| ALGEBRA EXERCISES |
TABLE OF CONTENTS
click a link to go to the questions on each topic
| A/ Exponents |
| B/ Factoring |
| C/ Rational Numbers (fractions) |
| D/ Equations |
| E/ Inequalities |
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1) Write each of the following expressions with only positive exponents.
| a) a2 b – ³ | b) 2a – ² | c) |
d) |
e) |
f) |
g)  |
h)  |
i)  |
j) (x–3y–7) 0. |
2) Find a numerical value for the questions in #1 if a = –2 and b = –3.
3) Simplify the following and find numerical values when possible.
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
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4) Factor completely.
| a) hx + hy + kx + ky | b) (a + b)2 + 2a + 2b | c) ax + by – bx – ay |
| d) x2 – xy + xz – yz | e) 10x3 – 90x | f) 3 – 48x² |
| g) 2a2 – 32b² | h) 4m2 – p2 – 16pq – 64q² | i) 25 – 10a + a2 – b² |
| j) x2 + 7x + 6 | k) a2 – 10a – 24 | l) 3a2 + 21a – 24 |
| m) 15 + m – 6m² | n) 5m2 + 3m – 2 | o) 8x2 – 31xy – 4y² |
| p) 18a2 + 19a –12 | q) 2x3 – 16y³ | r) a3 + 125b³ |
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C/ Rational Numbers (fractions)
5) Multiply and Divide as Indicated. Reduce to lowest terms.
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  | ||
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6) Add, Subtract, Multiply and Divide as Indicated. Reduce to lowest terms.
a)  |
b)  |
c)  | |
d)  |
e)  | ||
f)  |
g)  |
h)  | |
i)  |
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7) Solve the following equations. Check your answers.
| a) 3(4x – 1) = 9 – 4x | b) 5x – 3(x + 1) = 2(3x + 5) | c) 15w – 4 = 8w + 31 |
| d) 8y2 + 2y – 1 = 0 | e) 4x2 + 5cx – 9c2 = 0 | f) 2x2 + 2x = 3 |
g)  |
h)  |
i)  |
| j) | 2x – 3 | = 5 | k) | 5x + 7 | = | 2x – 3 | | l)  |
m)  |
n)  | |
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8) Solve these systems of equations. Check your answers.
a)
x – y = 2 |
b)
2x + y = 10 |
c)
3x – y = 5 |
d)
3x = y + 1 |
e)
3x – 2y = 13 |
f)
–3x + y = 8 |
g)
x – y = –1 |
h)
y + 6 = 0 |
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9) Solve these inequalities.
| a) 3x – 2 < x + 6 | b) 4x + 3 > 5x – 17 |
| c) | 3x + 1 | < 7 | d) | 5x – 4 | > 21 |
| e) x2 – 4x < 5 | f) 2x2 > 5x + 3 |
g)  |
h)  |
i)  |
j)  |
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