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precalc-worksheet

# precalc-worksheet - Simplify Assume that all variables...

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Pre-calculus review worksheet A list of basic arithmetic operations, laws of exponents, fac- torization rules etc. is on the inside of the cover of the the textbook. Linear functions. 1. Find an equation of the line through (3 , π ) parallel to the line y = 10 2. Find an equation of the line passing through ( - 1 , 2) and ( - 5 , 4) Polynomials. Perform the indicated operations 1. 3 5 x - 1 3 5 x + 1 2. (3 a + b ) 2 3. ( x - 2 y ) 3 Factoring. Factor each of the following polynomials: 1. 2 z 2 + z - 1 2. a 2 - 6 ab + 5 b 2 ( hint: easier to complete the square ) 3. 121 a 2 - 100 4. 8 r 3 - 27 s 3 Rational expressions (review long division!) Write each rational expression in lowest terms 1. 8 x 2 + 16 x 4 x 2 2. a a + 2 3. y 3 + 1 y 2 + y + 2 Equations. Solve each equation 1. 4 ( 2 p - (3 - p ) + 5 ) = - 7 p - 2 2. 2 b 2 + 4 b - 8 b 2 + 2 b - 4 b + 2 = - 4 b + 2 3. 1 x 2 - 2 x - 3 + 1 x 2 - 9 = 0 Inequalities. Solve each inequality 1. | x + 0 . 1 | > 2 2. - 1 y + 2 - 3 4 3.
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Unformatted text preview: Simplify. Assume that all variables represent positive num-bers. Write answers using only positive exponents. 1. y 9 y 7 y 13 2. ± a-7 b-1 b-4 a 2 ² 1 / 3 Simplify and write the answer as a single fraction without negative exponents. Assume all variables represent nonzero numbers and x 6 = y : 1. a-1 + b-1 2. ( x-2-y-2 )-1 / 2 Write each number without exponents 1. 125 2 / 3 2. ± 121 100 ²-3 / 2 Radicals. Simplify each expression by removing as many fac-tors as possible from under the radical. 1. p 32 y 5 2. p p 7 q 3-p p 5 q 9 + p p 9 q Rationalize each denominator 1. y √ y-√ 5 2. p p 2 + 1 + p p 2-1 p p 2 + 1-p p 2-1...
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