c The solution of the equation 5x 2x 11falls between what two consecutive integers? a. 0 and 1 b. 1 and 2 c. 2 and 3 d. 3 and 4 e.

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1 Algebra Topics COMPASS Review revised Summer 0 You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are basic calculators, scientific calculators, and approved graphing calculators. For more information, see the JCCC Testing Services website at or call Work out these problems and select the correct answer. 9. What are the solutions to the equation? 4 b. 4. c. 8 d. e.. The solution of the equation falls between what two consecutive integers? 0 and b. and c. and d. and 4 e. 4 and. If is subtracted from times the reciprocal of a number, the result is. Which of the following equations determines the correct value of? b. c. d. e. 4. Evaluate when 4 4 b. 0 c. 8 d. 74 e.. Evaluate y when b. 0 4 y and c. 0 d. 9 e.. What is the value of the epression y y 8when 0 and y? b. 8 c. 8 d. 0 e. 7. If and y 4 what is the value of y 4? 79 b. 8 c. 88 d. e If 9, then? b. c. d. e. 9. What is the value of the epression y y y when and y? k b. c. 0 d. 0. If then k? b. 8 c. d. e.. If +, 4, and + represent test scores, which of the following algebraic epressions represents the average (arithmetic mean) of the three test scores? + 4 b. 80 c. 4 d. 9 e. 9 7 e.

2 4. For all, which of the following is equivalent to? 7 7 b. c. d. 7 e. 7. Given the following graph, how long is AB? d. b. e. c. A B C 4. What is the distance between the and y intercepts of the line y4 8? 7 b. 8 c. 0 d. e. 4. Find the distance between 4,0 and, 4 b. 9 c. d. 9 e.. If 0 then 0? b. c. 4 d For all, = d. 4 b. 4 e. 4 c. e. 8. Which of the following is a factor of 0 8? b. 4 c. d. e Which of the following is equivalent to 8? 9 4 b. c. d. 7 4 e Add 0 =? 0 b. 0 c. 7 d. 8 e. 8. What is the solution of the equation? 4 4 b. 7 c. 4 d. e. 4 4

3 . A car salesman received a weekly salary of W dollars plus a % commission on his total sales S. Which epression best describes his weekly pay? W + S b. (W + S) (0.) c. 0.0W + S d. W + 0.0S e. W + S. Which of following is equivalent to y y y? y 8y 7y b. y y c. y 0y d. y y 8 e. y y 4. Solve for : 7 b. c. d. e. 8. John can complete a job alone in hours, and it takes Tim hours to do the same job alone. How long will it take them if they work together? hour b. hours c. hours d. hours e. hour. What is the value of when? b. 7 c. 8 d. 90 e The graph of the equation y will lie in which quadrants of the coordinate plane? I and II b. I and IV c. I, II, and III d. I, II, and IV e. I, II, III, and IV 8. Subtract: 9 b. c. 4 d. 9 e Multiply: b. c. d. e. 0. Solve this equation: b. 4. Which of the following lines is perpendicular to y b. c. d. y 4? y c. y 4 d. e. 0 y e. y4. How many ounces of a 0% alcohol solution must be mied with 0 ounces of a 0% solution, to make a 40% solution? 40 ounces b. 0 ounces c. 0 ounces d. ounces e. 0 ounces. Multiply and write your answer in a + bi form: i 4 i. 8 i b. i c. 0 i d. 8 i e. 8 i

4 4. What are the solutions of the equation:? 4, b. 4, c., d., e. 0,. What are the solutions of the equation: 90 0? 9 0, b., c., d., e.. What is the sum of the solutions to 7 0? b. c. 8 d. 7 e The graph of y has an -intercept of:,,0 b. 0, c., d 0, e.,0 8. Multiply: 8 8 b. 0 c. 0 d. 4 e Solve for : y z yz b. z y c. yz d. y z e. yz For all 0,? b. c. 8 4 d. e. yz y z 4. Simplify: 4 7a b c ab c a b. 9a b c c. abc d. 9ab c e. a b c c 4. If 0, which of the following is a value for? b. 0 c. 0 d. e. 0 a b 4. Simplify: 0 ab 7 ab for all a0, b 0 b. 7 a b c. 0b a ab d. 7 e. a b A car rental agency charges $ per day plus $0.0 per mile. Which of the following is an epression for the total charges in dollars of renting a car for one day and driving m miles 0.0m b. m 0.0 c..0m d. m e. 0.0m 4. At what y, coordinates do the following lines intersect? y y, y b., y c., y 9 d., y 9 e., y 4

5 4. Which of the following equations represents the line graphed? y d. y b. y e. y c. y 47. Simplify: 4 4 b. 4 c. d. e. 48. John and Susan are reading final eam research papers. John can read at a constant rate of pages per day. Susan reads 8 pages a day more than John. If it takes John full days to read all the final eam research papers and it takes Susan full days, how many pages a day is John reading? 0 pages b. 4 pages c. pages d. pages e. 4 pages 49. Ten times the reciprocal of a number is less than the original number. Which equation can be used to solve for the original number? 0 b. 0 c. 0 d. 0 e If r and l, which of the following is equivalent to rl r? b. 4 c. d. 7 e. 4 Answers to the Algebra Topics COMPASS Review. d. d. b 4. d. a. b 7. c 8. d 9. e 0. b. a. e. b 4. a. e. c 7. c 8. c 9. e 0. b. a. d. a 4. a. b. d 7. d 8. c 9. a 0. c. a. a. b 4. a. d. e 7. a 8. d 9. e 40. d 4. e 4. c 4. b 44. a 4. b 4. d 47. e 48. e 49. b 0. b

6 Solutions to the Algebra Topics COMPASS Review. What are the solutions to the equation 9? 4 Cross multiply to obtain: Solve the linear equation. So the solution falls in between and 4.. is subtracted from times the reciprocal of a number is written as the result is is written as = Putting this together gives 4. Given 4, substitute 4 in place of. ( 4) ( 4) () ( 4) Use order of operations to simplify 4 7. Given y and, substitute these values in place of and y: (Find common denominator) Given 0 and y, substitute these values in place of 0 8 (Use order of operations to simplify) and y:

7 7. Given and y 4, substitute these values in place of and y: (Use order of operations to simplify) 8. Solve the linear equation: Rewriting 9 as 8 9. Given and y substitute these values in place of and y: When we cross multiply, we obtain k. Multiplying the right side and combining like terms gives: k 8 Therefore k 8.. The average or (arithmetic mean) is found by adding up the test scores and dividing by since there are three tests Factor both the numerator and the denominator One way to find the length uses the distance formul The distance formula is d y y Point A has coordinates 4, and Point B has coordinates The distance formula is d y y To find the intercept, substitute y 0 into y The intercept is (,0) To find the y intercept, substitute 0 into y4 8. y 4(0) 8 y 0 8 y 8. The y -intercept is (0,-8) Substituting these values into the formula gives: ,4. Substituting these values into the formula gives: 7

8 . Substitute the values given into the distance formul Cross multiplying gives Squaring both sides gives To simplify, you need to distribute the minus sign first and then combine like terms = = = by factoring. 8. To factor 0 8, Method Start with and at the beginning of the parentheses:. Try different pairs of factors of -8 for the nd number in the parentheses. Then decide which will FOIL out correctly. The pairs of factors are: - and 8 and -8 - and 4 and -4 Of those choices, - and 4 give the correct factorization:. 4 Therefore, is a factor. Method Multiply the a and the c: times -8 = -4. Listing the pairs of factors of -4 results in: - and 4, and -4, - and, and -, - and 8, and -8, -4 and, -4 and Choose the pair that adds to +0: - and. Rewrite the quadratic epression by splitting up the b term into the pair you found above: (Now factor by grouping) ( ) 4 Factor out Therefore, to yield: 4 is a factor 9. To square a binomial, multiply it by itself Simplify each of the radicals, find a common denominator, and combine

9 . The solution is found by multiplying every term by the Least Common Denominator and then solving. LCD = The salesman will receive W dollars, plus whatever he makes on commission. His commission is (0.0)(S). Adding these together results in: W + 0.0S.. To find the one that is equivalent to ( y )( y y ) : Multiply (distribute) y to each of the terms in y y, and then multiply (distribute) to each of the terms in y y. y y y 0y 0y y 8y 7y 4. To solve the inequality, isolate (Note that dividing by a negative value reverses the inequality sign) 9

10 . Since John can complete the job in hours, he would get of the job done in hour. Since Tim can complete the job in hours, he would get of the job done in hour. Let stand for the time it takes them to complete the job together. Then of the job could get finished in hour. The equation would then be Multiply by the least common denominator on both sides of the equation. hours to complete the job together.. Given, substitute in place of y has a y-intercept of, and a slope of, so it is graphed as indicated below Quadrant I is the upper right, Quadrant II is the upper left, Quadrant III is the lower left, and Quadrant IV is the lower right. Therefore, the graph lies in Quadrants I, II, and IV. 0

11 8. To subtract, you must have common denominators. 9 Factor all denominators to find the least common denominator Note that the LCD is. ( )( ) ( )( ) Rewrite each fraction with the new LCD by multiplying each fraction by term(s) that are in the LCD but not in the original denominator. ( )( ) ( )( ) ( ) ( ) 4 ( )( )( ) ( )( )( ) ( )( ) ( )( ) 9. Factor all the numerators and denominators to obtain. ( )( ) ( )( ) Cancel like factors that appear in both the numerator and the denominator leaving you with: ( ) ( ) ( ) ( ) 0. To solve, isolate The slope of the given line is. A line perpendicular to the given line will have a slope that is the negative reciprocal,. The only line with a slope of is y.. Let the amount of 0% solution. Let 0 = the amount of the final 40% solution ounces of the 0% soluition. Multiply i 4 i (Note that i ) i i i i i i

12 4. Solve or 0 4,. Solve 90 0 (Same steps as #8 for the factoring part) 0 0 or 0,. Solve or 4 0, 4 The sum of the solutions, and 4, is At the -intercept, the y value will be zero. 0 The ordered pair is,0, since the value is, and the y value is To multiply ( 8)( 8), simplify the radicals first, then distribute. ( )( ) = 0 0 = 04 = 4 9. To solve,start by multiplying all terms by the LCD to eliminate fractions. The LCD is yz. y z yz yz y z yz z y z y yz z y yz (Factor out and then divide to isolate ) yz yz or z y y z 40. When dividing by a monomial, separate each term over the denominator and reduce. 0 0

13 4. To simplify, take out anything that has a nice square root 4. First, solve for. a a b b b c c a a b b b c c a b c c Since, we will substitute - for 0 ( a b ) 4. Use rules of eponents to simplify ab (a b ) a b a = 7 a b a b a bb a b 44. Let m represent the number of miles. Since the car agency charges $0.0 per mile, part of the cost would be $0.0m. They also charge the renter $ per day, so you need to add to get the total charges. 0.0m 4. One method is the addition method: Multiply the top equation by with the intent of eliminating the y when this equation is added to second equation. ( y) () 4y (add the two equations) y y 7 4 Since substitute this -value into one of the two original equations, to find y. y 4 y y The solution is:, y.

14 4. Method The y -intercept is -. Count up and to the right from that point, (0, -) to another point, such as (,0) to find the slope. The slope is. Substitute these two values into the slope-intercept form, y m b, to get y. Put this equation into standard form, since the choices are all in standard form ( A By C) ( y) y y y Method y y 0 Use the two intercepts (,0), and (0,-), to find the slope, using m 0 Substitute this slope and one of the ordered pairs into the in the point-slope form, y y m y 0 y Now change the form of the answer to standard form as in Method above., to get 47. To simplify, factor all numerators and denominators. Then take the reciprocal of the second fraction, and change division to multiplication. ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( ) 4 ( )( ) 48. Let be the number of pages John reads per day. Since it takes John full days, his total number of pages would be. Susan reads 8 pages more a day then John so her rate would be 8. Since it takes Susan full days, her total 8. number of pages would be Since they are reading the same research papers, the total number of pages will be equal, so John reads 4 pages a day. 49. Let = the original number. Then, = the reciprocal of the original number. Ten times the reciprocal of a number will be written as 0. less than the original number will be written as. The equation becomes Substitute in for the given variables, r and l and then simplify ()