Advanced Math Test Review

Rational Exponents

100

Solve 64^1/2

What is 8?

200

Solve x^2/3 - 8 = -4

What is +/- 8?

300

Solve 3x^3/4 - 6=0

What is 2^4/3?

400

Solve 5x^3/2 - 25 = 0

What is 5^2/3?

or cube root of 5²

500

Solve x^2/3 - 3/4 = -1/2

What is +/- 1/8?

Equations

100

Solve |2x-1|=5

What is x=3, x= -2?

200

Solve 2(x-3)-17=13-3(x+2)

What is x=6?

300

Solve 3/(x+6) + 1/(x-2) = 4/(x²+4x-12)

What is x=1?

400

Solve 4x⁴=12x²

What is x=0, x= +/- square root of 3?

500

Solve (square root of x+3) + 3 = x

What is x=6?

Complex Numbers

100

Solve square root of 5²-4(3)(7)

What is i square root of 59? 

200

Solve (-1 + square root of -5)²

What is -4 - 2i square root of 5?

300

Solve (-14 + square root of -12)/2

What is -7 + i square root of 3?

400

Solve (5+4i)(6-7i)

What is 58-11i?

500

Solve 7+4i/2-5i

What is -6+43i/29?

Completing the square/square root/quadratic formula

100

Complete the square and factor.

x² + 6x

What is (x+3)²?

200

Complete the square then use the square root property.

x²+ 4x-1

What is -2 +/- square root 5?

300

Complete the square then use the square root property.

9x²-6x-4

What is 1/3 +/- square root 5/3?

400

Solve by using the quadratic formula.

2x²+9x-5=0

What is 1/2, -5?

500

Solve by using the quadratic formula.

3x²-2x+4=0

What is (1 +/- i square root 11) / 3

Inequalities

100

Express the interval in set builder notation.

(-2,5)

What is {x|-2<x<5}?

200

Find the intersection between (-4,0) and [-2,1].

What is [-2,0)?

300

Solve 3 < 4x - 3 < 19

What is 3/2 < x < 11/2?

400

Solve -3|5x - 2|+20 > -19

What is -11/5 < x < 3? 

500

Solve (4x-3)/6 + 2 > (2x-1)/12

What is x > -19/6?