This is not going to be graded, this is to help you see what you need to review for the final.
Precalculus Final Exam Review (answers are posted on my website) triestmath.wordpress.com
1. Sketch the graph of the function. State the domain, range, and asymptote.
2. Expand the logarithmic expression.
3. Find the solution of the equation
, correct to 4 decimal places.
4. A culture contains 680 bacteria. After just 30 minutes the count is 3250. Find the number of bacteria after 3.5
hours. After how many minutes will the number of bacteria triple?
5. Suppose that the terminal point determined by t is the point
point determined by
.
6. If the terminal point determined by t is
7. If
on the unit circle. Fine the terminal
, find sin t, cos t, and tan t.
and the terminal point for t is in quadrant IV, find tan t + sec t.
8. The graph shown is one period of a function of the form
9. Find the period of the function
10. Find the measure of the central angle
7 ft.
. Determine the function.
and sketch its graph.
in a circle of radius 6 ft if the angle is subtended by an arc of length
11. For the pair of parametric equation, find a rectangular-coordinate equation by eliminating the parameter.
12. Two straight roads diverge at an angle of 65°. Two cars leave the intersection at 12:00 pm., one traveling at 43
mph and the other at 56 mph. How far apart are the cars at 1:45 pm? (to the nearest tenth of a mile)
13. Find the exact value:
14. Solve the equation
.
15. Solve the equation
.
16. Find the indicated side x. Please round the answer to the nearest tenth.
17. Find the reference angle for the given angle.
(a) -214
(b) -200
(c) 358
18. Find the exact value
(a)
(b)
19. Find the first five terms of the sequence
20. Given that the
(c)
d)
, where
term of an arithmetic sequence is 30 and the
.
term is 44, find the first term.
21. Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum.
5 + 25 + 125 + ...+ 15625
22. Use a table of values to estimate the value of the limit to two decimal places:
23. Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a
degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor
axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices,
and asymptotes. Then sketch the graph of the equation.
24. Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a
degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor
axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices,
and asymptotes. Then sketch the graph of the equation.
25. This system of linear equations has a unique solution. Find the solution using either Gaussian elimination or
Gauss-Jordan elimination.
26. Find x correct to one decimal place.
y = 25
27. Find an equation for the conic whose graph is shown.
28. Find the center and foci of the hyperbola.
29. A partial sum of an arithmetic sequence is given. Find the sum:
30. For the function f whose graph is given, state the value of the given quantity, if it exists.
31. State the dimension of the matrix.
32. Write the system of equations that corresponds to the matrix.
33. Perform the matrix operation.
34. Perform the matrix operation.
35. A partial sum of an arithmetic sequence is given. Find the sum:
36. If cos t =
and the terminal point for t in quadrant II, find cot t – csc t.
Answers will be posted on my website.
Precalculus Final Exam Review
Answer Section
1. Domain:
; Range:
; Asymptote:
2.
3. 0.9627
4. 38,737,362.8 bacteria; 21 minutes
see graph
5.
6.
7.
8.
y
5
4
3
2
1
–3.1415926536
x
–1
–2
–3
–4
–5
9.
10.
rad
11.
12. 95.0 miles
13.
14.
15.
16.
17.
3
3
149.3
a) 34
18. a)
25.
19.
26.
20.
b) 20
c)2
b)
x = 1, y = 3, z = 0
3, 8, 23, 68, 203
28.9
2
27.
21. geometric; 19,530
28. center (–3, 6), foci
29. 40.5
22. 0.25
30. 4
1
c)
d)
23. a)
parabola
b) V
c) F
d)
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
e)
31.
24. a)
hyperbola
c) F
d) V
e)
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
–4
–6
–8
–10
32.
33. The matrix operation is impossible.
34.
35. 40.5
SHORT ANSWER
36. – 2
b) C(3, -1)
10
x
f)