ACCUPLACER Arithmetic & Elementary Algebra Study Guide

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1 ACCUPLACER Arithmetic & Elementary Algebra Study Guide

2 Acknowledgments We would like to thank Aims Community College for allowing us to use their ACCUPLACER Study Guides as well as Aims Community College English Faculty for creating the Sentence Skills Study Guide.

3 Table of Contents Assessment Rules and Regulations Arithmetic Elementary Algebra Math Sequence back page

4 Merced Campus Lesher Student Services Center, Room #102 Los Banos Campus Building A, Room A119 The goal of the ACCUPLACER assessment test is to provide you and Merced College with useful information about your academic skills in English and math. Your assessment results, along with your educational background and interests will be used by counselors to determine your course options. ACCUPLACER is an adaptive test. Questions are selected for you on the basis of your answers to previous questions. This means the right questions are selected for you based on your ability level. Each test is untimed so that you can give each question as much thought as you need. You can change your answer to a particular question before moving on to the next question, but you cannot skip a question, or come back to it later to change your answer. Upon completion of your test, a score report will be generated and your results will be printed and given to you. Take this test seriously. Remember, your scores plus other educational experiences or performance will determine the course level at which you begin your higher education at Merced College. Retakes are not permitted unless approved by a counselor. NOTE: If English is NOT your primary language and you normally speak in your primary language and one of your goals at Merced College is to learn English, call (209) for more information about testing. Before you take the Merced College assessment test: > You must have your Merced College ID card > You should refresh your math skills 1

5 MERCED COLLEGE ASSESSMENT RULES Merced College strives to provide each student an appropriate environment in which to take the assessment test. Each student should have the opportunity to thoughtfully answer all questions to demonstrate his/her current knowledge and skill levels in English and math. In order to provide an environment that is free from distractions, the following rules are necessary: > Turn all electronic devices completely OFF (not on silent or vibration mode, i.e., cell phones) and place them off the desk. If we see or hear your cell phone, you will be removed from testing, no questions asked. > Family, friends, children and other companions are not allowed. > Personal calculators, dictionaries, translators, or other electronic devices cannot be used during assessment. > Raise your hand or motion to the assessment technician to signal the need to ask a question. > Talking to your seatmate or other students taking the test is not permitted. > Food and/or drinks are not permitted in the testing area. Important to Know Assessment or placement testing is on a first-come, first-served basis during scheduled testing times. Refer to the assessment calendar for dates and times. Allow at least 2 or more hours to complete your assessment. Your results for English and Math will determine how you will register yourself. Counselors are available if you need assistance. ACCUPLACER sample questions 2

6 Arithmetic Fractions Terms Numerator: which tells how many parts you have (the number on top) 3 Denominator: which tells how many parts in the whole (the number on the bottom) 4 Example: = 3/4 is 3 parts have a dot out of 4 Ex: Proper fraction: the top number is less than the bottom number. Ex: Improper fraction: the top number is equal to or is larger than the bottom number. Ex: Mixed Number: a whole number is written next to a proper fraction. 3

7 Common Denominator: is a number that can be divided evenly by all of the denominators in the problem The common denominator for these fractions will be 12. It also happens to be least common denominator. Reducing Fractions to Lowest Terms Example: Step 1: Find a number that goes evenly into the numerator and the denominator of the fraction. With the fraction to the left, the number that will go in evenly is 8. Step 2: Check to see whether another number goes evenly into both the numerator and denominator. Stop when there are no more numbers that can go into the fraction. In the example, the fraction can be reduced further by dividing it by 2. Changing Mixed Numbers to Improper Fractions Example: Change to an improper fraction. Step 1: Multiply the denominator by the whole number. 2 X 4 = 8 Step 2: Add the result to the numerator = 11 Step 3: Place the total over the denominator. 4

8 Adding and Subtracting Fractions With Different Bottom Numbers *Remember to change improper fractions to a mixed number. Multiplying Fractions 5

9 Dividing Fractions 6

10 DECIMALS Place the decimal point directly above its position in the problem. Then divide the same way as divide whole numbers. 7

11 Practice: 8

12 PERCENTS 9

13 Finding What Percent One Number Is of Another Finding a Number When a Percent of It is Given 10

14 11

15 Elementary Algebra Student Success Center Elementary Algebra Study Guide for the ACCUPLACER (CPT) The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra 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. I. Order of operations Simplify. Write answers in scientific notation. II. Sci- 12

16 III. Substitution IV. Linear equations in one variable Solve the following for x. V. Formulas VI. Word Problems 1. One number is 5 more than twice another number. The sum of the numbers is 35. Find the numbers. 2. Ms. Jones invested $18,000 in two accounts. One account pays 6% simple interest and the other pays 8%. Her total interest for the year was $1,290. How much did she have in each account? 3. How many liters of a 40% solution and an16% solution must be mixed to obtain 20 liters of a 22% solution? 4. Sheila bought burgers and fries for her children and some friends. The burgers cost $2.05 each and the fries are $.85 each. She bought a total of 14 items, for a total cost of $ How many of each did she buy? 13

17 VII. Inequalities Solve and graph on the number line. VIII. Exponents & polynomials Simplify and write answers with positive exponents. IX. Factoring 14

18 X. Quadratic Equations XI. Rational Expressions Perform the following operations and simplify where possible. If given an equation, solve for the variable. 15

19 XII. Graphing Graph each equation on the coordinate axis. XIII. Systems of Equations Solve the following systems of equations. 16

20 XIV. Radicals Simplify the following using the rules of radicals (rationalize denominators). All variables represent positive numbers. I. Order of Operations Answers 17

21 II. Scientific Notation All numbers in scientific notation have the following form: non zero digit rest of number 10 power. III. Substitution IV. Linear equations in one variable 18

22 V. Formula VI. Word Problems 1. Let x =.another number. forcing 2x + 5 =.One number.. x + 2x + 5 = 35 and x = 10. One number = 25 and another number = Let x = the dollars in the account paying 6% interest Then, 18,000. x = the dollars in the account paying 8%. The interest dollars are calculated by multiplying the total dollars in the account by the interest rate. Hence:.06 x = the interest earned by the first account.08 (18,000. x) = the interest earned by the second account. Adding up all the interest,.06x +.08(18,000. x) = 1,290. Solving, x = 7,500. So, Ms. Jones has $7,500 in the account paying 6% interest and $10,500 in the account paying 8% interest. 19

23 3. Use the following buckets: From the diagram, we get the equation:.4x +.16 (20. x) = 20(.22) x = 5 and the answer is 5 liters at 40% and 15 liters at 16%. 4. Let x = the number of burgers and 14. x = the number of fries. To get the total amount of money spent, multiply the number of items by the cost of the item x = the total dollars spent on burgers and.85 (14. x) = the total dollars spent on fries. The equation is: 2.05x +.85 (14. x) = Solving the equation, x = 6. Hence, she bought 6 burgers and 8 fries. VII. Inequalities Solve inequalities the same as equations with one exception. When both sides are multiplied or divided by a negative number, remember to switch the direction of the inequality. 20

24 VIII. Exponents & Polynomials IX. Factoring Steps to factoring: 1. Always factor out the Greatest Common Factor (If possible). 2. Factor the first and third term. 3. Figure out the middle term. 21

25 X. Quadratic Equations XI. Rational Expressions 1. Need to find a common denominator (factor denominators to see what you need), add, and then reduce (if possible) at the very end. 22

26 23

27 XII. Graphing 24

28 25

29 XIII. Systems of Equations XIV. Radicals 26

30

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