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Math 110 Notes: Review Topics Page 1 / 1 Review Make sure to point out that today is "Chapter R Amnesty Day" Start by taking your assigned section, with your group, and reviewing the material Use your book, and the provided handouts, to help guide you Summarize what's important, and what to look for Be ready to present (5 minutes – 10 tops) near the end of class. Topics: Set builder notation, roster notation? Finding the domain of a variable (Function notation – we’ll do this in 2.1) Pythagorean Theorem Applies to right triangles Def: Hypotenuse Exponents Rational Exponents Radicals Using the TI-83 to get exponents, etc a2 b2 c2 Areas, Volumes of various shapes This is a great opportunity to emphasize the whole 'perfect squares' thing, and that if we have the final term equal to ½ the middle term, squared, we know we can factor the expression into a perfect square. This is particularly pertinent, since in the next lectre, we'll be looking at 'solving a quadratic equation by completing the square', and the 'why do we use this particular formula?' question can probably be best answered by preemptively showing them how to factor expressions into perfect squares. Add, subtract, multiply (FOIL) polynomials Dividing polynomials Diff. of 2 Squares: x 2 a 2 x a x a Perfect Squares: x a 2 x 2 2ax a 2 Factoring Diff of 2 cubes: Sum of 2 cubes: x a x a x ax a x 3 a 3 x a x 2 ax a 2 3 3 2 2 x a 2 x 2 2ax a 2 Factoring By Grouping: Start with 4 terms (say), then reverse of the distributive property for multiplication twice, ending up with ax bc ax bd , which can then be factored into ax bc d Factoring 2nd degree polynomial: x 2 bx c Factoring 2nd degree polynomial: ax 2 bx c Factor it into: x Dx E 1. 2. Where D + E = b, and D*E = c 3. Figure out a*c Find 2 integers (d,e) that multiply to a*c, and add to b Rewrite the original expression as: ax 2 dx ex c 4. Factor that by grouping Rational Expressions: Combine factoring w/ basic fraction stuff. Lotsa' canceling Simplify/Reduce To Lowest Terms: numerator/denominator don't have any common factors (other than 1/-1, obviously) Radicals: Point out that 9 gets us only the positive root, while x 9 Don’t forget to VERIFY the answer, when solving a radical equation Graphing stuff – we’ll do this in 1.3, etc. 2 Math 110 x2 9 x 9 © 2004, Michael Panitz ®2004, Michael Panitz Page 1 / 1