ACCELERATED PRECALCULUS STUDY GUIDE FOR THE SLO
I CAN...
MODEL WITH CONICS by graphing, writing conic equations, comparing conic equations, identifying key features, and writing equations in alternate forms.
1.
Standard G.GPE.3(+)Write the standard form equation for the ellipse given by 16x2 + 9y2 – 64x + 36y – 44 = 0.
2.
Standard G.GPE.3(+)Identify the equation of the ellipse that has :
co-vertices (2, 4) and (2, 0) and
foci (5, 2) and (-1, 2).
3.
Standard G.GPE.3(+)Identify the equation of the hyperbola that has co-vertices (2, 4) and (2, 0) and
foci (5, 2) and (-1, 2).
4.
Standard G.GPE.3(+)Identify the conic section represented by 3y2 + 20x = 23 + 5x2 + 12y.
5.
Standard (G.GPE.3(+))Find the equation of a circle with its center at and a radius of 4.
6.
Standard (G.GPE.3(+))Find the equation of the ellipse shown below.
7.
Standard (G.GPE.3(+))Find the equation of the hyperbola graphed below.
8.
Standard (G.GPE.2)Find the focus and the directrix for the given parabola:
9.Find an equation of the perpendicular bisector of the segment connecting the points and .
10.Find the focus of the parabola:
11.Graph
12.Find the center and radius of
13.Write an equation in standard form for the ellipse with foci (7, 0) and (–7, 0) and y-intercepts of 6 and
14.Find the distance between point and point , then find the midpoint of .
15.Identify the focus and directrix of the parabola given by
16.Sketch the graph of the parabola.
17.Write the standard form of the equation of the parabola with its vertex at (0, 0) and focus at .
18.Open-ended: Write an equation of a parabola that opens down and has its vertex located in Quadrant II.
19.Graph
20.Sketch the graph of .
21.Write the standard form of the equation of the circle that passes through the point (1, –6) with its center at the origin.
22.Sketch the graph of
23.Write an equation of the ellipse with a vertex at (–8, 0), a co-vertex at (0, 4), and center at (0, 0).
24.A skating park has a track shaped like an ellipse. If the length of the track is 66 m and the width of the track is 42 m, find the equation of the ellipse.
25.Graph
26.Graph the equation and identify the asymptotes:
27.Find the asymptotes and sketch the hyperbola.
28.Find the equation of the circle with center (2, –6) and radius of 4.
29.Write the equation of the circle in standard form. Identify the radius and center.
30.Classify the conic section. If it is a circle, an ellipse, or a hyperbola, find its center. If it is a parabola, find its vertex.
31.Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola.
32.A satellite dish has a parabolic cross section with a focus that is 3 feet from the vertex. The cross section is placed on a coordinate plane with the vertex at and opening to the right.
a. Find the coordinates of the focus and the equation of the directrix. Explain your answers.
b. Write an equation for the cross section of the satellite dish. Explain your answers.
c. If the satellite dish is 4 feet deep, find the diameter of the satellite dish at its opening.
d. If the opening of the satellite dish has a circumference of , how deep is the dish?
33.The vertical cross section of a cooling tower at a nuclear reactor has a shape that can be described by the equation with x and y in feet.
a. Find the diameter of the tower at its narrowest point. Explain your answer.
b. The distance from the center of the hyperbola to the bottom of the tower is twice the distance from the center of the hyperbola to the top of the tower. If the tower is 180 feet tall, find the diameter of the top of the tower. Explain your answer.
34.A local television station in Marshall County has a range of 50 miles.
a. Write an equation that represents the region covered by this television station. Explain your answer.
b. Can a person who lives 18 miles to the East and 35 miles North of the station watch this television station? Explain.
35.Writing: How is the equation of a vertical ellipse like the equation of a vertical hyperbola? How are the equations different?
36.Writing: How is the equation of an ellipse like the equation of a circle? How are the equations different?
I CAN...
Work with trigonometric functions, use the unit circle (degrees and radians), apply and graph trigonometric functions, create inverse trigonometric functions to solve equations, prove identities, use the law of sines and cosines, and apply all to real-world situations.
____37.
Standard (F.TF.1))Which of the following is equivalent to ?
a. / 51.20°b. / 86.43°
c. / 106.98°
d. / 128.57°
38.
Standard (F.TF.3(+))?
39.
Standard (F.TF.3(+))?
40.
Standard (F.TF.3(+))?
41.
Standard (F.TF.2)Point P is on the unit circle at an angle of . What are the coordinates of Point P?
42.
Standard (F.TF.2)Determine the area of on the unit circle below.
43.
Standard (F.TF.3)=
44.
Standard (F.TF.3)Find the exact value of the .
45.
Standard (F.TF.2)Find the exact value of the .
____46.
Standard (F.TF.3)Which of the following is a coterminal angle with ?
a. /b. /
c. /
d. /
47.
Standard (F.TF.5)The period of the graph shown below is
____48.
Standard (F.TF.5)Which graph represents the function in the interval?
a. /b. /
c. /
d. /
49.
Standard (F.IF.7)In physics class, Wesley noticed the pattern shown in the accompanying diagram on an oscilloscope.
Which equation best represents the pattern shown on the oscilloscope?
50.
Standard (F.IF.7)The path traveled by a roller coaster is modeled by the equation . What is the maximum altitude of the roller coaster?
____51.
Standard (F.IF.7e))Choose the correct equation for the graph below.
a. / / c. /b. / / d. /
____52.
Standard (F.IF.7e))Choose the correct graph for
a. / / c. /b. / / d. /
53.
Standard (F.BF.4)Determine the value of on the unit circle, below.
54.
Standard (F.TF.6))Evaluate
55.
Standard (F.TF.7)Solve for on the interval .
56.
Standard (F.TF.7)Solve for x on the interval .
57.
Standard (F.TF.7)Solve on the interval
____58.
Standard (F.TF.4 (+))a. /
b. /
c. /
d. /
____59.
Standard (F.TF.9(+))The expression is equivalent to:
a. /b. /
c. /
d. /
60.
Standard (F.TF.9(+))Find if and if lies in quadrant IV.
____61.
Standard (F.TF8)Which of the following is a correct Pythagorean Identity?
a. /b. /
c. /
d. /
____62.
Standard (F.TF.8)Which is a trigonometric identity?
a. /b. /
c. /
d. /
63.
Standard (F.TF.9)Use trigonometric identities to simplify.
64.
Standard (G.SRT.10(+))Find the measure of to the nearest whole degree.
65.
Standard (G.SRT.11(+))Two planes leave an airport at the same time. One plane is flying 650 mph at a bearing of 37° E of N, and the other is flying at 825 mph at a bearing 53° W of N. How far apart (to the nearest mile) are the planes after flying for 2 hours?
66.
Standard (G.SRT.10(+))Given in which Solve the triangle.
67.
Standard (G.SRT.10(+))Given in which , , and . Solve the triangle.
____68.
Standard (G.SRT.10)Which formula below is the Law of Sines?
a. /b. /
c. /
d. /
69.Graph y = cos x
70.Find THE EXACT VALUE of given that sin A = with A and cos B = with .
71.Graph
72.What are the amplitude and Period for?
73.Write the equation of the resulting graph when is translated down three units.
74.Write the equation of the resulting graph when is translated two units to the left.
75.Sketch one cycle of the graph of the function.
76.Given that and , find the values of the other five trigonometric functions of .
77.Simplify the following expression:
78.Simplify the following expression:
79.Simplify the following expression:
80.Solve in the interval 0° 360°.
81.Solve in the interval
82.Suppose the depth of the tide in a certain harbor can be modeled by , where y is the water depth in feet and t is the time in hours. Consider a day in which represents 12:00 midnight. For that day, when are high and low tide and what is the depth of each?
83.Write two x-values at which the function has a maximum.
84.Write the equation for the sine function below. (The period is 2.)
85.Find the exact value of sin 225° using a sum or difference formula.
86.If cos = and terminates in the first quadrant, find the exact value of cos 2.
87.Use a half-angle formula to find the exact value of
I CAN...
Perform operations on matrices, use matrices in applictions, and use matrices to represent and solve systems of linear equations.
88.
Standard (A.REI.8)A bank teller is counting 95 bills totaling $960. The number of $10 bills is 6 more than 4 times the number of $20 bills. The number of $5 bills is 2 less than 2 times the number of $20 bills. How many bills of each denomination did the bank teller count?
89.
Standard (A.REI.8)Solve the following system of equations using matrices.
90.
Standard (A.REI.8)Rewrite the following system of equations in matrix form.
91.
Standard (N.VM.5)Find the inverse of matrix A below, if it exists.
92.
Standard (N.VM.5)Find the inverse of matrix A below, if it exists.
Find the inverse of the matrix , if it exists.
93.
Standard (N.VM.8)Perform the indicated operation.
94.Sketch the graph of the equation .
95.A company stocks items A, B, and C at each of its two stores. Use matrix multiplication to determine the value of the inventory at each store.
____96.Lawrence's parents pay him a base allowance of $20 per week and $3.55 per hour for extra chores he completes. Mrs. Johnson pays Lawrence $7.15 per hour to lifeguard at the city pool. Which equation models Lawrence's total weekly income?
a. / / c. /b. / / d. /
I CAN...
Exten my understanding of complex numbers and their operations through graphical representations, and perform operations on vectors and use vector operations to represent various quantities.
97.
Standard (N.VM.4)Given vectors , find .
98.
Standard (N.VM.4b)What are the magnitude and direction of the resultant vector w = 4u – 5v if u = and
v = .
99.
Standard (N.VM.4)Given vector u = and vector v = , find u – v.
100.
Standard (N.VM.5)Find the direction of the resultant vector .
101.Find the direction angle of the vector.
102.Give the component form of the vector u that has the magnitude described.
103.An airplane is flying due north at 430 miles per hour. A wind begins to blow in the directionat 54 miles per hour. Find the bearing the pilot must fly the aircraft to continue traveling due north.
Identify the initial point of vector v.
104.terminal point is
ACCELERATED PRECALCULUS STUDY GUIDE FOR THE SLO
Answer Section
1.ANS:
PTS:1DIF:2NAT:G.GPE.3(+)LOC:UNIT 1
2.ANS:
PTS:1DIF:3NAT:G.GPE.3(+)LOC:UNIT 1
3.ANS:
PTS:1DIF:3NAT:G.GPE.3(+)LOC:UNIT 1
4.ANS:
Hyperbola
PTS:1DIF:2NAT:G.GPE.3(+)LOC:UNIT 1
5.ANS:
Question # 5
PTS:1DIF:1REF:#5NAT:GPE.3
TOP:Conics
6.ANS:
Question #6
PTS:1DIF:2REF:#6NAT:GPE.3
TOP:Conics
7.ANS:
Question #7
PTS:1DIF:2REF:#7NAT:GPE.3
TOP:Conics
8.ANS:
focus: ,directrix:
Question #8
PTS:1DIF:2REF:#8NAT:GPE.3
TOP:Conics
9.ANS:
PTS:1DIF:Level BREF:MAL21285
TOP:Lesson 9.1 Apply the Distance and Midpoint Formulas
KEY:midpoint formula | perpendicular bisector | slopeBLM:Knowledge
NOT:978-0-618-65615-8
10.ANS:
(3, 0)
PTS:1DIF:Level AREF:MAL21286
TOP:Lesson 9.2 Graph and Write Equations of ParabolasKEY:focus | parabola
BLM:KnowledgeNOT:978-0-618-65615-8
11.ANS:
PTS:1DIF:Level AREF:MAL21315
TOP:Lesson 9.4 Graph and Write Equations of EllipsesKEY:graph | ellipse
BLM:KnowledgeNOT:978-0-618-65615-8
12.ANS:
center (–1, 5); r = 4
PTS:1DIF:Level BREF:MAL21339
TOP:Lesson 9.6 Translate and Classify Conic Sections
KEY:solve | equation | circle | radius | centerBLM:Knowledge
NOT:978-0-618-65615-8
13.ANS:
PTS:1DIF:Level BREF:MAL21350
TOP:Lesson 9.6 Translate and Classify Conic SectionsKEY:equation | standard form | ellipse
BLM:KnowledgeNOT:978-0-618-65615-8
14.ANS:
midpoint = (, )
distance =
PTS:1DIF:Level BREF:MAL21278NAT:NCTM 9-12.GEO.2.a
TOP:Lesson 9.1 Apply the Distance and Midpoint Formulas
KEY:points | midpoint | distance formulaBLM:Knowledge
NOT:978-0-618-65615-8
15.ANS:
Directrix: x = 1
Focus: (–1, 0)
PTS:1DIF:Level BREF:MAL21290
TOP:Lesson 9.2 Graph and Write Equations of ParabolasKEY:parabola | directrix | axis
BLM:KnowledgeNOT:978-0-618-65615-8
16.ANS:
PTS:1DIF:Level BREF:MAL21293
TOP:Lesson 9.2 Graph and Write Equations of ParabolasKEY:graph | parabola
BLM:KnowledgeNOT:978-0-618-65615-8
17.ANS:
PTS:1DIF:Level BREF:MAL21296
TOP:Lesson 9.2 Graph and Write Equations of Parabolas
KEY:parabola | directrix | equation | focusBLM:Knowledge
NOT:978-0-618-65615-8
18.ANS:
an equation of the form where h > 0 and k > 0, such as
PTS:1DIF:Level BREF:MAL21301
TOP:Lesson 9.2 Graph and Write Equations of ParabolasKEY:parabola | equation | vertex
BLM:ComprehensionNOT:978-0-618-65615-8
19.ANS:
PTS:1DIF:Level BREF:MAL21303
TOP:Lesson 9.3 Graph and Write Equations of CirclesKEY:circle | graph | plot
BLM:KnowledgeNOT:978-0-618-65615-8
20.ANS:
PTS:1DIF:Level BREF:MAL21306
TOP:Lesson 9.3 Graph and Write Equations of CirclesKEY:graph | circle
BLM:KnowledgeNOT:978-0-618-65615-8
21.ANS:
PTS:1DIF:Level BREF:MAL21313
TOP:Lesson 9.3 Graph and Write Equations of CirclesKEY:equation | circle
BLM:KnowledgeNOT:978-0-618-65615-8
22.ANS:
PTS:1DIF:Level BREF:MAL21318
TOP:Lesson 9.4 Graph and Write Equations of EllipsesKEY:graph | ellipse
BLM:KnowledgeNOT:978-0-618-65615-8
23.ANS:
PTS:1DIF:Level BREF:MAL21323
TOP:Lesson 9.4 Graph and Write Equations of Ellipses
KEY:equation | vertex | ellipse | co-vertexBLM:Knowledge
NOT:978-0-618-65615-8
24.ANS:
PTS:1DIF:Level BREF:MAL21324
TOP:Lesson 9.4 Graph and Write Equations of EllipsesKEY:ellipse | equation | word
BLM:ApplicationNOT:978-0-618-65615-8
25.ANS:
PTS:1DIF:Level BREF:MAL21327
TOP:Lesson 9.5 Graph and Write Equations of Hyperbolas
KEY:graph | equation | conic | hyperbolaBLM:Knowledge
NOT:978-0-618-65615-8
26.ANS:
asymptotes: y=x
PTS:1DIF:Level BREF:MAL21329
TOP:Lesson 9.5 Graph and Write Equations of Hyperbolas
KEY:graph | equation | asymptote | conic | hyperbolaBLM:Knowledge
NOT:978-0-618-65615-8
27.ANS:
Asymptotes:
PTS:1DIF:Level BREF:MAL21333
TOP:Lesson 9.5 Graph and Write Equations of HyperbolasKEY:graph | hyperbola | asymptotes
BLM:KnowledgeNOT:978-0-618-65615-8
28.ANS:
PTS:1DIF:Level BREF:MAL21338
TOP:Lesson 9.6 Translate and Classify Conic SectionsKEY:equation | circle | radius | center
BLM:KnowledgeNOT:978-0-618-65615-8
29.ANS:
Center: (4, –1)
Radius: 3
PTS:1DIF:Level BREF:MAL21341
TOP:Lesson 9.6 Translate and Classify Conic SectionsKEY:equation | circle | radius | center
BLM:KnowledgeNOT:978-0-618-65615-8
30.ANS:
Hyperbola
Center: (–7, 8)
PTS:1DIF:Level BREF:MAL21345
TOP:Lesson 9.6 Translate and Classify Conic Sections
KEY:parabola | ellipse | circle | conic | hyperbolaBLM:Knowledge
NOT:978-0-618-65615-8
31.ANS:
Hyperbola
PTS:1DIF:Level BREF:MAL21347
TOP:Lesson 9.6 Translate and Classify Conic Sections
KEY:parabola | ellipse | circle | conic | hyperbolaBLM:Knowledge
NOT:978-0-618-65615-8
32.ANS:
a. The focus would be at the point where each unit represents one foot. Since the parabola opens to the right, the directrix must be a vertical line. The directrix must also be the same distance from the vertex as the focus. Therefore, the equation of the directrix is .
b. Because the parabola opens to the right, the equation is in the form with . The equation is therefore .
c. feet
d. If the circumference of the dish is , the diameter of the dish must be 16. Therefore, we want to find the value of the parabola at by solving for x: . So the satellite dish is about 5.3 feet deep.
PTS:1DIF:Level CREF:A2.09.02.ER.03
TOP:Lesson 9.2 Graph and Write Equations of Parabolas
KEY:Parabola | real-world | extended responseBLM:Application
NOT:978-0-618-65615-8
33.ANS:
a. 60 feet; the equation representing the vertical cross section is the equation of a hyperbola. The vertices of the equation are and . The two vertices are the points on the branches of the hyperbola that are closest together. Therefore the diameter of the tower at its narrowest point is 60 feet.
b. About 93.72 feet; the distance from the center of the hyperbola to the top of the tower is feet. Substituting 60 into the equation for y yields feet, this is the radius, therefore the diameter of the top of the tower is about 93.72 feet.
PTS:1DIF:Level CREF:A2.09.05.SR.01
TOP:Lesson 9.5 Graph and Write Equations of Hyperbolas
KEY:Hyperbola | real-world | short responseBLM:Application
NOT:978-0-618-65615-8
34.ANS:
a. Since the range is 50 miles in every direction, the region covered by the television station is a circle with radius 50. If we put the area on a coordinate plane with the station at the origin, the equation for the points on the circle that are the maximum distance that this station can reach is then .
b. Yes; The distance to the station is . So the distance to the television station is about 39.4 miles which is within the 50 mile range of the television station.
PTS:1DIF:Level BREF:A2.09.03.SR.07
NAT:NCTM 9-12.NOP.3.b | NCTM 9-12.PRS.4
TOP:Lesson 9.3 Graph and Write Equations of Circles
KEY:Circle | distance | real-world | short responseBLM:Application
NOT:978-0-618-65615-8
35.ANS:
Sample answer: When written in standard form, the equations have the same terms, one involving the square of x and the other involving the square of y. The order of these terms is also the same, with the term involving y coming first. In both equations, the values of h and k indicate the center of the graph, and the values of a and b indicate the vertices. The equations are different in that the terms of the ellipse equation are added, while the terms of the hyperbola equation are subtracted.
PTS:1DIF:Level CREF:MAL21337
NAT:NCTM 9-12.PRS.1 | NCTM 9-12.CON.2 | NCTM 9-12.GEO.4.e
TOP:Lesson 9.5 Graph and Write Equations of HyperbolasKEY:hyperbola | ellipse
BLM:AnalysisNOT:978-0-618-65615-8
36.ANS:
Sample answer: When written in standard form, the equations have the same terms, one involving the square of x and the other involving the square of y, added together. In both equations, the values of h and k indicate the center of the graph, and the values of a and b indicate the vertices. The equations are different in that the terms of the ellipse equation have denominators (always two unequal numbers), while the terms of the circle equation do not have denominators.
PTS:1DIF:Level CREF:MAL21326
NAT:NCTM 9-1.PRS.1 | NCTM 9-1.COM.2 | NCTM 9-1.PRS.4
TOP:Lesson 9.4 Graph and Write Equations of EllipsesKEY:ellipse | circle
BLM:AnalysisNOT:978-0-618-65615-8
37.ANS:DPTS:1DIF:1REF:#9
NAT:F.TF.1
38.ANS:
PTS:1DIF:1REF:#10NAT:F.TF.3
39.ANS:
Undefined
PTS:1DIF:2REF:#11NAT:F.TF.3
40.ANS:
PTS:1DIF:2REF:#12NAT:F.TF.3
41.ANS: