1. Express in terms of i: a.

Revised Spring 2010

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−4

b.

− 12

c.

−3

d.

− 3 • − 12

e. 2i • 5i

f.

− 7i • 9i

2. Perform the indicated operations: a. (5 − 2i ) − (3 − 7i ) b.

(2 + 6i ) + (3 − 7i )

(− 5 + 7i ) + (5 − 2i )

c.

(13 + 9i ) − (− 6 + 8i )

d.

e.

(4 − 5i )

2

f.

(7 − 2i )(7 + 2i )

g.

(3 + 4i )(5 + 2i )

h. (2 − 3i )(2 + 3i )

3. Solve by factoring: a.

x 2 − x = 42

b. 2 x 2 − 5 x = 7 d. x 2 + 10 x = 39

c.

y 2 + 10 y + 21 = 0

4. Solve by the square root principle: a. x 2 = 81 b. x 2 + 49 = 0

c.

(x − 3)

2

= 25

d.

(x + 10)

2

=8

e.

( y + 5)

2

= −9

f.

( y − 1)

2

= 15

Math 030 Review for Exam #4

Revised Spring 2010

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5. Fill in the missing term that makes the expression a perfect square trinomial. Factor the resulting expression. a. x 2 + 16 x + _____ b. x 2 − 2 x + _____

c. x 2 − 10 x + _____

d. x 2 + 14 x + _____

________________________________________________________________

6. Solve by completing the square. Simplify any radicals: a. x 2 + 4x − 1 = 0

b.

x 2 − 2x − 7 = 0

c.

y2 − 6y − 7 = 0

d.

y 2 + 8 y = −25

7. Solve by using the quadratic formula. Simplify any radicals: a. x 2 + 2x + 3 = 0 2 x 2 + 10 x − 5 = 0

b.

x 2 + 3x − 1 = 0 x 2 + 5 x = −6

c.

d.

e. x 2 + 6 x − 12 = 0 f. 2 x 2 + 2 x − 27 = 0 __________________________________________________________________ 8. Find the vertex and the equation of the axis of symmetry. Make a table of values and graph the equation on graph paper. a. y = x 2 + 2 x − 4 b.

y = −x 2 + 4x − 5

c. y = −2 x 2 − 4 x + 3

d. y = x 2 + 2 x

Math 030 Review for Exam #4

9.

Revised Spring 2010

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3

Identify the vertex, the equation of the axis of symmetry, and the y-intercept for each equation. Then graph each equation on a piece of graph paper. a.

y = ( x − 2) − 4

2

Vertex: _____, y-intercept: _______,

Axis of symmetry: _____,

b.

y = −( x + 3) + 2

2

Vertex: _____, y- intercept: _____,

Axis of symmetry: _____,

c. y = (x + 3)

2

Vertex: _____, y- intercept: _____,

Axis of symmetry: _____,

__________________________________________________________________ 10. Find the equation of each circle with the given center and radius. Graph the circle. a. Center : (− 5,−3) b. Center: Radius: r = 4 Radius: r = 5

(4,−2)

c. Center: (0,7 ) Radius: r = 3 _____________________________________________________________________ 11. Identify the center, the radius, and graph the circle. a. x 2 + y 2 = 9 b. c. Center: __________Radius: __________

(x − 3)2 + ( y + 4)2

(x + 2)2 + ( y − 3)2

= 36

= 25

Center: __________ Radius: __________ Center: __________ Radius: ___________

Write the equation of a circle in standard form by completing the square. Identify the center and radius. d. x 2 + y 2 + 6 x + 18 y + 65 = 0 e. x 2 + y 2 − 10 x + 2 y − 23 = 0

Math 030 Review for Exam #4

1.a. 2i 1.e. –10 2.c. 19 + i 2.g. 7 + 26i 1.b. 2i 3 1.f. 63 2.d. 5i 2.h. 13

Revised Spring 2010

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1.c. i 3 2.a. 2 + 5i 2.e. − 9 − 40i 3.a. x = -6, and x=7 4.a. x = -9, and x= 9 4.e.

1.d. -6 2.b. 5 - i 2.f. 53 3.b x= -1 and

3.c.

y = -7, and y = - 3

3.d. x = -13, and x= 3 4.d. x = −10 ± 2 2 5.b. 1; ( x − 1) 2

4.c. x = -2, and x = 8 5.a. 64; ( x + 8)

2

y = −5 ± 3i

2

7 2 4.b. x = −7i and x = 7i 4.f. y = 1 ± 15 x=

5.d. 49; ( x + 7 ) 6.d. y = −4 ± 3i

2

6.a. x = −2 ± 5 7.a. x = −1 ± i 2

6.b. x = 1 ± 2 2 7.b. x =

− 3 ± 13 2

5.c. 25; ( x − 5) 6.c. y = -1, and y=7 7.c.

x=

8.c.

− 5 ± 35 2

2

7.d. x = -3, and x = -2 8.d. y = x + 2 x Vertex: (-1, - 1) Axis of symmetry: x=-1 2

7.e. x = −3 ± 21 8.a. y = x + 2 x − 4 Vertex: (-1, - 5) Axis of symmetry: x = -1 2

− 1± 55 7.f. x = 2 2 8.b. y = − x + 4 x − 5

Vertex: (2, -1) Axis of symmetry: x = 2 x 0 1 2 3 4 y -5 -2 -1 -2 -5...