Pre Calc Mid Term Review

Key Features

100

Find the vertical asymptote(s).

(x^2-2x-8)/(x^2+8x+12)

x = -2

200

DOUBLE JEOPARDY

Find the horizontal asymptote.

(8x^5+x^2)/(2x^2+4x^5)

y = 2

300

Find the hole(s)

(x^2+6x+5)/(x^2+8x+15)

x = -5

400

Find the x-intercept(s)

((x+6)(x+3))/(x-3)

x= -6 & -3

500

(4x-4)/(x-1)

Find the y-intercept of the function. 

y=4

Factoring & Synthetic Division

100

Factor the following polynomial

x^2+x-6

(x+3) (x-2)

200

Factor the following polynomial.

x^2-121

(x+11) (x-11)

300

Divide the following:

(2x^3+14x^2-4x-48) / (x+2)

2x^2+10x-24

400

DOUBLE JEOPARDY

Divide the following.

(x^3-13x^2+51x-63)/(x-7)

x^2-6x+9

500

Factor the following polynomial.

2x^2+9x-18

(x+6) (2x-3)

Rational Equations

100

Solve the following for x. 

((x+5)/8)=(7/4)

x=9

200

Solve the following for x. 

(5x+4)/(2x)=(1/2)

x=-1

300

((5x-9)/(x-7))=((8)/(x-7))+3

DOUBLE JEOPARDY

Solve the following for x.

x=-2

400

Solve the following for x. 

((2x-4)/(2x))=((6)/(2x))+2

x=-5

500

Solve the following for x. 

((2)/(x+1))+((1)/(x-1))=((1)/(x^2-1))

x=(2/3)

Logarithmic Equations

100

DOUBLE JEOPARDY

Write the logarithm in exponent form.

log₃27=x

3^x=27

200

Find the value of x. 

log₄x=2

x=16

300

Condense the logarithm expression.

2log₇4 + log₇2

log₇64

400

Condense the logarithm expression.

2ln(6) - ln(4)

ln(9)

500

Solve the logarithm equation for x. 

log₆(3x-11)+log₆2=log₆(4x-8)

x=7

Exponential Equations

100

Write the exponent expression in log form. 

81^1/2=9

log₈₁9=0.5

200

Write the exponent expression in log form. 

e^x=21

ln21=x

300

Calculator needed. Round to 4 decimal places.

Solve each equation for x.

7^x=15

x=1.3917

400

Calculator needed. Round to 4 decimal places.

Solve each equation for x.

22^2x=9

x=0.3554

500

DOUBLE JEOPARDY

Calculator needed. Round to 4 decimal places.

Solve each equation for x.

5+6^2x-9=14

x=5.1131