Math 1010, Fall 2011 Instructor: Marina Gresham Terms Midterm 3 Review Exponent Polynomial - Monomial - Binomial - Trinomial - Standard Form - Degree - Leading Coefficient - Constant Term Difference of Squares Factor Greatest Common Divisor (GCD) Prime Number Perfect Square (Cube, etc.) Rational Expression/Function Principal Root Even Root ( n x where n is even) Odd Root ( n x where n is odd) Rational Exponent Radical Rationalize a Denominator Conjugate (i.e. 2 + 5 and 2 5) Quadratic Equation Equation in Quadratic Form Complete the Square Quadratic Formula - Discriminant Imaginary Number Complex Number - Real Part - Imaginary Part Complex Conjugate Formulas and Rules to Use The following formulas/rules will be given to you on the test: a m a n = a m+n (a m ) n = a mn a m = 1 (for a 0) am a 3 + b 3 = (a + b)(a 2 ab + b 2 )
Math 1010 Instructor: Marina Gresham Midterm 3 Review 2 Formulas and Rules to Know (ab) m = a m b m ( a ) m a m = (for b 0) b bm a 0 = 1 (for a 0) 0 0 is undefined am a = n am n ( a ) ( ) m m b = (for a, b 0) b a (a + b)(a b) = a 2 b 2 ( Difference of Squares ) (a + b) 2 = a 2 + 2ab + b 2 x m n = n x m = ( n x) m n a n b = n ab (for a, b R) n a b = n a n b (for a, b R) Solutions to ax 2 + bx + c = 0: x = b ± b 2 4ac 2a i = 1 (a + bi)(a bi) = a 2 + b 2 Some Things To Remember (a + b) m a m + b m Before factoring to solve an equation, make sure you get it in the form (polynomial) = 0. When simplifying a rational expression, be sure to record any lost information about what values of x are not allowed! If you plug in a for x in some polynomial and get 0, then (x a) is a factor of that polynomial. For even roots, you have a principal (positive) root, and a negative root, and if the root is given in the problem it is assumed to refer to the principal root. If you have an odd root, then there is no choice... it is either positive or negative.
Math 1010 Instructor: Marina Gresham Midterm 3 Review 3 When solving equations with radicals and exponents, make sure to always raise both sides to the same power or take the same root of both sides. a b = (i a)(i b) = i 2 a b = ab a b ( a)( b) = ab... Always translate to i form first! Be Able To... Work on problems that cover topics you struggle with. Look at problems both at the beginning and end of each suggested range, and keep in mind that the higher-numbered problems are generally more difficult. I have made note of a few problems that touch on a particularly important or tricky skill. Pay special attention to these and the problems that I have written out on this sheet (non-book problems). Homework problems and problems like them are a good guide for your study. The book also provides mid-chapter quizzes and chapter tests, with answers. That is another good resource. Simplify and evaluate expressions using the rules of exponents Section 5.1: 1-100 Add and subtract polynomials (and understand related terminology) Section 5.2: 1-26, 69-84 (*23-26) Multiply poynomials (you can ignore the book s instructions to use a particular method FOIL, horizontal format, vertical format just use what you re comfortable with) Section 5.3: 1-92 (*77, 83) Write an integer as a product of its prime factors and use that to find the GCD of multiple integers or expressions Section 5.4: 1-20 (*19) Factor a polynomial Section 5.4: 21-50, 55-123 (*75, 115, 123) Section 5.5: 1-20, 37-50, 67-92, 99-120 (*17, 83, 117) Solve a polynomial equation by factoring Section 5.6: 1-82 (*79) Section 8.1: 1-20 Find the domain of a rational function by factoring Section 6.1: 1-22 (*19, 21)
Math 1010 Instructor: Marina Gresham Midterm 3 Review 4 Simplify rational expressions Section 6.1: 43-80 (*65) Multiply and divide rational expressions Section 6.2: 9-60 Add and subtract rational expressions (and identify the least common multiple, which should be used as the least common denominator) Section 6.3: 1-34, 41-82 (*31, 75) Use long division to divide two polynomials Section 6.5: 61-72 (*63) Extra: 2x4 4x 3 + 3x 2 5x 2 x 2 Use long division to factor a polynomial Section 6.5: 73-80 Extra: 5x 3 2x 2 2x 1 (Factor by first finding a value of x that makes the polynomial 0) Simplify and evaluate radical expressions and translate back and forth between radicals and rational exponents Section 7.1: 1-68, 73-128, 143-148 (*37, 57, 83, 123) Section 7.2: 1-54 (*25) Identify the domain of a function with a radical or rational exponent Section 7.1: 149-158 (*153) Extra: Find the domain of f(x) = x 1/8 + 3x + 2 Rationalize a denominator Section 7.2: 55-72 Add and subtract expressions with radicals Section 7.3: 1-56 Multiply and divide expressions with radicals Section 7.4: 1-50, 71-74 Find the conjugate of a radical expression and use that to simplify/rationalize denominators Section 7.4: 57-70, 75-98 (*93) Solve radical equations Section 7.5: 5-62, 73-76
Math 1010 Instructor: Marina Gresham Midterm 3 Review 5 Solve quadratic equations (using all methods covered in the sections below) Section 8.1: 21-80 (*77) Section 8.2: 1-68 (*49, 59) Section 8.3: 5-40, 49-64 Solve equations in quadratic form Section 8.1: 101-130 Solve equations that reduce to quadratic equations Section 8.2: 73-78 (*73, 77) Section 8.3: 89-92 Use the discriminant to identify the types of solutions to a quadratic equation Section 8.3: 41-48 Use i-form to simplify complex and imaginary expressions Section 7.6: 1-42, 55-108 (*29, 103) Solve basic complex equations Section 7.6: 47-54 Find and use a complex conjugate Section 7.6: 109-144 (*131, 143)