Prerequisites: Fundamental Concepts of Algebra

Algebraic Expression and Real Numbers

100

Evaluate

(2x+3y)/(x+1), x=-2 and y = 4

What is

-8

?

200

Evaluate

x^2-3(x-y), x=8 and y=2

What is 46?

300

List all numbers from the given set that are rational numbers:

-9, -4/5, 0, 0.3, sqrt3, pi, sqrt49

What is

-9, -4/5, 0, 0.3, sqrt49

?

400

Determine whether the given statement is true or false: 

sqrt5 <= sqrt5

What is true?

500

Evaluate:

(|x|-|y|)/(x-y), x=2 and y=-5

What is

-3/7

?

Exponents and Scientific Notation

100

Simplify:

(-3x^4y^6)^3

What is

-27x^12y^18

?

200

Simplify:

(11x^5)(9x^12)

What is

99x^17

?

300

Simplify:

((-15a^4b^2)/(5a^10b^-3))^3

What is

(-27b^15)/a^18

?

400

Multiply:

(3xx10^4)(2.1xx10^-8)

What is

6.3xx10^-4

?

500

Divide:

(8.4xx10^-2)/(4xx10^6)

What is

2.1xx10^-8

?

Radicals and Rational Exponents

100

Evaluate:

sqrt(25-16)

What is 3?

200

Use the product rule to simplify the expression:

sqrt(2x^2)*sqrt(6x)

What is

2xsqrt(3x)

?

300

Use the quotient rule to simplify:

(sqrt(200x^3))/(sqrt(10x^-1))

What is

2x^2sqrt5

?

400

Rationalize the denominator:

7/(sqrt5-2

What is

7sqrt5+14

?

500

Simplify using properties of exponents:

(125x^9y^6)^(1/3)

What is

5x^3y^2

?

Polynomials

100

Perform the indicated operations and state the degree:

(5x^2-7x-8)+(2x^2-3x+7)-(x^2-4x-3)

What is

6x^2-6x+2

 and with 2?

200

Find the product:

(8x^3+3)(x^2-5)

What is

8x^5-40x^3+3x^2-15

?

300

Find the product:

(3x+2)^2

What is

9x^2+12x+4

?

400

Find the product:

(x-2)^3

What is

x^3-6x^2+12x-8

?

500

Find the product:

(1-y^5)(1+y^5)

What is

1-y^10

?

Factoring

100

Factor completely:

x^2-2x-15

What is

(x-5)(x+3)

?

200

Factor completely:

6x^2-11x+4

What is

(3x-4)(2x-1)

?

300

Factor completely:

9x^2-25y^2

What is

(3x+5y)(3x-5y)

?

400

Factor completely:

4x^2+4x+1

What is

(2x+1)^2

 or 

(2x+1)(2x+1)

?

500

Factor completely:

64x^3+27y^3

What is

(4x+3y)(16x^2-12xy+9y^2)

?