Download MATH 102: College Algebra TEST 3 REVIEW Name: Date: Score

MATH 102: College Algebra
TEST 3 REVIEW
Name: ______________________________
Date:______________ Score:____________
QUESTION (Show all work)
1)
Find the equation of the circle of radius 7 with its center at the origin.
2)
Find the center and radius of the circle 4 x 2 + 4 y 2 − 32x − 40y + 148 = 0
3)
Find the vertex of the parabola y = 2 x 2 + x − 2
4)
Find the vertex of the parabola y = 10 − 2 x − x 2
5)
Find the coordinates of the vertex for the function y = x 2 + 4 x + 4
ANSWER
6)
7)
Which equation describes an ellipse?
[A]
− 4 x 2 + 11x − 8 y 2 + 5 y = 6
[B]
6 x 2 + 11x + 6 y 2 − 4 y + 5 = 0
[C]
− 2y 2 + 11y + 2 x 2 + 6 x − 4 = 0
[D]
− 4 y 2 + 11x + 5 y = −4
Find an equation of the parabola in standard form with vertex
( -3, 3), axis of symmetry y = 3 , and passing through the point (3,-1)
8)
Graph the parabola: y = −(x − 2)2 + 2
9)
Sketch the graph of
10)
Graph: x 2 + 4 x + y 2 + 6 y = 0
(x + 5)2 + (y + 4)2 = 9
MATH 102 TOPIC 15 PRACTICE TEST
Page 2
11)
12)
13)
14)
Find the center, vertices, and foci for the ellipse:
x2 y 2
+
=1
36 81
Obtain an equation for an ellipse with major axis of length 8 and foci at
(7,1) and (1,1) .
Graph:
(x − 4 )2
9
+
(y − 3)2
4
=1
Graph and show the asymptotes:
x2 y 2
−
=1
25 4
15)
Simplify the equation and graph: − x 2 + 9 y 2 − 4 x + 18y − 31 = 0
16)
Determine the vertices, asymptotes, and foci of the hyperbola defined by
(x + 3)2 − 4(y + 3)
2
25
= 1.
MATH 102 TOPIC 15 PRACTICE TEST
Page 3
17)
−2 −2
4
Evaluate: − 4
4 −2
0 −4 −2
18)
⎧ x − 4 y = 11
Use Cramer’s rule to solve: ⎨
⎩5 x + y = 6
19)
⎧ x − 3y + 4 z = 3
⎪
Write the augmented matrix for the system ⎨ 2x − 5y + 6z = 6
⎪−3x + 3y + 4z = 6
⎩
Then perform elementary row operations to complete the first column of the
solution.
20)
Write the partial fraction decomposition of
MATH 102 TOPIC 15 PRACTICE TEST
−3
(x + 3)(x + 4)
Page 4
21)
Solve the system:
22)
⎧ 2 x + y + 4z = −4
⎪
y + 4z = 2
⎨
⎪4 x + 3 y + 12z = 4
⎩
⎧ x + 2 y − 3z = 3
⎪
Use Cramer’s rule to solve: ⎨3 x − 2y − z = −23
⎪2 x − y − 3z = −16
⎩
ANSWERS
1.
x 2 + y 2 = 49
12.
(x − 4 )2
16
2.
center (4, 5); radius = 2
13.
(y − 1)2
+
=1
7
y
10
−10
10 x
−10
MATH 102 TOPIC 15 PRACTICE TEST
Page 5
3.
⎛ − 1 , − 17 ⎞
⎝ 4
8⎠
14.
10 y
–10
10
x
–10
4.
15.
( -1, 11)
10 y
–10
10
x
–10
(y + 1)2 − (x + 2)2
4
5.
16.
(-2, 0)
36
=1
vertices: (− 2,−3 ), (− 4,−3 )
⎛ − 6 − 29
⎞ ⎛ − 6 + 29
⎞
foci: ⎜
,−3 ⎟ ,⎜
,−3 ⎟
⎜
⎟⎜
⎟
2
2
⎝
⎠⎝
⎠
6.
7.
[A] Note the coefficients of the squared terms.
(y − 3)
2
=
8
3
(x + 3 )
17.
18.
112
⎛ 5 , − 7⎞
⎝ 3 3⎠
19.
8.
⎡1 − 3 4 3⎤
⎥
⎢
⎢2 − 5 6 6 ⎥
⎥
⎢
⎢⎣− 3 3 4 6 ⎦⎥
y
5
–5
5
x
–5
9.
Circle with center (-5, -4), radius 3
20.
10.
Circle with center (-2, -3), radius
11.
Center : (0, 0), Vertices : (0,−9),(0,9) , Foci :
21.
13
(0,−3 5 )(, 0,3 5 )
MATH 102 TOPIC 15 PRACTICE TEST
Page 6
22.
−3
3
+
x +3 x +4
inconsistent
(-4, 5, 1)
⎡1 − 3 4
3⎤
⎥
⎢
⎢0 1 − 2 0 ⎥
⎥
⎢
⎢⎣0 − 6 16 15 ⎥⎦