FINAL EXAM REVIEW

CONIC SECTIONS

100

Identify conic section

What does it look like?

x=-6(y+1)²-4

parabola

facing left

200

Identify the conic section

x²+y²-6x-4y-3=0

CIRCLE

(x-3)²+(y-2)²=16

300

Identify conic section

x²+4y²-6x-7=0

(x-3)² +4y²=16

Ellipse

400

Identify conic section

11(x+3)²-2(y+1)²=22

hyperbola

tree trunk

(-3, -1)

500

9(y-1)²-4(x-3)²=36

Hyperbola

C(3,1)

Not tree trunk

Review I

100

Find inverse of

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

^and

Is this function one to one?

f(x)= .75x + .5

y=x²+2

Yes, it is a line

200

SOLVE

-5x-4y=2

4x-5=y

(2, -3)

300

SOLVE
x²+y²=17

x²-2y²=-31

(1, 4)

(-1, 4)

(-1, -4)

(1, -4)

400

Find sum of first 35 terms

5, 9, 13

a₃₅=141

s₃₅=2555

500

Find sum of first 12 terms of this sequence

-2, 3, 8

d=5

a₁₂=53

s₁₂=306

Review II

100

Solve

|-5x+4| < -10

No solution

200

f(x)= (x-5)/(x²-16)

x cannot be -4 or 4

300

What does this graph look like?

What is the domain?

h(x)=-x²+2x-3

parabola facing down

all real numbers

400

Find sum of geometric seq.

100 + 20 + 4 + ...

r=5

s=125

Review III

100

Solve

-3x<12 or 5x+1<11

x>-4 or x<2

200

Given a₁=6 and r=3

find a₈

=13122

300

Find a₇ given 25, 5, 1, ...

= 1/625

400

Find 10th term of sequence

3, 10, 17

d=7 

a₁₀=66

500

Solve

|2x-3| = |4x+9|

x=-1

x=-6

Review IV

100

Solve

-2|1/3x +5| +6=6

x= -15

200

Solve

(x+7)^1/2 -4=2

x=29

300

(12x+24)^1/2 = 6(x)^1/2

x=1

400

Solve

(x+7)^1/2+ (x)^1/2=7

x=9

500

Rationalize the denominator

(14x³)^1/2 / (6x⁴)^1/2

(21x)^1/2 / 3x