Download Review Sheet - Exam #1

Review Sheet - Exam #1
1.) Write the standard form of the equation of the specified circle.
Center: (-2,5)
Radius: 3
2.) Find the x- and y-intercepts of the graph of the equation:
2x  3y  0
3.) How many real solutions are there in the following quadratic equation:
( x  6)( x  1)  12
4.) Solve the equation for x,
3 2
x  8 x  20  0 , by factoring.
4
5.) Solve the equation for x:
2ax  ( xb  4ab)  5b
6.) Solve the equation for x:
2
1
2


x  6x  8 x  4 x  2
2
7.) Solve the equation for x, x 2  6 x  2  0 , by completing the square.
8.) Solve the equation for x, 2  2 x  x 2  0 , using the quadratic formula.
9.) Write the following complex number in standard form:
10.) Write the following in standard form:
i
2i

3  2i 2  i
11.) Solve the equation for x:
x 3  2 x 2  3x  6  0
12.) Solve the equation for x:
1 5
 60
x2 x
13.) Solve the equation for x:
31  9 x  x  5
14.) Solve the equation for x:
3x  2  x  3  1
15.) Solve the equation for x:
x 2  6 x  3x  18
3  4i
1  8i
Graph and write your final answer in interval notation for questions 16-20.
16.) Solve the following inequality for x:
1
5
(8 x  1)  3x 
2
2
17.) Solve the following inequality for x:
9  2 x  2  1
18.) Solve the following inequality for x:
x3
4
2
19.) Solve the following inequality for x:
x 2  3x  4
20.) Solve the following inequality for x:
x2  4x  5
 2
7 x
21.) What is the y-intercept of the line passing through the points (-2,6) and (4,-3)?
22.) Find the equation of the line in slope-intercept form through the points (-2,3) and (7,4).
23.) Find the equation of the line in slope-intercept form through the point (1,7) and parallel to
the line passing through the points (2,5) and (-2,1).
1 
24.) Find the equation of the line in slope-intercept form through the point  ,3  and is
2 
2
x  3.
perpendicular to the line y 
3
25.) Ahmed plans to invest his $8000 into two different bank accounts for one year. One
account pays 6% simple interest and the other account pays 3% simple interest. Ahmed wants to
earn a total of $375 in interest. How much money should he invest into both accounts?
26.) Students are traveling in two cars to a football game 135 miles away. The first car leaves on
time and travels at an average speed of 45 miles per hour. The second car starts .5 hours later
and travels at an average speed of 55 miles per hour. How long will it take the second car to
catch up to the first car?
27.) For what values of k does the equation 5 x 2 5 x  k  0 have no real solutions?
28.) Simplify i 243

 


 

29.) Simplify 2   16  5   64
30.) Simplify 1   12   4   3
Concepts and Formulas

Tests for symmetry

How to find x-intercepts and y-intercepts

Quadratic Formula:

Knowing what the discriminant b 2  4ac tells you!!

Completing the Square

Factoring

Distance = Rate * Time

Interest:

Standard form of a Circle: ( x  h) 2  ( y  k ) 2  r 2
where center – (h, k) and radius = r

Slope:

Point – Slope Form of a Line: ( y  y1 )  m( x  x1 )

Slope – Intercept Form of a Line: y  mx  b

Parallel – same slope

Perpendicular – negative reciprocal slope

Standard form for Complex numbers: a  bi

Rules for Absolute Value:
X  p if and only if X  p or X   p
x
 b  b 2  4ac
2a
I = Prt
m
y 2  y1
x 2  x1
X  p if and only if  p  X  p
X  p if and only if X  p or X   p

Properties of Inequalities