PreReq Review

Question 1

Factor Completely: 9x^2+3x-3xy-y

Answer 1

(3x+1)(3x-y)

Question 2

Factor Completely: 42x^4+35x^2-28

Answer 2

7(2x^2-1)(3x^2+4)

Question 3

Simplify: [ (x+1)^3(x-2)+3(x+1)^2 ] / (x+1)^4

Answer 3

[x^2+x+1] / (x+1)^2

Question 4

Solve: 0=x^3+4x^2+3x+12

Answer 4

x=-4, ±√(3)

Question 5

Solve: (x+3)^2 < 4

Answer 5

-5<-1

Question 6

Solve: |5x-1| > 9

Answer 6

x2

Question 7

Solve the system:
x-y+1=0
y-x^2=-5

Answer 7

(-2,-1)(3,4)

Question 8

Solve the system:
x^2-4x+3=y
-x^2+6x-9=y

Answer 8

(2,-1)(3,0)

Question 9

Write the equation of the line that passes through the point (2, -1) and has a slope of -1/3

Answer 9

y=-x/3 - 1/3

Question 10

Write the equation of the line that passes through the points (2,4) and (-3,6)

Answer 10

y=-2x/5 + 24/5

Question 11

Write the equation of the line that passes through the point (4,-3) and is perpendicular to 3x+2y=4

Answer 11

y=2x/3 - 17/3

Question 12

Find the domain: y = 3 / (x-2)

Answer 12

x≠2

Question 13

Identify the range:

f(x) = {x x≥0
1 -1≤x<-1

Answer 13

(-∞,-3)[0,∞)

Question 14

Identify any asymptotes: y=2x^2 / (3x^3-4x+1)

Answer 14

x=1, [-3±√(21)] / 6

y=0

Question 15

sec(π/6)

Answer 15

2/√(3)

Question 16

sin(7π/3)

Answer 16

√(3)/2

Question 17

tan(π)

Answer 17

0

Question 18

cos(π/3)

Answer 18

1/2

Question 19

Simplify: (tan^2x csc^2x - 1) \ (cscxtan^2xsinx)

Answer 19

cscx-cot^2x

Question 20

Simplify: sec^2x-tan^2x

Answer 20

1

Question 21

Solve: cos^2x=cosx+2 0<2π

Answer 21

x=π

Question 22

Solve 2sin(2x)=√(3) 0<π

Answer 22

x= π/6, π/3

Question 23

Solve: cos^2x+sinx+1=0 0< 2π

Answer 23

x= π, π/2

Question 24

If cosΩ = 10/17, what does sinΩ= ?

Answer 24

±√(189)/17

Question 25

Solve: 3x^2-2x<6

Answer 25

x= [1±√(19)] / 3

Question 26

If f(x)=3x+2 and g(x)=9x^2-10, what does fºg(2)=?

Answer 26

80

Question 27

Find the intercepts of f(x) = √(x-1) + 12

Answer 27

(145, 0)

Question 28

Given f(x)=5x^2-x, evaluate

[f(x+h) - f(x)] / h

Answer 28

10x+5h-1