Algebra 2 Finals Review

Systems

100

Solve the system of equations using substitution:

y = 7x + 20

-x + 3y = -20

x = -4,  y = -8

200

Solve the system of equations using elimination:

-4x + 3y = 3

12x - 8y = -4

x = 3, y = 5

300

Solve this system by graphing.

y=6-2x

y=-4x+16

(5,-4)

400

Solve this system using any method.

6x+7y+0z= -24

-9x-4y+3z=18

-5x-7y+z=34

x=3

y=-6

z=7

Quadratics and Complex Numbers

100

Factor:  6x²-23x+7

(3x-1)(2x-7)

200

Solve the quadratic:

3z²-10z=-12+3z

x=4/3 and x=3

300

Solve: 

4a²-20a+17=0

a=(5+2(2^1/2))/2

a=(5-2(2^1/2))/2

reminder this is in radical form*

400

Solve the quadratic. [HINT: Solutions are COMPLEX!]

x²-3x+13=x

x=2+3i

x=2-3i

Polynomials

100

State the Degree of the Polynomial:

-3x⁵+2x³-3x+4

5

200

Factor the Polynomial completely:

2x³+4x²-6x

2x(x-1)(x+3)

300

List all the possible rational zeros:

x⁵-3x⁴+2x²-12

+&- 1,2,3,4,6,12

400

Find all real zeros of the function:

x³-2x²-5x+6

1,-2,3

Radicals & Rational Exp.

100

Rewrite into radical form.

35^7/4

See board for answer* 

200

Rewrite in exponential form.

See board for function*

93^5/8

300

Solve the radical equation:

sqrt(2x+7)=5

x=9

400

Solve the radical equation.

sqrt(2x-9)=-1

No Solution

Miscellaneous

100

What is the end behavior of the function?

f(x)=-6x³+2x²-7x+9

f(x)-> negative infinity as x->infinity

f(x)-> infinity as x->negative infinity

200

f(x)=x+1

g(x)=3x-7

Find (f-g)(x)

-2x+8

300

Simplify: (12x³y⁷)/(30x⁶y)

(2y⁶)/(5x³)

400

f(x)=2x-9

g(x)=sqrt(x)

Find g(f(x)).

sqrt(2x-9)