CP Algebra II Exam Review
Name: ______________
1. Simplify the following expressions:
a.
7 + 32 ¸ 2(3 - 5) - 4 =
2
2. Classify the numbers 2, –1.1, 0,
2 + (24 ¸ 2× 4)
=
5
b.
1
, π,
5
2 , -7 and 3i by placing them in the appropriate category.
Numbers should only be written once.
Real Numbers
Irrational
Rational
Integers
Wholes
Naturals
3. Write
equation
point-slope form that passes through 1, -3 and is perpendicular to 3x - 7 y = 8.
(
4. Convert to standard form:
)
7
5
x = 2y 5
3
(
)
5.
Write the equation of the line that passes through -5, 8 and is parallel to x = 7 .
6.
Write an equation of the line that passes through (–2, 5) and (1, 7) in all 3 forms.
the
of a line in
7.
Given the graph, find the equation.
a.
b.
Equation:____________________
Equation:_________________
8. Determine if each graph is a function. State the domain and range.
a.
b.
X
–3
–3
–1
0
3
Y
–2
3
1
4
5
Function: YES or NO?
Function: YES or NO?
Domain:
Domain:
Range:
Range:
y = 2 x - 3 -5
b.
9. Graph
a.
Graph y = -3 x +1 + 6
Domain:
Range:
Domain:
Range:
10. Write the equation that represents the graph. Then state its domain and range in interval
notation.
a.
Equation _________________
Domain__________________
Range___________________
b.
Equation ________________
Domain_________________
Range__________________
c.
Equation ________________
Domain_________________
Range__________________
11. Graph the piecewise function:
ì
5,
x < -3
ï
2
ï
f (x) = í ( x - 2 ) , -2 < x £ 2
ï
x>2
ïî 2 x - 4 ,
12. Solve. For inequalities sketch the solutions on a number line as well as state them in interval
notation.
a.
x -5 = 4
e.
2x + 8 + 4 = 0
b.
3+ x = 2x - 4
c. 6 - 3x < 9
d.
13.
x + 3 - 9 < -5
x -4 ³3
g.
-6 £ 2( x + 5) £ 8
h.
2x - 7 ³ 5
Sketch each inequality.
a.
14.
f.
y £ 2(x - 4)2 +1
Solve each system by substitution.
3
y = - x +1
a.
4
4 y = -3x - 8
b.
b.
y>-
2x + 8y = -8
3x - 5y = 22
5
x+3 +4
2
15.
Solve each system by elimination.
a.
16.
8x - 3y = -11
2x - 5y = 27
b.
-3x + 4 = -2 y
2 y + 4x = 10
Solve by elimination.
ì-2x + 3y - z = -25
ï
í3x - 7 y + 2z = 54
ï4x + 8y - 5z = -76
î
17.
Determine whether each matrix has an inverse.
a.
18.
é 3 2ù
ê
ú
ë-5 4 û
Find the inverse of each matrix.
b.
é 3 1 ù
ê
ú
ë 6 2 û
é6 -4 ù
ê
ú
3
-2
ë
û
a.
19.
ì x + 3y = 22
Use matrices to solve í
î2x - y = 2
20.
Solve the system of inequalities.
a.
21.
ì y £ 2x -1
í
î y ³ -3x + 4
b.
b.
é 5 0ù
ê
ú
ë-2 1û
ì
y £5
ï
x³4
í
ï 3.5x + 2.5y £ 35
î
Without a calculator solve each equation. You must use factoring, completing the square,
and the quadratic formula each once. (Show all work!)
a. 2x + 8x +1 = 0
2
b. x - 6x = -10
2
c. 2x 2 - 4x - 70 = 0
22. Graph:
Vertex:
y-intercept:
x-intercept(s):
Axis of Symmetry:
Domain:
Range:
23. Express the equation for each quadratic in factored form, vertex form and standard from.
a.
b.
24. Simplify.
a. i 41
(
) (
b. 2 + i - 3 7 -11i
)
c.
25.
(10 - 4i)(2 + 3i)
d.
Factor.
a.
x 2 - 64
c. 3xv 3 -12xv 2 + 30x 2v 4
26.
27.
5+ i
3- i
b.
2x 2 -15x - 27
d.
x 2 +13x + 36
Evaluate.
a.
f (3) if f (x) = x 2 + 5x +1
b.
h(-2) if h(x) = -2x 3 + 8x -11
c.
b(x + 2) if b(x) = x 2 - 6x + 2.
d.
v(3x -1) if v(x) = 2x 2 - 3x + 7.
b.
(x
d.
(2 + x)(5x 2 + 3x + 2)
Simplify.
a.
c.
(3x
6
) (
- 2x 4 + 3x 2 - 5 + x5 - 5x 3 + 6x
3x 2 ( -2x 3 - x 2 + 3x + 3)
)
2
+ 2x) - ( 4x 2 - 2x - 2)
28.
Simplify.
a.
d.
a 25
(a )
3 7
( x ) ( 3x )
10 4
(a ) b
n 3
g.
29.
3 2
b.
b 5 2c 4
18b 2b 7
c.
e.
æ 5 ö2æ x ö3
ç 5÷ ç ÷
è x ø è 4ø
f.
5
a 4b m
h.
Divide.
x 4 - 2x 3 - 7x 2 + 8x +12
a.
x -3
3
2
c. (6x + 8x -18x - 20) ¸ (3x - 5)
æ 2d ö 4
ç 3÷
è 3d ø
i.
b.
æ 5 ö2
ç 8÷
èy ø
(a x ) 5 b11
a 2b y
æ a -1b 2c ö-3
ç 2 3÷
è 2a bc ø
2x 4 + 5x 3 -16x 2 - 45x -18
2x +1
4
2
c. (x + x - 20) ¸ (x - 2)