# The Spiral by ert554898

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```									 Precalculus Spiral

Final exam preparation questions
Algebra
Graphing
Exponential
Trigonometry
Stat/probability
Functions: find f(2) and f(-3)
 1.) f ( x)  3x3  4 x 2  10 x  7
 2.) g ( x)  2 x 4  5 x3  6 x 2  7
 3.) h( x)  6 x3  3x 2  8 x  2
Composition: find f(g(x))
 1.) f ( x) 3x  2.......g ( x)  5x  2
 2.) f ( x)  x 2  5......g ( x)  3x  4
 3.) f ( x)  x 2  4 x  2......g ( x)  x  2
Operations: Subtract and multiply
 1.) f ( x)  2 x  4.....g ( x)  3x  5
 2.) f ( x)  x 2  4....g ( x)  3 x  1
 3.) f ( x)  5 x  2.....g ( x)  x 2  3
Y = mx + b
 1.) (-3, 2), (-4, 1)
 2.) (5, -2), (2, 4)
 3.) (-3, 4), (2, 4)
Inverse: find f-1
 1.) f ( x)  3x  2
 2.)   g ( x)  x  5
3

 3.) h( x)  2 x  4
5
Synthetic Division: divide
 1.) (3x3  7 x 2  4 x  2)  ( x  2)
 2.) (2 x 4  3x 2  3x  5)  ( x  2)
 3.) (3x3  4 x 2  5 x  2)  ( x  4)
Parent graphs
 Draw the parent graphs for:   x 2 , x3 , x 4 , x , x , 3 x

 Find Domain and Range for each graph
Transformations- describe them
 1.) y  x  4  3
 2.) y   x 2  5
 3.) y  x  4  7
Transformations- write equation
 1.) x2, up 2, left 5, reflect over x-axis
 2.) absolute value, wider, right 2
 3.) square root, thinner, down 3
Transformations: find them from graph, then
find the domain
Piecewise- find equation
Piecewise: Graph
 1.)   f ( x)  x  2, x  2
x 2  3, x  2

 2.)   g ( x)  3x, x  0
 x 2  2, x  0
Domain- equation
 1.) f ( x)        2x  4
x 2  7 x  12

 2.) g ( x)         x 5
2 x 2  x  15

 3.)            3x  1
h( x )  3
x  25 x
Asymptotes- equation-VA &HA
 1.) f ( x)         x
x2  x  6
x2
 2.) g ( x) 
6 x 2  33x  42

 3.)          3x 2
h( x )  2
x 4
Asymptotes- graph-VA &HA
Roots-given roots- find equation, then graph
 1.) roots of 3 and -5,
 2.) roots of 2, -2, 0
 3.) roots of 2, 2i, -2i
Roots- roots from graph
Roots- Find roots from equation
 1.) f ( x)  x 3  3 x 2  4 x  12
 2.) g ( x)  x 2  4 x  7
 3.) h( x)  4 x  25 x
3
Factor: trinomials and grouping
 1.) y  x  121
2

 2.) y  12 x  8 x  15
2

 3.) y  x  4 x  5 x  20
3           2

 4.) y  x  5 x  x  5
3         2
b  b 2  4ac
2a

 1.) f ( x)  x 2  6 x  4
 2.) g ( x )  2 x  4 x  3
2

 3.) h( x)  3 x  2 x  3
2
Graph
 1.) y  5 x  2
 2.) y  4 x  2
 3.) y  2 x  2
Solve- log and ln
 1.) log 3 4 
 2.) log 7 12 
2 x
 3.) 7  14
 4.) 115 x  2  25.75
 5.) 8e .5 x  36
 6.) 34.3  13e 1.4 x
 7.) log 4 (3 x  4)  2
 8.) log 2 x  log 2 5  7
 9.) 2 log 3 x  5
Properties: expand
 1.)          2 3
log4 x y       z

 2.) ln
x( y  5)
z4

 3.) log
x2  4
x
Properties: condense
 1.)   log( x  3)  log( x  3)  log x

 2.)   6log x  7 log y  4log z

 3.)   ln 3  3ln x  1 ln x
2
Word problems- interpret variables
nt
 r
Compounded     A  P 1  
 n

Continuous
A  Pe      rt

Population
P(t )  Ce   kt
Word Problems
 1.) If \$3000 is invested at 3.5% interest compounded
quarterly, what is the value after 10 years?

 2.) If \$9500 is invested at 5% interest compounded daily,
what is the value after 7 years?

 3.) Problem # 2 compounded continuously.
Word Problems (2)
 4.) You invest \$2500 in an account that earns 7% interest
compounded continuously. When will it double?

 5.) You invest \$4550 in an account that earns 4.5% interest
compounded continuously. When will it be worth \$10,000?

 6.) You invest \$1000 in an account that is compounded
monthly. In 5 years it is worth \$1475. Find the rate.
Word Problems (3)
 7.) The initial amount of bees is 50. They grow at a rate of
10% a day compounded continuously. Find the number of
bees in 20 days.

 8.) The initial amount of a mass of radium is 4.5 tons. It
decays at a rate of -.5% compounded continuously. Find the
amount of radium in 100 years.
Convert
 To degrees:
 1.) 3
4
 2.) 5

3
 3.)
8
 1.) 225°
 2.)-300°
 3.) 280°
Evaluate
 1.) sin 30
3
 2.) cos
4
 3.)   tan 90
 4.) sec(150 )
 5.) csc 
6
 6.) cot 
Given trig- find trig
 1.) If sinΘ = ¾ in quadrant II, find cotΘ

 2.) If cosΘ = -2/7 in quadrant III, find sinΘ

 3.) If cscΘ = 3 in quadrant I, find tanΘ
Graph- describe the graph
 1.) y = 3cosΘ -2
 2.) y = cos(Θ-2)
 3.) y = 3cos 2Θ -2
 4.) y = 3cos(2Θ-2)

 1.) y  2sin(3 )  4
 2.) y  3cos(   )  5

 3.) y  4 csc(  )
2
Simplify
 1.) sin 2  cos2  sec       tan 

sin 2 
 2.)
1  cos 

 3.)   sin 2  cos  cot 2 
cos3 
Solve
 1.) 2 cos 2 x  cos x  0
 2.) 2 cos 2 x  cos x  1  0
 3.) sin x  1  0
2

 4.) 25 tan x  25  0
2
Law of Sines
 1.) mA  20, mC  100, c  10, a  ?

 2.) mA  35, mB  75, a  5.4, b  ?

 3.) mA  23, mB  34, a  3.23, c  ?
Law of Cosines
 1.)a = 3, b = 4, c = 7, angle A = ?

 2.) a = 4, b = 7, c = 11, angle B = ?

 3.) a = 2, b=3, c = 8, angle B = ?
Combinations
 1.) From a group of 10 men and 12 women, how many
committees of 5 men and 5 women be formed?

 2.) From a group of 14 men and 8 women, how many
committees of 5 men and 6 women be formed?

 3.) From a group of 12 men and 15 women, how many
committees of 6 men and 4 women be formed?
Independent/dependent
 1.) A license plate has 7 characters in it where the first 4 are
letters and the last 3 are numbers. If numbers and letters are
allowed to be repeated, how many can be created?

 2.) A license plate has 7 characters in it where the first 4 are
letters and the last 3 are numbers. If numbers and letters are
not allowed to be repeated, how many can be created?

 3.) A license plate has 7 characters in it where the first 4 are
numbers and the last 3 are letters. If numbers and letters are
allowed to be repeated, how many can be created?
Replacement
 You have 3 green, 5 purple, and 6 red pens. Two are chosen
at random without replacement. Write an expression
describing:

 Red then green
 Red then red
 Purple then red
 Purple then green
 Purple then purple
 Green then purple
Histograms
Box and Whisker/IQR/Q1Q2Q3

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