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Worksheetsprecalculus
Total questions: 122
Worksheet time: 8hrs 54mins
Name
Class
Date
1.
Which conic is given by (x-4)2 = 8(y - 3)?
a)
Hyperbola
b)
Ellipse
c)
Circle
d)
Parabola
2.
What are the coordinates of the center and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
(x - 4)2 + (y - 3)2 = 25 ?
a)
Center (4,3)
Radius = 5 units
Radius = 5 units
b)
Center (4,3)
Radius = 25 units
Radius = 25 units
c)
Center (-4,-3)
Radius = 25 units
Radius = 25 units
d)
Center (-4,-3)
Radius = 5 units
Radius = 5 units
3.
Find the ordered pair for the focus of the conic pictured.
a)
(5, 4)
b)
(3, 6)
c)
(1, 4)
d)
(3, 2)
4.
Find the equation of the figure shown.
a)
(x-5)2 + (y-3)2 = 25
b)
(x+5)2/4 + (y+3)2/9 = 1
c)
(x-5)2/2 + (y-3)2/3 = 1
d)
(x-5)2/4 + (y-3)2/9 = 1
5.
Find the equation of the figure shown.
a)
(x-1)2/16 - (y+2)2/4 = 1
b)
(x+1)2/16 - (y-2)2/4 = 1
c)
(y+2)2/4 - (x-1)2/16 = 1
d)
(x-1)2/4 - (y+2)2/2 = 1
6.
The foci of an ellipse are located at (-2, 3) & (2, 3), where is the center?
a)
(0, 3)
b)
(3, 0)
c)
(-2, 0)
d)
(2, 0)
7.
Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -7, -3), (13, - 3)
foci ( - 5, -3 ) , (11 , -3)
what is the a and b value of the ellipse?
Vertices ( -7, -3), (13, - 3)
foci ( - 5, -3 ) , (11 , -3)
what is the a and b value of the ellipse?
a)
a = 10 , b = 6
b)
a = 6 , b = 10
c)
a = 36 , b = 100
d)
a = 100 , b = 36
8.
A hyperbola has vertices at (0, -1) and (4, -1) and foci at (-2, -1) and (6, -1). What is the value of b2?
a)
12
b)
144
c)
4
d)
16
9.
Which conic's equation has only 1 squared term?
a)
Parabola
b)
Circle
c)
Ellipse
d)
Hyperbola
10.
Find the ordered pairs of the vertices of the conic pictured.
a)
(-4, -4) and (6, -4)
b)
(4, 4) and (-6, 4)
c)
(-1, -1) and (-1, 9)
d)
The conic has no vertices.
11.
Which is the equation to find c on an ellipse?
a)
c2 = a2 + b2
b)
c2 = a2 - b2
c)
1/4d
d)
(x-h)2 + (y-k)2 = r2
12.
(y-4)2 = -8(x+1)
What direction does this parabola open?
What direction does this parabola open?
a)
up
b)
down
c)
left
d)
right
13.
(y-4)2 = -8(x+1)
What are the coordinates for the focus?
What are the coordinates for the focus?
a)
(1,4)
b)
(-1,6)
c)
(-1,2)
d)
(-3,4)
14.
(x+3)2 = 4(y+5)
What is the equation of the directrix?
What is the equation of the directrix?
a)
x = 4
b)
x = 2
c)
y = -4
d)
y = -6
15.
Write the equation of a circle with center (7, 0) with radius 3.
a)
(x - 7)2 + y2 = 9
b)
x2 + (y -7)2 = 9
c)
(x - 7)2 + y2 = 3
d)
x2 + (y -7)2 = 3
16.
What number would go in the blank?
a)
-2
b)
-4
c)
-8
d)
-16
17.
In the equation
(x+2)2+(y+3)2=49, what is the center of the circle?
(x+2)2+(y+3)2=49, what is the center of the circle?
a)
(2, 3)
b)
(3, 2)
c)
(-3, -2)
d)
(-2, -3)
18.
Classify the conic section.
a)
Circle
b)
Ellipse
c)
Line
d)
None of these
19.
Which is the equation of a circle with center (2, 1) that passes through (2, 4)?
a)
(x – 2)2 + (y – 1)2 = 9
b)
(x – 2)2 + (y – 1)2 = 3
c)
(x + 2)2 + (y + 1)2 = 9
d)
(x + 2)2 + (y + 1)2 = 3
20.
What are the vertices of the hyperbola?
a)
(0, 3) and (0, -3)
b)
(-4, 3) and (-4, -3)
c)
(0, 1) and (0, -1)
d)
(4, 0) and (-4, 0)
21.
What are the vertices of the hyperbola?
a)
(0, 5) and (0, -5)
b)
(5, 0) and (-5, 0)
c)
(0, 25) and (-25, 0)
d)
(0, 0) and (0, 5)
22.
What is the directrix of the parabola
(x - 4)2 = 8(y + 3)?
(x - 4)2 = 8(y + 3)?
a)
y = - 3
b)
x= 5
c)
y= - 5
d)
y= 2
23.
What is the focus of the following parabola?
(y + 5)2 = -12 (x - 2)
(y + 5)2 = -12 (x - 2)
a)
(2, - 5)
b)
( -5, 2)
c)
(1 , -5 )
d)
(-1, -5 )
24.
True or False?
When the x-part is squared, the parabola opens up or down.
When the x-part is squared, the parabola opens up or down.
a)
True
b)
False
25.
What is the center of the ellipse?
a)
(0, 0)
b)
(1, 5)
c)
(1, 0)
d)
(0, 1)
26.
Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?
a)
( - 2, 2)
b)
(- 2, 4)
c)
(2, -2)
d)
(-2, 1)
27.
What direction does the parabola open?
(y-9)2 = -40(x+4)
(y-9)2 = -40(x+4)
a)
Up
b)
Down
c)
Left
d)
Right
28.
What is "a" in the equation:
(y-9)2 = -40(x+4)
(y-9)2 = -40(x+4)
a)
- 10
b)
10
c)
- 40
d)
40
29.
How WIDE will this parabola be?
a)
12
b)
3
c)
(2,3)
d)
24
30.
What number would go in the blank?
a)
-2
b)
-4
c)
-8
d)
-16
31.
Given the following, write the equation of the ellipse.
a)
A
b)
B
c)
C
d)
D
32.
Given this directrix and vertex, what would the equation of the parabola be?
a)
(y-2)2 = 12(x-1)
b)
(y-2)2 = 6(x-1)
c)
(x-1)2 = 12(y-2)
d)
(x-1)2 = 6(y-2)
33.
Put the ellipse in standard form
a)
A
b)
B
c)
C
d)
D
34.
What should replace the blue square in the equation?
a)
-8y
b)
-2y
c)
+2y
d)
+8y
35.
Given the equation of the ellipse and the C value, write the foci ordered pair
a)
(4 ± 7.42, -2)
b)
(4, - 2 ± 7.42)
c)
(- 4 ± 7.42, 2)
d)
( - 4, 2 ± 7.42)
36.
Given the equation of the parabola, where would the VERTEX be? (put in standard form)
a)
( 3 , 3)
b)
(24, 3)
c)
( - 24, 3)
d)
(-3, 3)
37.
What are the vertices of the ellipse?
a)
(0, 0)
b)
(7, 1) and (-1, 1)
c)
(3, -5) and (3, 7)
d)
(3, 1)
38.
Which direction does this parabola open?
a)
Up
b)
Down
c)
Left
d)
Right
39.
Write an equation for the ellipse with each set of characteristics. Then answer the questions.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
What is the center of this ellipse? ___________________________
Write the equation in standard form_________________________
a)
(4, 6)
b)
( - 4, 3)
c)
(6, 4)
d)
(4, -3)
40.
What is the center of the ellipse?
a)
(0, 0)
b)
(1, 5)
c)
(1, 0)
d)
(0, 1)
41.
What are the vertices of the ellipse?
Write the equation in standard form:
a)
(0, 0)
b)
(7, 1) and (-1, 1)
c)
(3, -5) and (3, 7)
d)
(3, 1)
42.
a)
Vertical Hyperbola
b)
Vertical Ellipse
c)
Horizontal Hyperbola
d)
Horizontal Ellipse
43.
What are the asymptotes of the hyperbola in the picture?
a)
y = x and y = –x
b)
y = 2x and y = –2x
c)
y = 1/2x and y = –1/2x
d)
y = 2x and y = 4x
44.
Which type of conic section is this equation?
a)
circle
b)
ellipse
c)
hyperbola
d)
parabola
45.
Find the equation of the figure shown.
a)
(x-1)2/16 - (y+2)2/4 = 1
b)
(x+1)2/16 - (y-2)2/4 = 1
c)
(y+2)2/4 - (x-1)2/16 = 1
d)
(x-1)2/4 - (y+2)2/2 = 1
46.
Which type of conic section is this equation?
a)
circle
b)
ellipse
c)
hyperbola
d)
parabola
47.
Which conic section is represented by the equation
9x2 - 4y2 - 54x - 40y - 55 = 0
Rewrite the equation in standard form
____________________________________
a)
Circle
b)
Ellipse
c)
Hyperbola
d)
Parabola
48.
Write the equation of the circle with a radius of 3 and a center of (4, 2).
a)
( x - 4)2 + (y - 2)2 = 3
b)
( x - 2)2 + (y - 2)2 = 32
c)
( x - 4)2 + (y - 2)2 = 32
d)
( x + 4)2 + (y + 2)2 = 32
49.
What are the foci of the ellipse?
a)
(-3,1 + √3) and (-3,1 - √3)
b)
(±√3,0)
c)
(0,1) and (-6,1)
d)
(-3 + √3,1) and (-3 - √3,1)
50.
a)
Vertical Ellipse
b)
Vertical Hyperbola
c)
Horizontal Ellipse
d)
Horizontal Hyperbola
51.
Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -7, -3), (13, - 3)
foci ( - 5, -3 ) , (11 , -3)
What is the a and b value of the ellipse? _______________________
a)
(x+7)2/10 + (y+3)2/6 = 1
b)
(x-3)2/100 + (y+3)2/64 = 1
c)
(x+7)2/36 + (y+3)2/100 = 1
d)
(x-3)2/100 + (y+3)2/36 = 1
52.
A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form?
What are the equations for the asymptotes?
__________________________________________________
a)
x²/25 + y²/11 = 1
b)
x²/5 - y²/11 = 1
c)
x²/11- y²/25 = 1
d)
x²/25 - y²/11= 1
53.
Given sin α = -3/5, cos α = -4/5 and cos β = (2√5)/5, sin β = (-√5)/5
Please find the sum and difference:
sin (α+β)=
Please find the sum and difference:
sin (α+β)=
a)
0
b)
(-2√5)/25
c)
(√2-√6)/4
d)
(√8)/4
54.
Use Sum or Difference Identities to find the exact value of each expression.
cos(75°)
cos(75°)
a)
1/4
b)
( √(6) - √(2) ) / 4
c)
(√(6) + √(2)) / 4
d)
(-√(6) - √(2)) / 4
55.
Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
a)
-1/5
b)
24/25
c)
-24/25
d)
-25/24
56.
Use the Half-angle formulas to find the exact value of each expression
sin 22.5º
sin 22.5º
a)
√(2 + √3)/2
b)
√(2 - √2)/2
c)
√(2 + √2)/2
d)
√(2 - √3)/2
57.
a)
Vertical Ellipse
b)
Vertical Hyperbola
c)
Horizontal Ellipse
d)
Horizontal Hyperbola
58.
a)
Vertical Hyperbola
b)
Vertical Ellipse
c)
Horizontal Hyperbola
d)
Horizontal Ellipse
59.
In the equation (x-3)2+(y+4)2=121, the radius of the circle is
a)
242
b)
11
c)
121
d)
22
60.
Which parabola opens down with a vertex at (-3, 4)?
a)
y = (x + 3)2 - 4
b)
y = -(x + 3)2 - 4
c)
y = (x + 3)2 + 4
d)
y = -(x+3)2 + 4
61.
Find the equation of the figure shown.
a)
(x-1)2/16 - (y+2)2/4 = 1
b)
(x+1)2/16 - (y-2)2/4 = 1
c)
(y+2)2/4 - (x-1)2/16 = 1
d)
(x-1)2/4 - (y+2)2/2 = 1
62.
Find the equation of the figure shown.
a)
(x-1)2/16 - (y+2)2/4 = 1
b)
(x+1)2/16 - (y-2)2/4 = 1
c)
(y+2)2/4 - (x-1)2/16 = 1
d)
(x-1)2/4 - (y+2)2/2 = 1
63.
What direction does the parabola point?
a)
Up
b)
Down
c)
Left
d)
Right
64.
Change the following equation to standard form
x2+y2-4x+12y-8=0
x2+y2-4x+12y-8=0
a)
(x+2)2+(y-6)2=48
b)
(x-2)2+(y+6)2=48
c)
(x-6)2+(y-2)2=48
d)
(x+2)2+(y-6)2=48
65.
Write in component form.
a)
<0, 4>
b)
<8, 2>
c)
<2, 8>
d)
<0, 2>
66.
Find the magnitude of the vector <10, -8>
a)
2
b)
12.81
c)
6
d)
18
67.
Find the component form of a vector whose initial point is (5, 7) and terminal point is (1, 10)
a)
<-4, 3>
b)
<4, -3>
c)
5
d)
<6, 17>
68.
Find the component form of a vector whose magnitude is 10 and direction is 150°.
a)
<10, 150>
b)
<-8.66, 5>
c)
<6.99 , -7.14>
d)
10i + 150j
69.
Find the direction angle for the vector <5, -2>
a)
338.20°
b)
21.80°
c)
291.80°
d)
68.2°
70.
Which point represents (-4, 4π/3)
a)
F
b)
E
c)
B
d)
A
71.
Convert the polar coordinates to rectangular form.
(6, 2π/3)
(6, 2π/3)
a)
( -3, 3)
b)
(3, 3√3)
c)
(-3, 3√3)
d)
(3, -3√3)
72.
Convert to rectangular form: (-1, -3π/4)
a)
(√2/2, √2/2)
b)
(-√2/2, -√2/2)
c)
(-1, -3/4)
d)
(-1, 3/4)
73.
Find the modulus (absolute value) of the complex number. Also state which quadrant the point lies in.
-3 + i
a)
√10, Quadrant 2
b)
√10, Quadrant 3
c)
2, Quadrant 2
d)
3, Quadrant 3
74.
Find the modulus (absolute value) of the complex number. Also state which quadrant the point lies in.
-3 + i
a)
√10, Quadrant 2
b)
√10, Quadrant 3
c)
2, Quadrant 2
d)
3, Quadrant 3
75.
Express this complex number in rectangular form.
4 ( cos π /3 + i sin π /3)
a)
2 + 2√3 i
b)
2 + √3 i
c)
2 - 2√3 i
d)
-2 + 2√3 i
76.
Express the complex number in polar form.
-2 + 5i
a)
5.39 ( cos 1.95 + i sin 1.95)
b)
5.39 ( cos 65.06 + i sin 65.06)
c)
2.65 ( cos 1.95 - i sin 1.95 )
d)
2.65 ( cos 65. 06 - i sin 65.06 )
77.
What is the inverse in the given coordinates {(18,6), (6,2), (27,9), (21,7), (15,5)}
a)
{(6,18), (2,6), (9,27), (7,22), (5,15)}
b)
{(6,18), (6,2), (9,27), (7,21), (5,15)}
c)
{(6,18), (2,6), (9,27), (7,21), (5,15)}
d)
{(6,18), (2,6), (9,27), (7,21), (15,15)}
78.
What is the inverse in the given coordinates {(7,42), (9,54), (6,36), (2,12), (3,18)}
a)
{(42,7), (54,9), (36,6), (12,2), (18,8)}
b)
{(42,7), (54,9), (36,6), (2,12), (18,3)}
c)
{(42,7), (54,9), (6,36), (12,2), (18,3)}
d)
{(42,7), (54,9), (36,6), (12,2), (18,3)}
79.
Does the following graph have an inverse?
a)
No, because this graph is not one-to-one function
b)
No, because this graph not a function
c)
Yes, because this graph is a function
d)
Yes, because this graph is one-to-one and onto function
80.
What is the inverse in the given coordinates {(10,20), (7,14), (8,16), (5,10)}
a)
{(20,10), (14,7), (8,16), (10,5)}
b)
{(20,10), (14,7), (10,5), (16,8)}
c)
{(14,7), (8,16), (10,5), (20,10)}
d)
{(10,20), (14,7), (16,8), (10,5)}
81.
What is the inverse of the function f(x)=3x+12
a)
f⁻¹(x) = ⅓x+12
b)
f⁻¹(x) = ⅓x-12
c)
f⁻¹(x) = ⅓x+4
d)
f⁻¹(x) = ⅓x-4
82.
What is the inverse of the function f(x)=x+2
a)
f⁻¹(x) = x-2
b)
f⁻¹(x) = x+2
c)
f⁻¹(x) = -x+2
d)
f⁻¹(x) = -x-2
83.
Does the following graph have an inverse?
a)
Yes, because this graph is one-to-one function
b)
Yes, because this graph is a function
c)
No, because this graph is not one-to-one function
d)
No, because this graph not a function
84.
Does the following graph have an inverse?
a)
Yes, because this graph is one-to-one function
b)
Yes, because this graph is a function
c)
No, because this graph is not one-to-one function
d)
No, because this graph not a function
85.
What is the inverse in the given coordinates {(1,16), (2,17), (32,47), (10,25)}
a)
{(17,2), (47,32)}, (16,1), (25,10)}
b)
{(16,1), (17,2), (47,37), (25,10)}
c)
{(16,1), (17,2), (47,32), (22,10)}
d)
{(17,2), (47,37)}, (16,1), (25,10)}
86.
What is the inverse in the given coordinates {(5,8), (6,9), (7,10), (8,11)}
a)
{(8,5), (6,9), (10,7), (11,8)}
b)
{(8,5), (6,9), (10,7), (8,11)}
c)
{(8,5), (9,6), (7,10), (11,8)}
d)
{(8,5), (9,6), (10,7), (11,8)}
87.
What is the inverse of the function f(x)=(x-2) ∕ (2x+3)
a)
f⁻¹(x) = (3x-2) / (2x-1)
b)
f⁻¹(x) = (-3x-2) / (2x-1)
c)
f⁻¹(x) = (3x-2) / (1-2x)
d)
f⁻¹(x) = (-3x-2) / (1-2x)
88.
Does the following graph have an inverse?
a)
Yes, because this graph is one-to-one function
b)
Yes, because this graph is a function
c)
No, because this graph is not one-to-one function
d)
No, because this graph not a function
89.
Does the following graph have an inverse?
a)
Yes, because this graph is one-to-one function
b)
Yes, because this graph is a function
c)
No, because this graph is not one-to-one function
d)
No, because this graph not a function
90.
What is the inverse in the given coordinates {(1,8), (2,16), (3,24), (4,32)}
a)
{(8,1), (2,8), (3,24), (4,32)}
b)
{(8,1), (16,2), (3,24), (32,4)}
c)
{(8,1), (2,16), (3,24), (32,4)}
d)
{(8,1), (16,2), (24,3), (32,4)}
91.
What is the inverse in the given coordinates {(5,20), (0,24), (7,28), (8,32)}
a)
{(32,8), (28,7), (20,5), (24,0)}
b)
{(32,2), (28,7), (20,5), (24,0)}
c)
{(20,5), (24,0), (28,7), (32,2)}
d)
{(20,5), (24,0), (28,8), (32,8)}
92.
What is the inverse in the given coordinates {(31,21), (74,64), (94,84), (95,85)}
a)
{(31,21), (64,74), (84,94), (85,95)}
b)
{(31,21), (64,74), (94,94), (85,95)}
c)
{(21,31), (64,74), (84,94), (85,95)}
d)
{(21,31), (64,74), (84,94), (95,95)}
93.
Does the following graph have an inverse?
a)
Yes, because this graph is one-to-one and onto function
b)
Yes, because this graph is a function
c)
No, because this graph is not one-to-one function
d)
No, because this graph not a function
94.
If f(x) = 3x-5 and f⁻¹(a) = 6, then find the value of a?
a)
-8
b)
-4
c)
0
d)
13
95.
What is the inverse of the function f(x)=4-2x
a)
f⁻¹(x) = 2x-½
b)
f⁻¹(x) = 2x+½
c)
f⁻¹(x) = 2+½x
d)
f⁻¹(x) = 2-½x
96.
sin-1(-1/2)
a)
π/3
b)
π/6
c)
5π/6
d)
-π/6
97.
tan(sin-1(-1/2))
a)
√3
b)
√3/3
c)
-√3
d)
-√3/3
98.
tan(sin-1(-1/2))
a)
√3
b)
√3/3
c)
-√3
d)
-√3/3
99.
cos-1(√(3)/2)
a)
π/3
b)
2π/3
c)
π/6
d)
5π/6
100.
sec-1(-2)
a)
π/3
b)
2π/3
c)
π/6
d)
5π/6
101.
tan-1(√(3))
a)
π/3
b)
2π/3
c)
π/6
d)
5π/6
102.
tan-1(√(3))
a)
π/3
b)
2π/3
c)
π/6
d)
5π/6
103.
csc-1(-√(2))
a)
π/4
b)
3π/4
c)
-π/4
d)
-3π/4
104.
sin-1(-1) =
a)
π/2
b)
0
c)
-1
d)
-π/2
105.
cos-1(0) =
a)
π/2
b)
π
c)
1
d)
none of these
106.
sin(cos-1(0))=
a)
0
b)
1
c)
π/2
d)
π
107.
sin-1(√(2)/2) =
a)
π/4
b)
π/3
c)
π/2
d)
π
108.
tan(cos-1(-1))=
a)
undefined
b)
0
c)
½
d)
1
109.
tan(sin-1(1))=
a)
undefined
b)
0
c)
½
d)
1
110.
tan(sin-1(-1/2))=
a)
√(3)
b)
√(3)/3
c)
-√(3)
d)
-√(3)/3
111.
cos-1(- √(3)/2) =
a)
π/3
b)
2π/3
c)
π/6
d)
5π/6
112.
tan-1(-√(3))=
a)
π
b)
-π/6
c)
-π/3
d)
-π/4
113.
What range of angles for inverse cosine?
a)
[0, π]
b)
[0, 2π]
c)
[-π/2, π/2]
d)
[π/2, 3π/2]
114.
What is the range of angles for inverse sine?
a)
[0, π]
b)
[0, 2π]
c)
[-π/2, π/2]
d)
[π/2, 3π/2]
115.
What is the range of angles for inverse tangent?
a)
(0, π/2)
b)
(-π/2, π/2)
c)
(0, π)
d)
(0, 2π)
116.
sec²x −1
a)
sin²x
b)
cos²x
c)
tan²x
d)
cot²x
117.
1 + tan²x
a)
sin²x
b)
cos²x
c)
csc²x
d)
sec²x
118.
sin²x + cos²x + 1
a)
0
b)
1
c)
2
d)
3
119.
-(sin²x + cos²x)
a)
-1
b)
1
c)
-2
d)
2
120.
1/ cot x
a)
tanx
b)
sinx
c)
cosx
d)
cotx
121.
(cot²x) / (cscx+1)
a)
cscx +1
b)
cscx−1
c)
secx−1
d)
secx+1
122.
(sinx - cosx) / (sinxcosx)
a)
cosx−sinx
b)
sinx−cosx
c)
cscx−secx
d)
secx−cscx
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