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam to YOUR instructor. USEFUL FORMULAS y = mx + b y y 0 = m(x x 0 ) x = b ± b 2 4ac 2a I = P rt i = 1 i 2 = 1 A 2 B 2 = (A + B)(A B) A = P + P rt log a MN = log a M + log a N A 3 + B 3 = (A + B)(A 2 AB + B 2 ) A 3 B 3 = (A B)(A 2 + AB + B 2 ) d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 ( x1 + x 2, y ) 1 + y (x h) 2 + (y k) 2 = r 2 a 2 + b 2 = c 2 f(x + h) f(x) h d = rt f(x) = a(x h) 2 + k ( b ( 2a, f b )) 2a log a M N = log a M log a N log a M p = p log a M log b M = log a M log a b log a a = 1, log a 1 = 0 log a a x = x, a log a x = x

16 Multiple Choice Section: 1. Find f 1 (x) given that f(x) = x 5. (a) f 1 (x) = 5x + 5 (b) f 1 (x) = x 5 (c) f 1 (x) = x 5 (d) f 1 (x) = 5x + 5 (e) f 1 (x) = x Express 1 log b 2 log c + 4 log d as a single logarithm and, if possible, simplify. 3 (a) log b1/3 c 2 d 4 (b) log b d c 2 (c) log b 1/3 c 2 d 4 (d) log b1/3 d 4 c 2 (e) log b d4 c 2 3. Determine the y-intercept of the function g(x) = x 3 (x 1)(x + 1) 2. (a) (0, 0) (b) (0, 1) (c) ( 1, 0) (d) (0, 1) (e) (1, 0) Page 2

17 4. Determine the vertical asymptote(s) of the function g(x) = 3x 6 x 2 + x 20. (a) x = 5, x = 2, x = 4 (b) x = 2, x = 4 (c) x = 5, x = 2, x = 4 (d) x = 5, x = 4 (e) x = 5, x = 2 ( ) x 3 5. Express ln y 2 z 4 as a sum or difference of logarithms. (a) 3 ln x ln y + 2 ln z (b) 3 ln x ln y 2 ln z (c) 3 ln x + 2 ln y 4 ln z (d) 3 ln x 2 ln y 4 ln z (e) 3 ln x ln y + ln z 6. Identify the leading coefficient and degree of the following polynomial: 2x 3 + x 2 x 4 + 7x 1. (a) Leading coefficient: -2; Degree: 3 (b) Leading coefficient: -1; Degree: 4 (c) Leading coefficient: -2; Degree: 4 (d) Leading coefficient: -1; Degree: 3 (e) Leading coefficient: -1; Degree: 5 Page 3

18 7. Use the Intermediate Value Theorem to determine if the function f(x) = 6x 3 5x 2 + 5x 12 has at least one real zero between a = 1 and b = 2. (a) f(1) and f(2) have opposite signs, therefore it cannot be determined if the function f has a real zero between 1 and 2. (b) f(1) and f(2) have the same sign, therefore the function f has a real zero between 1 and 2. (c) f(1) and f(2) have opposite signs, therefore the function f has a real zero between 1 and 2. (d) f(1) and f(2) have the same sign, therefore it cannot be determined if the function f has a real zero between 1 and Identify the end behavior for the function f(x) = 8x 6 2.5x 4 4x 7. (a) (d) (b) (c) 9. Solve the exponential equation: 5 2x 3 = 125. (a) x = 3 (b) x = 3 2 (c) x = 3 5 (d) x = 2 (e) x = 2 5 Page 4

19 10. Solve and write your answer in interval notation: 2x 3x 6 < 0. (a) (0, 2) (b) (, 0) (c) (2, ) (d) (, 0) (2, ) (e) There is no solution. 11. Which is the inverse of the following relation: {(1, 4), ( 2, 3), ( 5, 2), (3, 7)}? (a) {(1, 4), ( 2, 3), ( 5, 2), (3, 7)} (b) {(4, 1), (3, 2), ( 5, 2), (3, 7)} (c) {(1, 4), (3, 2), ( 2, 5), (7, 3)} (d) {(4, 1), (3, 2), ( 2, 5), (7, 3)} (e) {(4, 1), (3, 2), ( 5, 2), (7, 3)} 12. Convert the equation Q = t x to a logarithmic equation. (a) log t Q = x (b) log Q x = t (c) log x t = Q (d) log t x = Q (e) log x Q = t Page 5

20 13. Find the maximum number of zeros and the maximum number of turning points that the graph of the function f(x) = 2x 5 + 6x 7 7x 8 8x 6 can have. (a) Zeros: 7; Turning points: 6 (b) Zeros: 7; Turning points: 7 (c) Zeros: 7; Turning points: 8 (d) Zeros: 8; Turning points: 7 (e) Zeros: 8; Turning points: Determine the zeros of f(x) = x 4 (x + 2) 2 and their multiplicities. (a) -2 with multiplicity 1; 0 with multiplicity 4 (b) 2 with multiplicity 2 ; 0 with multiplicity 4 (c) -2 with multiplicity 4; 0 with multiplicity 2 (d) 2 with multiplicity 1 ; 0 with multiplicity 1 (e) -2 with multiplicity 2; 0 with multiplicity Determine the horizontal asymptote, if any, of the function f(x) = 2x x 3 + 4x 3. (a) y = 2 7 (b) y = 0 (c) y = 2 7 (d) y = 5 2 (e) There is no horizontal asymptote. Page 6

21 16. Solve and write your answer in interval notation: 2x (a) (, 7] (b) (, 7] [ 7, ) (c) [ 7, ) (d) [ 7, 7] (e) (, 7] 17. Solve and write your answer in interval notation: x 2 2x + 1 > x + 5. (a) (, 1) (4, ) (b) (1, ) (c) (, 1) (4, ) (d) ( 1, 4) (e) (, 4) 18. Find log (a) (b) 0.25 (c) (d) (e) e Page 7

22 19. Consider the function f(x) = 2 x 3. Workout Section: You must show all your work. No work, no credit. (a) Find the inverse function, f 1 (x). (b) Find the domain of f 1. (Write your answer in interval notation.) Page 8

23 20. Solve for x: 10 x = x. Multiple Choice Workout Total Points: Score: Page 9