- 1. Which of the following is NOT a root of y = 60x4 + 90x3 - 90x2 - 60x?
A) -1/2
B) 3/2
C) -2
D) 0
- 2. Which of the following is NOT a valid solution to the following trig equation: sin2x + cos2x - tan x csc x = -1?
A) π/3
B) 5π/3
C) 7π/3
D) 4π/3
- 3. Which of the following is NOT a root of y = x3 - 2x2 - 5x + 6?
A) 6
B) 3
C) -2
D) 1
- 4. Which of the following is NOT a valid solution to the following trig equation: 3 cos B + sec B = 5
A) 1.336 radians
B) 7.619 radians
C) 4.947 radians
D) 1.434 radians
- 5. Which of the following statements is NOT true for the polynomial x4 + x3 - 3x2 - x + 2?
A) Has double root at 1
B) Has relative maximum at its y-intercept
C) Has domain of x E R
D) Has root at -2
- 6. Which of the following statements is NOT true for the polynomial x3 + 5x2 - 8x - 48?
A) It's an odd function
B) Has positive orientation
C) Can be factored as (x - 3)(x + 4)2
D) Has double root at -4
- 7. Which of the following statements is NOT true for the polynomial x4 + 10x3 + 35x2 + 50x + 24?
A) Has no positive roots
B) Has roots at -1, -2, -3, -4
C) Has no complex roots
D) Always concave up
- 8. What is the remainder when x7 - 48x6 + 13x4 + 29x3 - x2 + 16 is divided by (x + 4)? (Type the number only, not the divisor)
- 9. Which of the following is NOT a valid solution to this trig equation: 3 sin2x + 7 = 9 sin x + 5?
A) 2.758 radians
B) 0.2441 radians
C) 2.897 radians
D) 6.527 radians
- 10. Find a reference angle for 68π/135 radians. Kindly include the word radians in your answer.
- 11. Which of the following is NOT a valid solution to this trig equation: 3 cos2ø sin ø + 8 cos ø sin ø = 12 sin ø?
A) 2π
B) π/2
C) π
- 12. f(x) = x4 + 5x3 - 10x2 + 20x - 56 has 4 roots. They include all of the following except....
A) 2
B) -7
C) 2i
D) i
- 13. Which of the following is NOT a factor of 59x33 + 472y6?
A) x11 + 2y2
B) 59
C) x22 - 2x11y2 + 4y4
D) x11 - 2y2
- 14. Which of the following is NOT true for y = log2(x + 1) - 3?
A) Has no inverse function
B) Domain is x > -1
C) Range is y E R
D) Graph has an asymptote
- 15. Which of the following graphs would not have asymptote(s)?
A) Exponential Function
B) 4th degree Polynomial
C) Logarithmic Function
D) Hyperbola
E) Tangent Function
- 16. Find the eccentricity: 9x2 + 40y - 18x + 5y2 = 46
A) 0.5345
B) 0.6666
C) 1.5
D) 0.8018
E) 0.8944
- 17. sin Z = 11/61 and Z is an angle in the 2nd quadrant. Find the exact value for tan Z.
- 18. sin Z = 11/61 and Z is an angle in the 2nd quadrant. Find the exact value for sec Z.
- 19. sin Z = 11/61 and Z is an angle in the 2nd quadrant. Find the exact value for sin 2Z. (No decimals)
- 20. Find the 2nd derivative of 4x5 - 5x4 + 11x3 - 22x + 1005. Remember to use the ^ key for powers.
- 21. The polar coordinate (7, 3π/4) is at the same place as ALL of the following except:
A) (7, 11π/4)
B) (-7, -π/4)
C) (7, 7π/4)
D) (-7, 7π/4)
E) (7, -13π/4)
- 22. 3x2 + 4xy - 5y2 + 6x + 7y - 8 = 0. What is it?
A) Rotated Circle
B) Rotated Ellipse
C) Rotated Hyperbola
D) Rotated Cubic
E) Rotated Parabola
- 23. 3x2 + 4xy - 5y2 + 6x + 7y - 8 = 0. What is the angle of rotation?
A) 26.56 degrees
B) 31.72 degrees
C) 63.44 degrees
D) 78.68 degrees
E) 13.28 degrees
- 24. Which of the following is not a conic?
A) Cubic
B) Hyperbola
C) Circle
D) Parabola
E) Ellipse
- 25. In the expansion of (2x - 6)5, what is the coefficient of the x3 term?
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