The study guide does not look exactly like the exam but it will help you to focus your study efforts.

Transcription

1 Mat 0 Eam Study Guide Solutions Te study guide does not look eactly like te eam but it will elp you to focus your study efforts. Here is part of te list of items under How to Succeed in Mat 0 tat is on my syllabus. Put aside time to study for tis class every day. One suggestion is to rewrite your notes after eac class. Tere is no substitute for writing out problems. You literally sould do 0 or more problems for eac unit of te course. Tere are usually eamples completely worked out in te book for te types of problems assigned for you to utilize before attempting omework. Te back of te book as answers for te odd numbered problems. You sould always do some of tese before attempting te required problems to elp you know if you are on te rigt track. Typical Eam Directions: Use pencil. Simplify all solutions. Sow your work. Clearly identify your final solutions. No calculators. Do not leave negative eponents in your final solutions unless you are required to. Your Notes combined wit te required problems will give you te best idea of wat types of problems you sould study to prepare for te eam. Te book as plenty of problems of te following type to use as practice. Simplifying radicals: Sections 7., 7., 7., and 7. Solving radical equations: 7.6 Comple numbers: 7.8 Here are some additional problems to use as practice wit special attention paid to functions.. Simplify eac radical epression. (Assume tat all variables are nonnegative.) Some solutions may require te use of i notation. 0 c) 9 y y y e) 6m = 8 m 7 6 = d) 6 =8i f) 8 8 an even root always gives positive answer

2 . Rewrite eac eponent epression in radical form. b b. Rewrite eac radical epression in eponent form. 6 6 m m. Evaluate eac epression using eponent properties. Te solution sould be a number wit no eponents or radicals Simplify eac epression using eponent properties. Do not use radicals. Do not leave negative eponents in final solutions. c) (Add eponents.) (Subtract eponents.) (Multiply eponents. Rewrite w/out negative.) 9 6. Write eac of te following epressions in te form: p were p is a real number. 6 c)

3 7. If one leg of a rigt triangle measures cm and te ypotenuse measures 0 cm, ow long is te oter leg? Let a and b be te lengt of te legs and c be te lengt of te ypotenuse. a b c Ten: b 0 b 8 Te oter leg measures b 8 cm If one leg of a rigt triangle is and te ypotenuse measure is, wat is te lengt of te oter leg? a b c Ten: b b b Tis is te lengt of te oter leg of te rigt triangle. 8. Wat is te distance between te points, and,6? 6 d y y 9 Wat are te coordinates of te midpoint of te segment tat joins, and,6? Midpoint, y y 6,, 9. Determine if te given epression is rational, irrational, or imaginary. i = Imaginary rational irrational (Tis is still a real number) Can be written as

4 0. Solve eac radical equation. Ceck your solutions. c) y y y y 0 y y y y 0 0 y y,8 (Ceck bot solutions.) y Only 8 works! y (Ceck te solution. It works) 7 8. List te real part and te imaginary part of eac comple number. 7i 6 i Real part = Real Part = 6 Imaginary part = 7i Imaginary part = i

5 . Answer and simplify eac question based on te given functions. Rationalize all denominators. f ( ) 7 p( ) Domain of p(). Use interval notation. ( is any real number), f(8) f(8) 8 8 c) p() 8 d) f e) Domain of g(). Use interval notation. (solve 0), e) Find all suc tat g ( ). Square bot sides and ten solve. Solution. 7 f) f ( ) f ()

6 . Write te function for eac grap. y (down ) y (left ) y (rigt, up ) y (slope -/, b = ). Grap eac of te following functions using te metods taugt in class. f ( ) f ( ) d) left units upside down, rigt, up

7 f ( ) e) f ( ) upside down line wit slope / and y-intercept - c) f ( ) f) rigt unit and down units f( ) left units

8 Mat 0 C 7 Practice Solutions Use pencil. Simplify all solutions. Sow your work. Clearly identify your final solutions. No calculators. Do not leave negative eponents in your final solutions.. Simplify eac radical epression. (assume tat all variables are nonnegative) 6b = 7 6b f) 9 y y y k) y y y m m g) 9 y 6 y y l) 7 8y y y c) 6 = ) a = a a m) 6 d) 6 = 8i i) 8 6m = m 7 n) 9 = e) 0 j) 0 = i. Simplify eac radical epression. Rationalize all denominators. = = = 7 0 c) d) 0 e) 9 = 9 f) y y y y y. Rewrite eac eponent epression in radical form. b b. Rewrite eac radical epression in eponent form. 6 6 m m. Evaluate eac epression using eponent properties. Te solution sould be a number wit no eponents or radicals Page of

9 6. Write te epression as a single radical. (Hint: First convert to eponents.) t t t t t t 0 t 0 t t t 7. Determine if te given epression is rational, irrational, or comple (nonreal). Comple (nonreal) OR Imaginary rational irrational 8. Simplify eac comple number epression. i i 8 i i i 7i 7i i i c) i i i d) 7i 7i i 7i 7 e) i i i 7 = i 0i 0 i 7i i 8i i i 9 i f) g) 9 ii i ) i i i i i i 0i 9i i 9 6i 9i 9 i 9. Solve eac radical equation. Sow your work. Ceck your solutions. 8 c) 6 no solution Solve eac radical equation. Ceck your solutions. c) y y y y y y y y 0 0 y y,8 (Ceck bot solutions.) y Only 8 works! y (Ceck te solution. It works) Page of

10 7 8. Answer and simplify eac question based on te given functions. Rationalize all denominators. f ( ) g( ) Domain of p(). Use interval notation. ( is any real number), Domain of g(). Use interval notation. (solve 0), c) f(8) f(8) 8 8 p( ) d) e) p() 8 (for fun ) f ( ) f (). Grap eac of te following functions using te metods taugt in class. f ( ) d) f ( ) f ( ) e) f ( ) Page of

11 c) f ( ) f) f( ). List te real part and te imaginary part of eac comple number. Real part = Real Part = 6 8 Imaginary part = Imaginary part =. Find te distance between te points ( ) and ( ). ( ( )) ( ) ( ) ( ). Use Pytagorean s Teorem to solve for te missing side in eac rigt triangle. (Sec 7.7) ( ) ( ) ( ) Page of

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