Final Review

Integer Rules

100

Solve.

-8(-9)

72

200

Solve.

-5² - (-5)

-20

300

Solve.

7(3² - 9)

0

400

Solve.

-9/0

undefined/no solution

500

Solve. Leave as a fraction

(-3)(-4) - (-5)(-2)
------------------
(-2)(11)

-1/11

Rational Numbers

100

Simplify.

63x⁵y³ + 36x²y²
------------------
9x²y

7x³y² + 4y

200

Simplify.

x² - 5x - 6
-------------
x² - 6x

(x + 1)/x

300

Subtract. Simplify your answer.

3x - 6              x + 2
--------    -      --------
2x                     2x

(x - 2)/x

400

Solve for x.

x            3           x - 1
---   +   ----    =  -------
2           6               4

-3

500

Divide.

x² + xy                                  5x² - 4xy
----------            divided by    -------------
2x² - xy - 3y                           4x² - 9y²

(2x + 3y)
-----------
(5x - 4y)

Polynomials

100

Simplify.

(3x + 5y)(2x - 3y)

6x² + xy - 15y²

200

Multiply.

(4x - 3y)²

16x² - 24xy + 9y²

300

Factor.

4m² - 7mn - 15n²

(4m + 5n)(m - 3n)

400

Solve for p.

p² -5p = -6

Hint: there are 2 numbers.

x = 2, 3

500

Simplify.

(-3x²y)²(2xy²)³

72x⁷y⁸

Equations

100

Solve for x.

6 - 10x = -34

x=4

200

Solve for x.

x/3 - 9 = 5

42

300

Solve for y.

ax + by = c

y = (c - ax)/b

400

Solve for h.

A = 1/2 (bh)

2A/b

500

Solve for x. 

2(5x - 1) - 2x = 3x + 8

2

Word Problems

100

When this expression is simplified, how many terms are in the simplified form?

7x - 3x + 2y - x

two terms

200

Find the value of 4x² + 2x + 5 when x = -3

35

300

The length of a rectangle is 3 less than 2 times its width. If the perimeter is 48 cm, find the length.

9 cm

400

The sum of two consecutive odd integers is 92. Find the larger of the two integers.

47

500

In a marathon, Eileen ran four times as many miles as Alan, and Susan ran two miles less than Alan. Together they ran a total of 28 miles. How many miles did Eileen run?

20 miles