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- Solve the equation (^) x x+ 1 − (^) x −^1 2 = 2 for x.
a) 3 ±
b) −^1 ±
c) − 1 ± √ 2 d) −^3 ±
- Find the equation of the circle passing through the origin and with the center (2, −1).
a) (x − 2)^2 + (y + 1)^2 = 25 b) (x + 2)^2 + (y − 1)^2 = 5 c) (x + 2)^2 + (y − 1)^2 = 25 d) (x − 2)^2 + (y + 1)^2 = 5
- Find the equation of the line through the point (2, −3) perpendicular to the line 2x − y = 1.
a) y = 2x − 7 b) y = − 12 x +^12 c) y = 2x + 8 d) y = − 12 x − 2
- Solve the inequality (^) x −^1 1 ≤ (^2) x^1 + 3.
a) (−∞, −4] ∪ (− 32 , 1) b) (−∞, −4] c) (− 32 , 1) d) (− 32 , 1) ∪ [4, ∞)
- Find the domain of the function f (x) =
√x x − 2. a) all real numbers b) (0, ∞) c) [0, 2) ∪ (2, ∞) d) [0, 1) ∪ (3, ∞)
- Solve the equation | 2 x − 1 | − 3 = 0 for x.
a) 2 only b) 2, − 1 c) 2, 1 d) 1 only
- Find (f ◦ g)(2) if f (x) = (^) x −x 1 and g(x) = x^2. a) 4 b) (^43)
c) (^) x 2 x (^) −^2
d) (^) x 22 x−^2
- Find the average rate of change of the function f (x) = x^2 − 2 x between 1 and 1 + h.
a) 4 h^ h−^4 b) (^4) h c) 4 d) h
- Find the maximum or minimum value (whichever is appropriate) for the function f (x) = 2+4x−x^2. State whether the value is maximum or minimum.
a) 6: maximum b) 2: minimum c) 2: maximum d) 6: minimum
- Find the inverse function of f (x) =^12 (x − 1)^3.
a) f −^1 (x) = √^32 x + 1 b) f −^1 (x) = √^32 x + 1 c) f −^1 (x) = 2x 13 + 1 d) f −^1 (x) = 2x 13 − 1
- Find the quotient and remainder for^4 x
(^4) + x (^3) − 2 x + 1 x^2 − 1. a) quotient: 4x^2 + x + 2, remainder: − 2 x + 3 b) quotient: 4x^2 + x, remainder: −x + 1 c) quotient: 4x^2 + x + 4, remainder: −x + 5 d) quotient: 4x^2 + x − 4, remainder: − 2 x − 1
- Determine the correct graph of the function f (x) = (x − 3)(x − 1)^2 (x + 2). a) - -
0
10
20 y –3 –2 –1 (^1 2) x 3 4
b)
0
10
20 y –3 –2 –1 (^1 2) x 3 4
c)
0
10
20 y –4 –3 –2 –1 1 x 2 3
d)
0
10
20 y –4 –3 –2 –1 (^1) x 2 3
- Find the sum of all zeros of f (x) = x^3 − 4 x^2 + x + 6.
a) 2 b) − 2 c) − 4 d) 4
- Find the number of distinct real zeros of f (x) = x^3 + 3x^2 + 4x + 12.
a) 3 b) 1 c) 2 d) 12
- Find the horizontal and vertical asymptotes of f (x) =^2 x^2 x^ + (^2) −^ x 9 − 1.
a) horizontal asymptote y = 2, vertical asymptotes: x = 3, x = − 3 b) horizontal asymptotes y = −1, y =^12 , vertical asymptotes: x = 3, x = − 3 c) horizontal asymptote y = 2, vertical asymptote: x = 3 d) horizontal asymptote y = 0, vertical asymptote: x = 3
- Evaluate log 3 2 − log 3 30 + log 3 5.
a) − 1 b) (^12) c) 154 d) (^13)
- Solve the equation log 3 x + log 3 (x + 8) = 2 for x.
a) 1, − 9 b) − 3 c) 1 only d) no solution
- Evaluate cos 12 πsin^512 π.
a)
b) 12 −
c) 12 +
d) −
- Determine the exact value of sin(cos−^1 13 ).
a) − 2
b)
c) −
d) 2
- How many solutions does the equation sin(2x) = cos(2x) have with 0 ≤ x < 2 π?
a) 2 b) infinitely many c) 1 d) 4
- How many solutions does the equation sin x + cos^2 x = 1 have with 0 ≤ x < 2 π?
a) infinitely many b) 3 c) 2 d) 1
FINAL- SAMPLE C
1. B 2. D 3. D 4. A 5. C 6. B 7. B 8. D 9. A 10. A 11. C 12. A
13. D 14. B 15. A 16. A 17. C 18. C 19. D 20. B 21. B 22. A 23.
C 24. B 25. B 26. A 27. C 28. D 29. D 30. B
