Algebra I: Semester 2 Review

Lines and Linear Systems

100

Graph x = 2.

vertical line through (2, 0)

200

If a linear system has infinitely many solutions, the lines are ______________.

coinciding

300

Find the slope of the line parallel to 3x - 2y = 9.

3/2

400

Solve the system:

y = 3x + 1

3x + 4y = -2

(-2/5, -1/5)

500

Is (-2, 3) a solution to the system?

y - 2x > 3, y < -x

no

Exponents

100

x⁷*x^-5

x²

200

3x⁸/(6x)

x⁷/2

300

(9y^3/2)²

81y³

400

Multiply: (3 x 10^-20)(12 x 10¹⁵)

3.6 x 10^-4

500

(-5a²b⁴)²(3a)^-2

25a²b⁸/9

Factoring and Solving Quadratic Equations

100

Factor: 30g² - 45g⁴

15g²(2 - 3g²)

200

Factor: x² + 3x - 28

(x + 7)(x - 4)

300

Solve for x: 3 - 2x² = 11

no real solution

400

Solve the equation: (x - 12)(x + 3) = 0

x = {-3, 12}

500

Solve for x: 6x³ + 45x² = -21x

x = {-7, -1/2, 0}

Polynomials

100

Name the degree: x⁷⁸y¹² + 2y

90

200

Multiply: (3x + 2)(x - 7)

3x² - 19x - 14

300

Find the difference: (3x³ - 24x² + 8) - (2x³ + 7x² + x - 2)

x³ - 31x² - x + 10

400

Simplify: (3x + 9)(3x - 9)

9x² - 81

500

(3x - 8)²

9x² - 48x + 64

Radicals

100

2*sqrt(3) - 6*sqrt(3)

-4*sqrt(3)

200

What is the conjugate of (4 + sqrt(66))?

4 - sqrt(66)

300

Simplify: -2*sqrt(720)

-24*sqrt(5)

400

Rationalize: 2/(sqrt(5) - sqrt(7))

-sqrt(5) - sqrt(7)

500

(sqrt(3) + 2*sqrt(8))²

35 + 8*sqrt(6)