Algebra I Semester 2 Review

Equations

100

Solve: -9 - x = x + 1

x = -5

200

Solve: 5(x-2) = 11 - 2x

x = 3

300

3(2 + 6x) = 6(1 + 3x)

All real numbers/infinitely-many solutions.

400

-2/3 y + 5 = 9/2

y = 3/4

500

Solve x^4 - 9 = 0

x = sqrt 3 or x = -sqrt 3

Radicals

100

What is the square root of 500?

10 sqrt 5

200

Find the square root of 100 x^3 y^4

10x y^2 sqrt x

300

Find the square root of 32x^2.

4|x| sqrt 2

400

Can 10, 24, and 26 be the sides of a right triangle?

Yes.

500

Suppose that 12 is the hypotenuse of a right triangle and one of the legs is length 10. What is the length of the other leg? Write your answer in simplest radical form.

2 sqrt 11

Absolute Value

100

Solve: |2x - 1| = 5

x = 3 or x = -2

200

Solve: -2|x+4| = 10

No solution.

300

Solve: |x - 9| < 5

4 < x < 14

400

Solve 9|x-4|/2 = 18

x = 8 or x = 0

500

Solve: 3|2x - 5| > 12

x > 9/2 or x < 1/2

Quadratic Equations

100

Solve 4x^2 + 5 = 105

x = 5 or x = -5

200

Solve n^2 - 8x + 12 = 0 by factoring.

n = 2 or n = 6

300

Solve y^2 + 10x = 11 by completing the square.

y = 1 or y = -11

400

Solve 3x^2 - 5x = 3 using the quadratic formula.

x = [5 +- sqrt(61)]/ 6

500

Find the x-intercepts of f(x) = 3x^2 - 11x - 20

x = -4/3 or x = 5 (-4/3, 0) and (5, 0)

Potpourri

100

What is the GCF of 16xy, 4x^2 y, and 8x y^2?

4xy

200

Multiply: (2x + 5)(-5x - 2)

-10x^2 - 29x - 10

300

Subtract: (3x^2 - 2x - 1) - (5x^2 - 3x + 9)

-2x^2 + x - 10

400

Solve 2n/3 + 4n/5 = 1/15

n = 1/22

500

Graph the parabola x^2 + 2x - 3 using any method. You must graph at least 5 points.

(Check on Desmos!)