Download NAME: MATH 3 Mid-term Exam Review Find mÐ1 and mÐ2. Justify

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MATH 3 Mid-term Exam Review
Find m1 and m2. Justify each answer.
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Algebra Determine the value of x for which j ║ k. Then find m1 and m2.
5. m1 = 7x + 14, m2 = 2x + 4
6. Use the diagram at the right to answer the questions.
a. Which angle is an exterior angle?
b. What are its remote interior angles?
c. Find m1 and m2.
Find the value of x and y.
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Algebra Find the values of m and n.
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Find the distance across the lake in each diagram.
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Algebra For what values of x and y must each figure be a parallelogram?
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Can you prove these to be parallelograms based on the given information? Explain.
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What is the value of x?
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Find the values of the variables.
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Algebra Solve for x.
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26. Error Analysis A classmate writes an incorrect proportion to find x. Explain and correct the error.
Determine the most precise name for each quadrilateral. Then find its area.
27. A(6, 3), B(2, 0), C(2, 5), D(6, 2)
28. A(1, 8), B(4, 6), C(1, 2), D(2, 0)
Explain why the triangles are similar. Then find the distance represented by x.
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Find the length of each darkened arc. Leave your answer in terms of π.
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Find the value of x.
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Find the value of each variable. For each circle, the dot represents the center.
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Algebra For what values of x and y must each figure be a parallelogram?
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For what values of the variables must ABCD be a parallelogram?
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43. Find x
44. Find x
45. Which angle measurements below CANNOT be an obtuse triangle?
a. 𝟔𝟎° − 𝟔𝟎° − 𝟔𝟎°
b. 𝟑𝟎° − 𝟔𝟎° − 𝟗𝟎°
c. 𝟖𝟎° − 𝟓𝟎° − 𝟓𝟎°
46. Are these three right triangles isosceles, scalene, or obtuse?
47. Assume tangent. Find x.
48. Find x.
d. 𝟏𝟎𝟎° − 𝟒𝟎° − 𝟒𝟎°
49. Describe any phase shift and vertical shift in the graph of each.
b. y = 2 cos (x  1) + 3
a. y = 3 cos x + 2
3 

c. y  sin  x 
 1
2 

50. Find the cos and sin values for each of the following degrees on the unit circle below:
a. 45
b. 120
210
d. 315
51. Simplify each trigonometric expression.
a. csc  tan 
b. sec  cos2 
52. Write a cosine function for each description. Assume that a > 0.
a. amplitude 2, period 1
b. amplitude
1
, period 
2
Write a cosine function for each graph. Then write a sine function for each graph.
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55. Find each value without using a calculator. If the expression is undefined, write undefined.
a. csc ()
b. cot
2
3
 11 
c. sec  

 6 
d. csc
3
4
56. Graphing Calculator Use a calculator to find each value. Round your answers to the nearest thousandth.
a. cot 42º
b. csc

6
c. csc (–2)
d. sec π
57. The graph below shows the height of ocean waves below the deck of a platform.
a. What is the period of the graph?
b. What is the amplitude of the graph?
Find the measure of each angle in standard position.
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60. Find the measure of an angle between 0° and 360° coterminal with each given angle.
a. 100°
b. 60°
c. 225°
d. 145°
Find the exact values of the cosine and sine of each angle.
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The measure  of an angle in standard position is given. Find the values of cos  and sin  for each angle.
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
6
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
3
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7
4
Use each circle to find the length of the indicated arc. Round your answer to the nearest tenth.
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Determine the number of cycles each sine function has in the interval from 0 to 2. Find the amplitude and
period of each function.
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Write an equation of a cosine function for each graph.
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