Download PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013

PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
UNIT CIRCLE
1. Find a positive and negative coterminal angle for each measure given:
3
9
a.
b.
c. 70
4
11
2. Find the complement and supplement for each measure given (if they exist)
2

15
a.
b.
c.
5
5
36
3. Convert to either degrees or radians (opposite of what is given)
7
a. 160
b.
4
4. Evaluate each of the following using a calculator
a. sin 60 12 '
b. cot 35
7. Find the reference angle for each of the following
5
17
a.
b.
3
12
29
18
c. cos1.2
5. Find the point (x,y) on the unit circle that corresponds to the given t
2
15
a. t 
b. t 
3
6
6. Evaluate the six trig functions of t:
2
a. t 
3
c.
b. t 
c. t 
9
4
2
3
c. 306
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Parabolas
I. State the vertex, focus, and directrix.
1. y 
1
2
 x  2
4
3. x  4 
1
2
 y  1
16
II. Write the equation of a parabola for each
5. vertex  0, 2  ; focus  0,1
6. vertex  2,1 ; directrix x  1
7. focus  2,0  ; directrix x  2
8. focus  1,3 ; directrix y  5
2. x  2 y 2
1
4. y  3   x 2
8
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Circles
Write the equation of the circle for each.
1) center ( -2, 5 ) and radius of 3 2
2) center ( 3 , 1 ) and contains the point ( 2 , - 5 )
3) the circle has x intercepts of (  6 , 0 )
4) endpoints of the diameter are ( - 4 , - 3 ) and ( 6 , 3 )
5) State the center and radius for each circle.
a) x 2 + y 2 = 10
b) x 2 + ( y - 1 ) 2 = 45
64
c) ( x - 4 ) 2 + ( y + 7 )
2
6) Write the equation of the circle in standard form and state the center and radius.
x 2 + y 2 + 8x - 2y - 21 = 0
=
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Ellipses and Hyperbolas
1. State the center, major axis, minor axis, foci, and vertices of the ellipse
4 x 2  8 y 2  64 ?
2. State the center, major axis, minor axis, foci, and vertices of the ellipse


3. Write the equation of the ellipse with foci  11,5 ,
x2 y 2

1
8
4

11,5 and a vertex  6,5
4. Write the equation of the ellipse with foci  0, 2 ,  4, 2 and minor axis length of 2
5. Write the equation of the ellipse in standard form 6 x2  4 y 2  12 x  16 y  2  0
6. State the center, transverse axis, conjugate axis, foci, and vertices of the hyperbola
y 2 x2
 1
9 16
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
7. State the center, transverse axis, conjugate axis, foci, and vertices of the hyperbola
 y  1   x  3
2
16
25
2
1
8. Write the equation of the hyperbola with foci 1, 3 , 1,5 and difference of focal radii
is 6
9. Write the equation of a hyperbola with center  2,1 ; vertex at  4,1 ; conjugate axis is
16
10. Write the equation of the hyperbola in standard form 9 x 2  y 2  54 x  2 y  71  0
17. Sketch the graph of the hyperbola
 x  1
9
2

y2
1
1
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Write the equation of a circle based on the given information:
1. Center: (-11, -8)
Radius: 4
3. x 2  8x  y 2  2 y  64
2. Center (-6, -15)
Radius : 5
4. Ends of a diameter (-17,-9) & (-19, -9)
Write the equation of a parabola based on the given information:
5. Vertex (0,0)
1 

Focus  0, 
32 

6. Vertex (0,0)
7. x 2  4 x  6 y  26  0
8. Focus (1,-2)
Directrix y  4
Directrix y  
1
8
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Write the equation of an ellipse based on the given information
9. Vertices 12,0,  12,0


Foci 2 11,0 ,  2 11,0

10. Center 0,2, 4,2
Minor Axis = 2
Write the equation of a hyperbola based on the given information
12. Vertices 5,1, 1,1
Foci 7,1,  1,1
11. Center  2,1, 4,1
Conjugate Axis = 16
Other Review
12. Simplify the radical
80
Find the value of  using inverse trig properties:
2
1
14. sin   
15. cos  
2
2
13. Simplify the radical
63
16. tan   1
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
Evaluate each of the following using a calculator
1. cos 50
2. tan 25 15'35"
3. csc12.26
Write the correct trig equation needed to solve for x, and then solve for x
4.
5.
B
A
20
66
45
x
12
C
B
C
A
x
Write the correct trig equation needed to solve for  , and then solve for 
6.
7.
32
C
B
B
43
16
12


A
A
C
Write the six trig equations for  based on the triangle. DO NOT SOLVE
8.
9.
A
B
C
11
3
8


C
B
A
10
PRE-CALCULUS ACADEMIC MIDTERM REVIEW PACKET 2013-2014
10. Given tan  
3
, sketch a triangle and determine the equations of  for the five other
7
trig functions
11. A flagpole stands in the middle of a flat, level field. 75 feet away from its base a
surveyor measures the angle to the top of the flagpole is 32 . How tall is the flagpole?
12. The height of an outdoor basketball backboard is 15 feet, and the backboard casts a
shadow 19 feet long.
a) Draw a right triangle that gives a visual representation of the problem. Label the
known and unknown quantities when  represents the angle of elevation.
b) Use a trigonometric function to write an equation searching for  .
c) Find the angle of elevation.