Sections P.1-­‐P.5 Exercises Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 1. Evaluate x 2 − 3(x − y) for x = 8 and y = 2 2. Find the intersection or the union of the set {1, 3, 7} ∩ {2, 3,8} . 3. Simplify the expression 14x 2 + 5 − [7(x 2 − 2) + 4] 4. It takes you 50 minutes to get to campus. You spend t minutes walking to the bus stop and the rest of the time riding this bus. Your walking rate is 0.06 miles per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic expression 0.06t + 0.5(50 − t) , a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine the total distance that you travel if you spend 20 minutes walking to the bus stop. Section P.2 Exponents and Scientific Notation 38
1. Evaluate 4 . 3
3
⎛ −15a 4 b 2 ⎞
2. Simplify ⎜
. ⎝ 5a10b −3 ⎟⎠
3. Simplify ( −3x 2 y 5 ) . 2
4. Evaluate (3 × 10 4 )(2.1× 10 3 ) . Section P.3 Radicals and Rational Exponents Part 1 1. Simplify 6x ⋅ 3x 2 . 2. Simplify 3 18 + 5 50 . 2
3. Simplify . 10
7
4. Simplify . 5 −2
Section P.3 Radicals and Rational Exponents Part 2 162x 5
1. Simplify 4
. 2x
4
(
2. Simplify 3x
2
3
)( 4x ) . 3
4
3. Simplify (125x 9 y 6 ) . 1
4. Simplify 12 x 4 y 8 . 3
Section P.4 Polynomials 1. Simplify (5x 2 − 7x − 8) + (2x 2 − 3x + 7) − (x 2 − 4x − 3) . 2. Simplify (7x 3 + 5)(x 2 − 2) . 3. Simplify (x + 2)3 . 4. Simplify (x − y)(x 2 + xy + y 2 ) . Section P.5 Factoring Polynomials Part 1 1. Simplify 9x 4 − 18x 3 + 27x 2 . 2. Simplify x 3 + 6x 2 − 2x − 12 . 3. Simplify 3x 2 + 4xy + y 2 . 4. Simplify 36x 2 − 49 . Section P.5 Factoring Polynomials Part 2 1. Simplify 25x 2 + 10x + 1 . 2. Simplify 8x 3 − 1 . 3. Simplify y 5 − 16y . 4. Simplify (x 2 + 4) 2 + (x 2 + 4) 2 . 3
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