Are You Read For Math Analsis? This is a District-Wide Summer Assignment for students taking Math Analsis in September 018. The Math Analsis teachers in all UCVTS programs will be using this for evaluation in their classes. Are ou read for Math Analsis? Net ear ou will be taking Math Analsis which is an honors level math course. It is a rigorous course that begins with fundamental algebra concepts and continues with the eploration of various functions and their graphs. All topics will be eplored numericall, graphicall and analticall. This summer packet is designed to help ou review the algebra concepts that will be the foundation for our success in Math Analsis net school ear. This summer packet is due the first da of school. It will be graded and gone over b our Math Analsis teacher, with an assessment given based on these topics in September. A successful outcome requires effective planning. This summer assignment provides a minimal number of eercises. It is strongl recommended that ou find additional practice resources for the topics that ou need etra help with. Do not wait until the end of the summer to look at this packet. You should work on this packet a little at a time. This will allow ou to have time to review the topics that ou are having trouble remembering. Schedule time to review and practice these topics. The following is a list of topics ou need to review and master: Algebra Topics to Review Polnomials: Add, Subtract, and Multipl Factoring: Common monomial factors, quadratics Solve equations: Multi-step equations, linear, absolute value & quadratic equations Rules of Eponents: Simplif epressions Rational Epressions: Simplif, Add, Subtract, Multipl, & Divide (Comple) Radicals: Simplif, Add, Subtract, Multipl, Divide (rationalize) Equations of lines: Find slope, Graph lines, find equations Graph Quadratic equations There are man resources available online. I suggest that ou start with the publisher of the tetbooks that ou used in Combined Algebra. The following links provide practice quizzes and tests to help ou identif the topics that ou need to practice. Algebra I: http://www.classzone.com/books/algebra_1/oltp_welcome.cfm Algebra II: http://www.classzone.com/books/algebra_/oltp_welcome.cfm You can easil find other student resources and practice opportunities if ou google the topic. Here are a few recommended resources. www.purplemath.com www.brightstorm.com www.hippocampus.org www.khanacadem.com
Are You Read For Math Analsis? Directions: Complete Part 1 on loose leaf. Show all work to receive full credit. Do NOT use a calculator. All of the eercises can be completed WITHOUT a calculator. Complete Part b sketching our graphs and showing our work in the space provided in this packet. 1. Find the sum and difference of polnomials. Make sure to combine like terms to simplif. 10 3 14 + 3 4 3 + 4 6 b.) [(6 8) ] [(1 7) (4 5)] 4 [3 + (3 + { 7} ) 4 + 5]. Find the product of polnomials. Then combine like terms and simplif. 3(4 + 10) b.) ( + 3)( + ) (4 4 7)( + 3) 3. Solve basic linear equations Solve for : 7-3 - 8 = 4 b.) 9 = 3(5 ) 8 3( 9) = -5 d.) 4 6 = 6 e.) 5 + 4 7 = 4 f.) 7(5 ) = 6(6 1) 4. Solve linear equations with fractions and decimals Solve for : 3 10 5 b.) 6 3 0.6a0.5a 4.5 3 9 5. Solve equations involving absolute value Solve for : 3 b.) 3 4 = 3 4 5 = 7 6. Simplif the following epressions completel using the Properties of Eponents. 6 5 b.) (3a 4 b 3 )(a 3 b) (z ) 5 d.) g.) 5 4 5abc 5abc 3 3 4 3 h.) ab 1 4 3 6ab c 1 14 8 e.) 3 3 i.) 5z 6 5z 6 3 j.) 4 4 () 3 f.) 4 0 3 1
Are You Read For Math Analsis? 7. Simplif completel using the Properties of Radicals. Assume all variables are positive. No decimals are allowed in our answers. All answers should be in simplified radical form. 9 b.) g.) 50 8 h.) 4 4 15 3 64 11 45 9 45 3 3 8. Rationalize the denominator and simplif each fraction. 3 1 b.) 5 3 d.) 3 40 6 e.) 18 3 f.) 3 8 0 9. Multipl, remembering to use special product rules when needed. Combine like terms to simplif our final answers. ( 3)( 3) b.) 5 4 6 d.) (-)(3+5) 10. Factor each epression b factoring out greatest common monomial factor(gcf). 5 0 b.) 4 3 4 4 9 3 4 3 3 11. Factor completel using an/all techniques studied in Combined Algebra. Hint: Start with GCF technique, if possible, and then use other techniques. 49 b.) 1 16 5 d.) 1 36 e.) 6 169 f.) j.) 9 1 4 g.) 4 3 5 6 15 18 5 45 h.) (factor b grouping) 3 3 36 i.) 8 38 10 1. Simplif the following Rational Epressions. 4 b.) 3 3 1 16 4 d.) 4 3 3 15 4 3 13. Perform the indicated operation and simplif 6 3 6 9 4 b.) 14 49 3 1 49 7 3 5 d.) 1 1 3 1
Are You Read For Math Analsis? 14. Simplif the following comple fractions. 1 1 1 b.) 1 1 1 15. Solve the following quadratic equations for the variable b either factoring, square root method, or quadratic formula. Use the appropriate technique for each equation. 8 0 b.) 10 5 0 9 36 d.) 3 9 16. Real Numbers. Consider the set 5 7 1, 5, 3,, 3.1, 0,,,, 0.333... 4 3 List all the: natural numbers b.) integers rational numbers d.) irrational numbers 17. Equations of lines Write the equation 3 4 8 in slope intercept form. Identif the slope and -intercept. b.) Write the equation of a line given the slope is -5 and the -intercept is 10. Write the equation of a line that passes through the point (6, -3) and has a slope of -. d.) Write the equation of a line that passes through the two points (1, 6) and (3, -4). 18. Solve the following sstems of equations: 3 4 5 1 b elimination b. b substitution 5 3 9 4 14 an method 3 4 1 c. an method 1 4
Are You Read For Math Analsis? Part II Graphing 1.) Graph the equation 3 15.) Graph the equation of a line whose slope is 1 and -intercept is - 3.) Graph the equation of the line whose slope is 0 and -intercept is 4. 4.) Graph the inequalit 4
Are You Read For Math Analsis? 5.) Graph the quadratic 1 6.) Graph the quadratic 5 7.) Graph the quadratic 8.) Solve the quadratic b factoring and 4 graph. 6
Are You Read For Math Analsis? Part III Isolating Variables Solve for the indicated variable in terms of the other variables in the boes. Solve for : a t v0 vfv0at Solve for : vf v0 t 1 vfv0 t Solve for : a v0 t v0t 1 at Solve for : a v0 vf v0 a
Are You Read For Math Analsis?