# PMEQ With Answers.pdf - Stony Brook University Mathematics...

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Stony Brook UniversityProficiency AlgebraMathematics DepartmentMAP 103Mark Lombardi, Thomas Rico, Julia ViroPractice Material for Exams and QuizzesOrder of arithmetical operations1.Calculate (without calculator) the value of the following expressions:a)34+1532·13b)-13+ 2·23-34c)-2 +35·23-2÷45Powers with integer exponents2.Calculate without calculator:a)2-5b)(-2)5c)125d)0-5e)15f)(-1)5g)23-5h)-2353.Calculate without calculator:a)65-3·252b)3-2-2-3c)(-3)-3·(-2)-2d)32-1-14-2+1204.Simplify the following expressions:a)x3·x4b)x-3·x4c)x-3·x-4d)(-x)3·x4e)(-x)3·(-x)45.Simplify the following expressions:a)x4x7b)x-4x7c)x-4x-7d)x4(-x)7e)x4x73f)x4x7-36.Simplify the following expressions:a)x2y3(2x)3b)(-3xy3)3(x2y)2c)(x3y2)2(xy2)-3d)(-xy4)-1(2xy2)3Polynomials7.Simplify the expressions (distribute and combine similar terms):a)3x2-x(2-4x)b)(x2-3x+1)(x-2)c)(2x2+x-2)(-x2-3x+1)1
28.Factor the following expressions:a)x2-1b)25-x2c)a2-4b2d)100x2-49y2e)1x2-99.Use the short multiplication formula to expand the following expressions:a)(x+ 1)2b)(x-2)2c)(3 +y)2d)(a+b)2e)(3x-1)2f)(4-x)2g)(-3a-5)2h)(ab+c)210.Find the value of the expression-4x2+x+3 forx= 2a-1. Simplify your answer.11.Letp(x) =x2+ 4x-1 andq(x) =x3+ 2x+ 1 be polynomials. Determine thedegrees ofp(x) andq(x). Finda)p(x)+q(x)b)p(-1)+3q(2)c)2p(x)-q(-2)d)p(x)q(x)e)p(x+ 1)2q(0)Rational expressions12.Perform the operations. Give the answer as a simple fraction.a)x-1x-xx-1b)x2+ 2x2x+ 4÷x3+ 2x22c)xy2-xyxy·y3y-1d)x+13x13.Find the value of the expressionx2-1x+ 1forx=1a. Simplify your answer.14.Simplify the following expressions:a)x2-1x+ 1b)x+ 24-x2c)x2+ 2x+ 1x+ 1d)x2-3xx2-6x+ 9Composing algebraic expressions15.The length of one side of a rectangle isxcm. The other side is 5 cm shorter.(a) Find an algebraic expression (in terms ofx) for the perimeter of the rectangle.Simplify this expression. Find the value of the expression ifx= 20 cm.(b) Find an algebraic expression (in terms ofx) for the area of the rectangle.Simplify this expression. Find the value of the expression ifx= 20 cm.16.Bob earnsxdollars per hour, Ann earns twice as much.(a) Compose an algebraic expression (in terms ofx) showing how much does Annearn per hour.(b) Compose an algebraic expression (in terms ofx) showing how much more willAnn earn than Bob, if she will work 3 hours and he will work 2 hours?
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