Algebra 2 Final Review Part 1

Inequalities and Equations

100

Solve:

3x - 8 > 2x - 1

x > 7

200

Solve:

-3 < 4x + 1 < 6

-1 < x < 5/4

300

Solve:

|-x + 7| > 3

x < 4 or x > 10

400

Consider A x A, where A = {-3, -2, -1, 0, 1, 2, 3}.

Find {(x,y) | -3 < x < 0 and 0 < y < 3}.

{(-2, 1), (-2, 2), (-1, 1), (-1, 2)}

500

The world land-speed record has been increasing linearly since 1898.  In 1898 the record was 39.2 mi/h and in 1970 the record was 622.3 mi/h.  What would the record be for the year 2008?

930.05 mi/h

Polynomials and Factoring

100

Completely Factor:

36y² - 100

4(3y + 5)(3y - 5)

200

Completely Factor:

24x³ - 84x² + 72x

12x(2x - 3)(x - 2)

300

Completely Factor:

x² - 2xy + y² - 36

((x - y) + 6)((x - y) - 6)

400

Solve by factoring:

4x² + 11x + 6 =0

x = -2,  x = -3/4

500

Completely Factor:

x² - 2xy + y² - r² + 8r - 16

((x - y) + (r - 4))((x - y) - (r - 4))

Radicals and Complex #s

100

Simplify:

(16x⁸y⁴)^1/4

2x²|y|

200

Simplify:

(8 - 5i)(2 - i)

11 - 18i

300

Find an equation with solutions at:

x = 3 + 4i

x = 3 - 4i

x² - 6x + 25=0

400

Solve:

x² - 3x + 5 =0

x = (3 + i root(11))/2

x = (3 - i root(11))/2

500

Solve for y:

((x + 2) / y²)^1/2 = k

y = +- root(x + 2) / k

Exponents and Logarithms

100

Condense:

1/2 log(x) - 3 log(y)

log(root(x)/y³)

200

Solve:

3^3x-2 = 27

x = 5/3

300

Solve:

log(x+19) - log(2x) = 1

x = 1

400

Solve:

log₃(5x + 7) = 2

x = 2/5

500

Solve:

|log₅(2x - 1)| = 2

x = 13, x = 13/25

Systems and Matrices

100

Find A^-1 if A = 

2  3
1  2

 2  -3
-1  2

200

Solve:

3x - 2y = 7

5x + 3y = -1

(1, -2)

300

Find A^-1 if A = 

3   1   2
1   0   1
-2 -1  1

-1/2   3/2   -1/2
3/2   -7/2   1/2
1/2   -1/2   1/2

400

Solve using Cramer's rule:

-4x - 2y = 3

3x - 5y = -4

(-23/26, 7/26)

500

Solve:

2x - y + 3z = 5
3x + 2y - z = 1
x - 3y + 4z = 0

(-2, 6, 5)