ALGEBRA EXERCISES

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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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 = 6 x – y = 2 b) 2x – y = 2 2x + y = 10 c) x + 2y = 11 3x – y = 5 d) 2x + y = 9 3x = y + 1 e) x2 + y2 = 26 3x – 2y = 13 f) x2 + y2 = 8 –3x + y = 8 g) x2 + y2 = 25 x – y = –1 h) y = x2 – 3x – 4 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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