Accelerated Pre-Calculus
Final REVIEW – Fall 2015
1. Classify the conic section and write its equation in standard form.
2. Classify the conic section and write its equation in standard form.
3. Identify the center and vertices of each. Then sketch the graph.
4. Use the information provided to write the standard form equation of the ellipse.
5. Identify the vertices and foci of each. Then sketch the graph.
6. Use the information provided to write the standard form equation of the hyperbola.
7. Given a triangle with a = 115, b = 64, and c = 78, find the area.
8. Given a triangle with a = 15, b = 4, and c = 12, find C.
9.
10.
11. Simplify: tan2x+1cosx
12. Simplify: sin3x+sinxcos2x
13. Given sin x = -35 and cos x =175, find tan x.
14. Solve the equation for 0≤θ<360°.
2 sin θ= -3
15. Evaluate: sin 75°. (Use the fact that 75° = 45° + 30°.)
16. Given cos θ = -511 and tan θ > 0, find sin 2θ.
17. Determine the period: f(x) = 12cosx5+23.
18. Graph each function using radians.
19. Evaluate: arctan (3).
20. Determine the quadrant in which the terminal side of an angle of 29π6 lies.
21. Give the exact value of tan 13π6.
22. Give the exact value of sec .
23. Which of the following angles is coterminal with θ =-11π12?
24. Find x for the triangle shown below.
a) 0.1047 b) 11.9638 c) 5.4256 d) 9.5547
7.2
37°
X
25. Find the measure of the indicated angle to the nearest degree.
26. Simplify.
27. Simplify. Choose “undefined” if the expression is undefined.
28. Evaluate the determinant.
29. Find the inverse of the matrix.
30. Write the coordinates of each point.
31. Determine whether each of the following pairs of vectors are orthogonal?
a) v = 3i – j, w = i – 3j
b) v = -4i + 2j, w = 2i + 4j
c) v = i – j, w = i + j
d) v = -2i + 4j, w = i – 2j
32. Given u = 3i – j + 4k and v = 2i – 5j + 3k, find the angle between u and v.
33. Which of the following parametric equations represent the equation of an ellipse with a horizontal major axis of 10, a vertical minor axis of 4, and a center at (5, -4)?
34. The polar equation r = 3 + 3cos (θ) produces a …
a) cardioid b) limacon c) circle with diameter 3 d) rose with 3 leaves
35. The polar equation r = 1 – 2cosθ produces a …
a) circle with diameter 2 b) limacon with an inner loop
b) rose with 4 leaves d) rose with 2 leaves
36. Convert r=96+3sinθ to rectangular form.