College Algebra Study Guide

1 Testing Center Student Success Center 1 August 2012 College Level Math Accuplacer College Level Math Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these samples will give you a good idea of how the test works and just what mathematical topics you may wish to review before taking the test itself. Our purposes in providing you with this information are to aid your memory and to help you do your best. and expanding polynomialsFactor the following polynomials:Expand the following: 22 32154560a ba ba b 9. 113xxx 2. 3 3223227211030x yx yx yx y 10. 223xy 3. 443226688x yx yxy 11. 3366xx 4. 22276xxyy 12. 2223xx 5. 426yy 13. 51x 6. 33756xy 14. 61x 7. 448116rs 8. 221x yx y of Rational Algebraic ExpressionsSimplify the following. Assume all variables are larger than 20354 4 18 5 32 7 162 3 5 8 2 27 3.

2 481x5. 26181216328 412xxxxx Linear Equations1. 3 2110xx 3. 226y yy 4. 21 331xxx B. Solving Quadratic & Polynomial Equations1. 82033yy 5. 210tt 2. 3224300xxx 6. 3324x 3. 3271x 7. 22125xx 4. 36922xxx 8. 251yy 2 October 2012 College Level Math C. Solving Rational Equations1. 12011yy 4. 211212555xxx 2. 22312339xxx 5. 2165aa 3. 212563318xx xxx 6. 21133xxxx x Absolute Value Equations1. 5 21 8z 4. 131244x 2. 5 72x 5. 17yy 3. 512x E. Solving Exponential 4. 21393xx 2. 3510100x 3. 1128x 5. 221248xx Logarithmic Equations1. 22log5log 1 5xx 4. lnln 210xx 2. 332 log1log 4xx 5. lnln2ln 3xx 3. 22log1log13xx 6. 2134xx G. Solving Radical 21 2 0y 4. 291 0xx 5 8x 5. 332 4 6x 21 0xx 6. 2472w InequalitiesSolve the following inequalities and express the answer graphically and using interval Linear Inequalities1.

3 3425x 3. 326314xx 2. 3351xx 310 5x 3 October 2012 College Level Math B. Solving Absolute value Inequalities: Solve and Graph. 1. 416x 3. 553x 2. 43 2 9x 4. 5 215x C. Solving Quadratic or Rational Inequalities 1. 23114 0xx 3. 203xx 2. 2654xx 4. 13027xxx V. Lines & Regions 1. Find the x and y- intercepts , the slope , and graph 6x + 5y = 30. 2. Find the x and y- intercepts , the slope , and graph x = 3. 3. Find the x and y- intercepts , the slope , and graph y = -4. 4. Write in slope -intercept form the line that passes through the points (4, 6) and (-4, 2). 5. Write in slope -intercept form the line perpendicular to the graph of 4x - y = -1 and containing the point (2, 3). 6. Graph the solution set of x - y 2. 7. Graph the solution set of -x + 3y < -6. VI. graphing Relations, Domain & Range For each relation, state if it is a function, state the domain & range, and graph it.

4 1. 2yx 6. 22xy 2. 2yx 7. 286y xx 3. 12xyx 8. yx 4. 13f xx 9. 3xy 5. 2259xfxx 10. 226321xhxxx VII. Exponents and Radicals Simplify. Assume all variables are >0. Rationalize the denominators when needed. 1. 338x 6. 26238549abab 2. 5 147 4 48 7. 33322272aab 3. 5153 8. 253 4. 3243353xyx 9. 3xx 5. 43940xy 4 October 2012 College Level Math VIII. Complex NumbersPerform the indicated operation and 49 5. 243i 6. 25i3. 169 7. 3245ii 4. 4 34 3ii Functions and : 31xfx : log 9 2x 2. Graph: 12xgx : 3logh xx 3. Express21864 in logarithmic form the properties of logarithms to expand as4. Express5log 25 2 in exponential form much as possible: 43logy5. Solve:2log4x long will it take $850 to be worth $1000 ifit is invested at 12% interest compoundedquarterly? of Equations & Matrices1. Solve the system:23761xyxy :1110 2 10201 2 0213 0 0 1 2.

5 Solve the system:22323620xyzxyzx y z the determinant:1231 3. Perform the indicated the Inverse:1212 13312231216 made $10 more than twice what Pete earned in one month. If together they earned $760, how muchdid each earn that month? woman burns up three times as many calories running as she does when walking the same distance. Ifshe runs 2 miles and walks 5 miles to burn up a total of 770 calories, how many calories does she burn upwhile running 1 mile? pole is standing in a small lake. If one-sixth of thelength of the pole is in the sand at the bottom of thelake, 25 ft. are in the water, and two-thirds of the totallength is in the air above the water, what is the lengthof the pole?Water Line Sand 5 October 2012 College Level Math XII. Conic Sections 1. Graph the following, and find the center, 2. Identify the conic section and put it into standard foci, and asymptotes if possible. form . a) 22(2)16xy a) 224120xxy b) 22(1)(2)1169xy b) 22918166471xxyy c) 22(1)(2)1169xy c) 229181664199xxyy d) 2(2)4xy d) 240xyx XIII.

6 Sequence and Series 1. Write out the first four terms of the sequence whose general term is 32nan 2. Write out the first four terms of the sequence whose general term is 21nan 3. Write out the first four terms of the sequence whose general term is 21nna 4. Find the general term for the following sequence: 2, 5,8,11,14, 5. Find the general term for the following sequence: 11244, 2,1, , ,.. 6. Find the sum: 6021kk 7. Expand the following: 4404kkkxyk XIV. Functions Let ( ) 29f xx and 2( ) 16g xx . Find the following. 1. ( 3)(2)fg 5. ()( 2)gf 2. (5)(4)fg 6. ( ( ))f g x 3. ( 1) ( 2)fg 7. 1(2)f 4. (5)(5)fg 8. 1(3)ff XV. Fundamental Counting Rule, Factorials, Permutations, & Combinations 1. Evaluate: 8!3! 8 3 ! 2. A particular new car model is available with five choices of color, three choices of transmission, four types of interior, and two types of engines. How many different variations of this model car are possible?

7 3. In a horse race, how many different finishes among the first three places are possible for a ten-horse race? 4. How many ways can a three-Person subcommittee be selected from a committee of seven people? How many ways can a president, vice president, and secretary be chosen from a committee of seven people. 6 October 2012 College Level Math XVI. Trigonometry 1. Graph the following through on period: ( ) sinf xx 2. Graph the following through on period: ( ) cos(2 )g xx 3. A man whose eye level is 6 feet above the ground stands 40 feet from a building. The angle of elevation from eye level to the top of the building is 72. How tall is the building? 4. A man standing at the top of a 65m lighthouse observes two boats. Using the data given in the picture, determine the distance between the two boats. 7 October 2012 College Level Math Answers I. Factoring and Expanding Polynomials When factoring, there are three steps to keep in mind.

8 1. Always factor out the Greatest Common Factor 2. Factor what is left 3. If there are four terms, consider factoring by grouping. Answers: 1. 2215(34)a b abb 2. 2(710)(3)x y yxy 3322322222227211030(7211030)(721 ) ( 1030)7 (3) 10(3)x yx yx yx yx y xyyxyx yxyyxyx y y xyxy 3. 3222(34)(1)x yxy 4. (23 )(2 )xy xy 5. 22(2)(3)yy 42266(2)(3)yyuuuu 6. 227(2 )(24 )xy xxyy 7. 22(32 )(32 )(94 )rs rsrs 8. 2(1)xy Hint: Let u=x+y 9. 3233xxx 10. 224129xxyy 11. 232 3 2x 12. 432410129xxxx 13. 54325101051xxxxx 14. 65432615201561xxxxxx Since there are 4 terms, we consider factoring by grouping. First, take out the Greatest Common Factor. When you factor by grouping, be careful of the minus sign between the two middle terms. When a problem looks slightly odd, we can make it appear more natural to us by using substitution (a procedure needed for calculus).

9 Let 2uy Factor the expression with u s. Then, substitute the 2yback in place of the u s. If you can factor more, proceed. Otherwise, you are done. Formula for factoring the sum of two cubes: 3322()()aba b aab b The difference of two cubes is: 3322()()aba b aab b When doing problems 13 and 14, you may want to use Pascal s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 8 October 2012 College Level Math II. Simplification of Rational Algebraic Expressions 1. 13 2. 38 3. 29x 4. 49 2 5. 62x III. Solving Equations A. Solving Linear Equations 1. 5x 2. 145x or 425 3. 3y 4. 1x B. Solving Quadratic & Polynomial Equations 1. 82,33y 2. 0, 3, 5x 3. 113,3 66ix 4. 10, 4x 5. 1322it 6. 2, 13xi 7. 3, 4x 8. 12110y C. Solving Rational Equations 1. 13y 1201112(1)(1)0(1)(1)1112(1)(1)(1)(1)011( 1) 2(1) 031 0yyyyyyyyyyyyyyyyy 2.

10 Working the problem, we get 3x . However, 3 causes the denominators to be zero in the original equation. Hence, this problem has no solution. If you have 4, you can write 4 as a product of primes (2 2). In square roots, it takes two of the same thing on the inside to get one thing on the outside: 42 22 Solving Quadratics or Polynomials: 1. Try to factor 2. If factoring is not possible, use the quadratic formula 242bbacxa where 20axbx c Note: 1i Example: 12122 2 3 2 3iii Solving Rational Equations: 1. Find the lowest common denominator for all fractions in the equation 2. Multiply both sides of the equation by the lowest common denominator 3. Simplify and solve for the given variable 4. Check answers to make sure that they do not cause zero to occur in the denominators of the original equation. 9 October 2012 College Level Math 3. 154x , 5a ,1x Absolute Value or 7z 5 21 85 29zz 5 29z or 5 29z 24z or 214z or 10x solution.