AAT HSEMESTER 2 REVIEW
Lets Get Rich
Rational s
Simplify
2
2
2 26 65 54
xx xxx
22( 1) 4
6 ( 1) 5( 1)
x x
x x x
2( 1)( 1) 4
6 ( 1) 5( 1)
x x x
x x x
4
15
Right Angle Trig
Solve the triangle
12 2cos cos ( ) 66.4
5 5A A
AB
C
2
5180 90 66.42 23.6 C
2 2 2
2
2 5
4 4
21 21
a
a a
Exponential Graphing
What is the horizontal asymptote for the function
3( ) 4 5xf x
y= -5
Bonus 100 Pts, what does the +3 do?
Shifts the graph 3 to the left.
Graphing Rationals
Find the vertical, horizontal asymptotes and holes of the function.
2
2
3 27( )
12
xf x
x x
23( 9) 3( 3)( 3) 3( 3)
( 4)( 3) ( 4)( 3) ( 4)
x x x x
x x x x x
VA: x=4
HA: y=3
Hole: x=-3
Rational Equalities
Solve the rational inequality
2 5 3
3 6 4y y
8 10 9
2
y
y
Probabilities
How many different ways can you pick a group of 3 from a set of 20 people?
1140
Right Angle Trig
Find cos(C)=
3cos
5C
AB
C
4
5
Right Angle Trig
Find csc(A)=
3sin( )
2A
AB
C
1
2
2csc()
3A
Unit Circle
The point is on unit circle in standard position. Find the six trig functions of the angle formed.
2 2sin csc 2
2 2
2 2cos sec 2
2 2tan 1 cot 1
B
2 2( , )2 2
Degrees/Radians
Convert to radians 120
2120
180 3
Degrees/Radians
Convert to degrees 7
9
7 180140
9
Logarithmic Equations
Solve 6 6log log 5 2x x
6log ( 5) 2x x
2 25 6x x
2 5 36 0x x
( 9)( 4) 0
9 4
9
x x
x or x
x
Degrees/Radians
Find a positive and a negative coterminal angle for 23 degrees
23 360 383
23 360 337
Logs!!!!
Write the following equations in log form.
3 7xe 3 log 7
3 ln 7ex
x
Law of Sines
Use the law of sines to solve the triangle .
180 37 48 95 C 48
B
37b
18m a
C
A
sin 95 sin 48
18 b
sin 95 18sin 48 13.4b b
sin 95 sin 37
18 a
sin 95 18sin 37 10.8a a
Logarithms
What is the domain and range for the basic exponential function.
Domain: All real numbers or, (-∞, ∞)Range: x>0 or, (0, ∞)
Right Angle Trig
The point (-1, 8) is on the terminal side of angle B in standard position. Find the six trig functions of B.
(-1,8)
-1
8
65
8 8 65 65sin csc
65 865
1 65cos sec 65
65658 1
tan 8 cot1 8
B B
B B
B B
Logarithmic Equations
Solve ln( 5) 12x
2( 5)x e
2 5x e
12.389x
Logarithmic Equations
Solve 3 3log (2 7) log (4 3)x x
2 7 4 3
4 2
x x
x
2
2
x
x
Probabilities
What is the probability of pulling a spade or a face card?
22/52=11/26