Download Midterm review sheets

Trig/Alg3
Midterm Review Day 1
Name ________________________
Date ________________ period ___
You will not be given a blank unit circle for the exam. I suggest putting a unit circle on
your cheat sheet.
1. Find both a positive and negative coterminal angle.
a.) -34 º
b.)

7
c.) 
9
3
c.) 
7
6
d.) 432º
2. Find the reference angle for each given angle.
a.)
2
3
b.) -430º
d.) 213º
3. Find the exact values for the following.
a.) sin
5
4
7
6
10
f.) csc 
3
c.) sec 
b.) tan 180°
d.) cos 150°
e.) cot (–330°)
4. Find two solutions of each equation.
a.) CosӨ =
c.) csc  2
2
2
0 < Ө < 360˚
b.) TanӨ = 1
0 < Ө < 2
d.) cos   
0 < Ө < 2
1
2
0 < Ө < 360˚
5. Convert from degrees to radians (or vice versa).
a.) 120º
b.) 
4
3
c.)
11
3
Solve the following triangles. Then, find the area of each triangle.
6. In  XYZ,  X = 13°, x = 12 cm and y = 5 cm.
7. In  GON, g = 8 in, o = 5 in, and n = 12 in.
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8. A tethered hot air balloon has two cables hanging from it. Each cable attaches to a stake in
the ground, hence, keeping the balloon tethered. One cable is 350 ft and the other is 400 ft. A
50° angle is formed where the cables attach to the bottom of the balloon. Determine the distance
between the two stakes on the ground.
Write the equation of the following lines in slope-intercept form.
4
9. Has y-intercept 9 and slope of  .
3
11. Contains the points (-3, 11) and (2, -5)
10. Contains the point (14, -6) and has slope of
1
.
7
12. Has x-intercept of -7 and y-intercept of 8.
13. Contains the point (15, -2) and is parallel to the line 4 x  5 y  15 .
14. Contains the point (12, -6) and is perpendicular to the line y  3x  5 .
Test the following for any type of symmetry.
15. y = x2 + 1
16. y = x3 - 1
Complete the square for each expression. Write the resulting expression as a binomial squared.
17. x2 – 18x + ________
18. x2 +7x + ________
Solve the following.
19. x2 – 8x – 20 = 0
20. 5x2 = 45
21. 4x2 – 7 = 93
22. -3x2 +4x + 2 = 0
Find the discriminant. Then, state the nature and number of solutions.
23. x 2  4 x  5  0
24. x 2  4 x  5  0
25. 4 x 2 20 x  25  0
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Find the distance and midpoint between the given points.
26. (1, 2), (5, 8)
27. (3, 12), (9, 4)
Find the inverse of the following functions.
28. y  x 2  3
29. y = 3x – 10
30. Are the following relations functions? Are they one-to-one?
Solve and express solution in interval notation.
31. 4( x  1)  2 x  3
32. Refer to the linear equation: 6 x  3 y  36
(a) Find the x-intercept.
(b) Find the y-intercept.
(c) Find the slope.
33. . Write an equation of a line, in slope-intercept form, that is (a) parallel to and
(b) perpendicular to the line 2 x  3 y  5 that goes through the point (2, -1).
(a) parallel
(b) perpendicular
Classify the set of ordered pairs as the function or relation.
34. {(0, 1), (1, -2), (2, 0), (3, 2)}
35. {(0, -1), (2, 2), (1, -2), (3, 0), (1, 1)}
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36. Refer to the function: f ( x)  7 x  2
(a) Find f (5)
(b) Find f ( x  4)
Determine the reference angle for each angle given.
37. 250
38. 330
Give one positive and one negative angle coterminal with the given angle:
39. 70
40. 400
41. Find the value of the six trigonometric functions for an angle, , in standard position having
the point (7, –24) on its terminal side.
42. Find sin , if tan  =
35
and  is in quadrant III.
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Multiple Choice Practice
4
5
30. Determine the linear velocity of a point rotating at an angular velocity of 17 
radians per second at a distance of 5 centimeters from the center of the rotating
object. Round to the nearest tenth.
a. 4.5 cm/s
b. 267 cm/s
c. 534.1 cm/s
d. 26.7 cm/s
31. Determine the angular velocity if 7.3 revolutions are completed in 5 seconds.
Round to the nearest tenth.
a. 9.2 rad/sec
b. 1.5 rad/sec
c. 2.9 rad/sec
d. 4.6 rad/sec
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