Math 030
Math 030 Review for Exam #4
1. Express in terms of i: a.
Revised Spring 2010
RH/DM
1
−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
RH/DM
2
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
RH/DM
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
1. Express in terms of i: a.
Revised Spring 2010
RH/DM
1
−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
RH/DM
2
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
RH/DM
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