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Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 1 of 14 Course Name: Precalculus: Analytic Geometry and Algebra Course ID: MTHH043060 Student: Student ID:
Generated Date: March 04, 2024 Test Version: R Test Progress Test 2 Progress Test 2 (Evaluation 52) covers the course materials that were assigned in Units 3 and 4. Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book, proctored test. You may not have access to notes or any of the course materials while you are taking the test. You may use your graphing calculator on
this test. ____ 1. Find the solution of this equation: A. no solution B. −3, −8 C. −3 D. −8 ____ 2. Given the function f
(x) = x
3
+ 3x
2
– x – 3, use synthetic division to find the value of f
(–2). A. −1 B. −21 C. 15 D. 3 ____ 3. Find the horizontal asymptote of this function, if one exists: A. y = 0 B. C. D. no horizontal asymptote exists Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 1 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 2 of 14
____ 4. Given the function f
(x) = x
3
+ 3x
2
– x – 3, use synthetic division to find the value of f
(1). A. – 6 B. – 8 C. 0 D. – 2 ____ 5. Which of the following equations is a quadratic function? A. y = 3x
2
– 2x + 5 B. y = 6x
3
– 3x
2
+ 4x + 2 C. y = + 2x – 7 D. y = 4x – 8 ____ 6. Use the discriminant, b
2
– 4
ac
, to determine the number of real roots for this quadratic equation: −x
2
+ 4x = −5. A. 3 B. 2 C. 1 D. 0 ____ 7. What is the y-intercept of f
(x) = x
2
+ x – 2? A. (0, 2) B. (0, –2) C. (2, 0) D. (–2, 0) ____ 8. Find the intercepts of the following linear function: 4x + 5y = 20. A. (0, 5) and (−4, 0) B. (5, 0) and (0, 4) C. (−5, 0) and (0, −4) D. (4, 0) and (0, 5)) Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 2 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 3 of 14
____ 9. What is the center of the hyperbola with the equation ? A. (−5, −4) B. (5, 4) C. (4, 5) D. (−4, −5) ____ 10. What is the graph of the hyperbola with the equation ? A. B. C. D. ____ 11. Determine the direction of the graph: 5x + 3y = 6. A. increasing B. decreasing C. horizontal D. vertical ____ 12. Find the x-intercepts of the function f
(x) = x
3
+ 3x
2
– x – 3. A.
(–1, 0) , (1, 0) , (3, 0) B. (–1, 0) , (1, 0) , (–3, 0) C. (–3, 0) , (1, 0) , (3, 0) D. (–3, 0) , (–1, 0) , (3, 0) Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 3 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 4 of 14 ____ 13. What is the degree of this polynomial function? 3x – 5x
2
+ x
4
.
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A. 3 B. 4 C. 1 D. 2 ____ 14. Use the cut-point method to find the solution set of the following inequality:(x + 4)(x – 5)(4x + 1) ≥ 0. What are the cut points? A. – 4, – 5, B. – 4, 5, – C. – 4, 5, D. – 4, – 5, – ____ 15. What is the y-intercept of the function f
(x) = x
3
+ 2x
2
– 5x – 6? A. (0, 5) B. (0, 6) C. (0, –6) D. (0, –2) ____ 16. Find the real zeros of the following polynomial function: f
(x) = x
3
– 8x
2
+ 12x – 5. A. 1, B. 1 C. 6, −6, 1 D. 1, ____ 17. Use long division to perform the following division: (x
3
– 2x + 5) ÷ (x
2
+ 2). A. x R 4x + 5 B. x R 4x – 5 C. x R −4x – 5 D. x R −4x + 5 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 4 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 5 of 14 ____ 18. What is the solution set to (x + 4)(x – 5)(4x + 1) ≥ 0?
A. { x | x ≤ −4 or − ≤ x ≤ 5 } B. { x | x ≤ −4 or ≤ x ≤ 5 } C. { x | −4 ≤ x ≤ − or x ≥ 5 } D. { x | −4 ≤ x ≤ or x ≥ 5 } ____ 19. What is the horizontal asymptote of f
(x) = ? A. y = 0 B. x = 0 C. x = 2 D. y = 2 ____ 20. Find the equation of each line with a slope of , that contains point (−1, 0). A. 3x – 5y + 3 = 0 B. 3x + 5y – 1 = 0 C. 3x + 5y + 3 = 0 D. 3x – 5y – 1 = 0 ____ 21. Which of the following equations is a linear function? A. 2
x – 3
y – 8 = 0 B. 2
x – 4
y
2
= 7 C. y + 7 = D. x
2
= 16 ____ 22. Find the solution set of the inequality, > 0. A. { x | – 2 < x < 3 } B. { x | – 3 < x < 2 } C. { x | x < – 2 or x > 3 } D. { x | x < – 3 or x > 2 } Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 5 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 6 of 14
____ 23. Find the slope of the line passing through this pair of points: (3, 2), (3, −1). A. 3 B. undefined C. 0 D. −3 ____ 24. Write the equation of the hyperbola with vertices (0, 4) and (0, 6), and foci of (0,
3) and (0, 7). A. B. C. D. ____ 25. Find the real roots or zeros of this polynomial function: (x
2
– 2x + 1)(x
2
– 4). A.
1, 2, −2 B. −1, 2, −2 C. 1, 2 D. 0, 1, −2 ____ 26. Describe the line and the shading of this inequality y ≥
−x + 4. A. dotted line, shading above the line B. dotted line, shading below the line C. solid line, shading above the line D. solid line, shading below the line ____ 27. Find the equation of the circle with the given information: C(3, −2), r = 6. A. (x – 3)
2
+ (y + 2)
2
= 36 B. (x + 3)
2
+ (y – 2)
2
= 36 C. (x + 3)
2
+ (y – 2)
2
= 6 D. (x – 3)
2
+ (y + 2)
2
= 6 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 6 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 7 of 14
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____ 28. What are the vertical asymptotes of f
(x) = ? A. x = 0, x = 2 B. x = –3, x = 3 C. y = –3, y = 3 D. y = 0, y = 2 ____ 29. Find the vertex of the parabola y = −(x + 1)
2
. A. (0, 0) B. (−1, 0) C. (1, 0) D. (−1, −1) ____ 30. Find the possible rational zeros of the given polynomial function: f
(x) = 3x
3
– 7x
2
+ 8x – 2. A. ±1, ±2 B. 1, 2 C. ±1, ±2, ± , ± D. 1, 2, , ____ 31. Use the quadratic formula to solve this quadratic equation: −3x
2
+ 5x +
1 = 0. A. B. C. D. ____ 32. Find the real roots of the function f
(x) = x
3
+ x
2
– 4x – 4. A. –1, 2, –2 B. 2, 1, –1 C. –2, 1, –1 D. 1, 2, –2 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 7 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 8 of 14
____ 33. What is the y-intercept of f
(x) = ? A. (0, –3) B. (0, 0) C. (0, 3) D. no y-intercept ____ 34. What is the correct graph of the function < 0? A. B. C. D. ____ 35. Find the slope of the line: 5x + 3y = 6. A. B. C. D. ____ 36. Find the domain of this function: . A. all real numbers B. { x | x ≠ 2 } C. { x | x ≠ 0 } D. { x | x ≠ −2 } ____ 37. Use synthetic division to perform the following division: (x
3
– 2x) ÷ (x + 2). A.
x
2
– 2x + 2 B. x
2
– 2x + 2 R −4 C. x
2
– 2x + 2 R 4 D. x
2
+ 2x – 2 R −4 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 8 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 9 of 14
____ 38. What are the foci of the ellipse with the equation 16x
2
+ 25y
2
= 400? A. (3, 0) and (–3, 0) B. (0, 3) and (0, –3) C. (4, 0) and (–4, 0) D. (0, 4) and (0, –4) ____ 39. What is the extreme point of f
(x) = x
2
– x – 6? A.
is a maximum B.
is a maximum C.
is a minimum D. is a minimum ____ 40. What is the x-intercept of f
(x) = ? A. (1, 0) B. (3, 0) C. (–3, 0) D. no x-intercept Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 9 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 10 of 14
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____ 41. What is the graph of f
(x) = ? A. B. C. D. ____ 42. Find the center and radius of this circle: x
2
+ y
2
– 12x – 64 = 0. A. C(6, 6), r = 100 B. C(0, 6), r = 10 C. C(6, 0), r = 10 D. C(6, 0) r = 100 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 10 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 11 of 14
____ 43. What is the graph of f
(x) = x
2
+ x – 2? A. B. C. D. Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 11 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 12 of 14
____ 44. What is the graph of the function f
(x) = x
3
+ 3x
2
– x – 3? A. B. C. D. ____ 45. Find the equation of the line given that it is perpendicular to 3x – 2y =
–4 and contains point (−2, −1). A. 2x – 3y = −3 B. 2x – 3y = 1 C. 2x + 3y = −3 D. 2x + 3y = −7 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 12 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 13 of 14
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____ 46. Find the solution set of the inequality –x
2
– 3x + 4 ≥ 0. A. { x | –4 ≤ x ≤ 1 } B. { x | x ≤ –4 or x ≥ 1 } C. { x | –1 ≤ x ≤ 4 } D. { x | x ≤ –1 or x ≥ 4 } ____ 47. Find the vertical asymptote of this function: A. x = −2, 5 B. x = 2, 3, −5 C. x = 2, −5 D. x = 3 ____ 48. Find the solution of this quadratic equation by factoring: 4x
2
+ 12x = −9.
A. x = 3, 4 B. x = 4, 9 C. D. ____ 49. What are the x-intercepts of f
(x) = −x
2
– 3x + 4? A. (1, 0) and (– 4, 0) B. (– 1, 0) and (4, 0) C. (0, – 1) and (0, 4) D. (0, 1) and (0, – 4) ____ 50. What is the focus of the parabola x
2
– 4y = 0? A. (0, –1) B. (–1, 0) C. (1, 0) D. (0, 1) Carefully review your answers on this progress test and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the online test submission page in the presence of your proctor. Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 13 of 14 Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 14 of 14
The University of Nebraska is an equal opportunity educator and employer. ©2024, The Board of Regents of the University of Nebraska. All rights reserved. Progress Test 2 - MTHH043060 - - Mar 04, 2024 - Page 14 of 14