PLACEMENT TEST PREPARATION GUIDE MATHEMATICS

PLACEMENT TEST PREPARATION GUIDE MATHEMATICS Taking Your Placement Tests Are you prepared? Placement testing is mandatory for all new students. Taking time to work through this Placement Test Preparation Guide will help you be ready to take your Math and English placement tests and be accurately assessed resulting in proper placement in courses that match your skill level and possible reduction of unnecessary coursework

COMPASS Mathematics Skills Placement Test The Mathematics Skills Placement Test helps determine if you have the skills to succeed in entrylevel college courses or if you need additional mathematics instruction. The Microsoft Windows calculator is the only one that you will be able to use on the Math Skills placement test at Tri-C. To practice with the Windows calculator, click Start, All Programs, Accessories, and Calculator. The calculator has two views standard and scientific. You can change the view by clicking on View and selecting the alternate version. Below is an eample of the standard view. Notice that the square root key is labeled sqrt and appears only on the standard view. This is an eample of the scientific view. Mathematics Preparation Guide 7/15/013

Go to the COMPASS Sample Test Questions at http://www.act.org/compass/sample/inde.html Find More Sample Questions near the bottom of the page. When you take the COMPASS Mathematics Placement Test at Tri-C, you will begin with the Algebra Placement Test. Click on the Numerical Skills/Pre-Algebra and Algebra link. Begin on page 6 with the algebra sample questions. As you work the sample problems, notice the amount of reading. Answer the sample questions and check your solutions with the correct answers on page 10. Net to each correct answer, you will see the content category for that question. Use the content category to find additional review resources online or at the library. Additional Online Math Resources: www.hippocampus.org www.purplemath.com www.khanacademy.org www.patrickjmt.com Depending on your answers to the algebra problems, you also may need to answer pre-algebra or college algebra problems. Practice in pre-algebra begins on page 1. After answering these sample questions, check your solutions with the correct answers on page 5 and note the content category for each question. If you have studied college algebra and/or trigonometry, answer those sample test questions by clicking on the College Algebra, Geometry, and Trigonometry link under More Sample Questions. When you have completed the Placement Test Preparation, you may test at any of the Tri-C testing centers. For additional placement testing information, contact the testing center of your choice. Brunswick University Center BUC 14 16.987.3877 Corporate College West CCW 1 16.987.5888 Eastern Campus ESS 1108 16.987.56 Metropolitan Campus MSS 103 16.987.4311 Western Campus WTLC GT 115 16.987.556 Westshore Campus SHCS 130A 16.987.3887 or 16.987.3888 The COMPASS placement test information in this preparation guide has been reproduced with permission from ACT, Inc. Mathematics Preparation Guide 7/15/013 3

Cuyahoga Community College Mathematics Placement Review Problem # (Algebra) Doctors use the term maimum heart rate (MHR) when referring to the quantity found by starting with 0 beats per minute and subtracting 1 beat per minute for each year of a person s age. Doctors recommend eercise 3 or 4 times each week for at least 0 minutes with your heart rate increased from its resting heart rate (RHR) to its training heart rate (THR), where THR RHR +.65( MHR RHR) Which of the following is closest to the THR of a 43-year-old person whose RHR is 54 beats per minute? A. 197 B. 169 C. 16 D. 134 Content Category: Substituting Values into Algebra Eercises Math 0910 E. 80 Solution: First make sure that you understand the formula given: THR RHR +.65( MHR RHR ) ( Training Heart Rate) ( Resting Heart Rate) +.65 ( Maimum Heart Rate) ( Resting Heart Rate) Notice that the question gives the resting heart rate (RHR) and a method to calculate the maimum heart rate (MHR): RHR MHR 54 0 Age 0 43 177 Now use this information and the above formula to find the training heart rate (THR). ( ) ( ) ( ) THR RHR +.65 MHR RHR THR THR 54 +.65 177 54 54 +.65 13 THR THR 54 + 79.95 133.95 Of the answers given, D. 134, is the closest to the calculated value of 133.95 beats per minute. Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 004 by ACT, Inc. Mathematics Preparation Guide 7/15/013 4

Cuyahoga Community College Mathematics Placement Review Problem #3 (Algebra) When getting into shape by eercising, the subject s maimum recommended number of heartbeats per minute (h) can be determined by subtracting the subject s age (a) from 0 and then taking 75% of that value. This relation is epressed by which of the following formulas? A. h.75( 0 a) B. h.75( 0) a C. h 0.75a D..75h 0 a E. 0.75( h a) Content Category: Setting Up Equations for Given Situation Math 0950 Solution: Notice in the question that h is used for heartbeats per minute and a is used for age. Also notice the key words and phrases that mean something mathematical a symbol or an operation: can be determined by Equals () subtracting the subject s age (a) from 0 Subtraction (0 a) then taking 75% of that value. Multiplication (.75 that value) So the subject s maimum recommend number of heartbeats per minute (h) can be determined by subtracting the subject s age (a) from 0 and then taking 75% of that value is given by: h ( a).75 0 The answer is A. Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 004 by ACT, Inc. Mathematics Preparation Guide 7/15/013 5

Cuyahoga Community College Mathematics Placement Review Problem #3 (Numerical Skills/Prealgebra) 3 1 1 If + + is calculated and the answer is reduced to simplest terms, what is the denominator of 4 3 3 the resulting fraction? A. 4 B. 1 Content Category: Operations with Fractions Math 0910 C. 6 D. 4 E. 3 Solution: First, recall the order of operations and work inside each set of parentheses. When adding or subtracting fractions you must have a common denominator. The lowest common denominator (LCD) in the first parentheses is 1 and each fraction can be written as an equivalent fraction with 1 in the denominator. Now subtract the numerators and bring the common denominator along. 3 3 3 4 9 8 9 8 1 4 3 4 3 3 4 1 1 1 1 Likewise, in the second parentheses, the LCD is 6 and each fraction can be written with 6 in the denominator. Now add the numerators and bring the common denominator along. 1 1 1 3 1 3 3+ 5 + + + 3 3 3 6 6 6 6 After doing these operations the question becomes: 3 1 1 1 5 + + + 4 3 3 1 6 The LCD of these resulting fractions is 1 and each fraction can be written with 1 in the denominator. 3 1 1 1 5 1 5 1 10 1 + 10 11 + + + + + 4 3 3 1 6 1 6 1 1 1 1 This result is already reduced to simplest form because the numerator and denominator do not contain a common factor. Note the question does not ask for the solution, but for the denominator. In this case B. 1 is the correct answer. Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 004 by ACT, Inc. Cuyahoga Community College Mathematics Preparation Guide 7/15/013 6

Mathematics Placement Review Problem #10 (Numerical Skills/Prealgebra) If the total cost of apples is b cents, what is a general formula for the cost, in cents, of y apples? A. B. C. D. E. b y by y b by b y Content Category: Ratios and Proportions Math 0950 Solution: Set up a proportion to solve this question: Cost1 Cost # of apples # of apples 1 Using the given information: b cents apples Cost yapples Now cross multiply: ( Cost)( apples) ( bcents)( yapples) Divide both sides by apples and simplify the result: ( Cost) ( apples) ( apples) ( y apples ) ( apples ) ( bcents) Cost by cents The answer is D. Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 004 by ACT, Inc. Mathematics Preparation Guide 7/15/013 7

Cuyahoga Community College Mathematics Placement Review Problem #13 (Algebra) For all 4, which of the following is equivalent to the epression below? + 1+ 3 + 4 A. + 3 B. + 8 Content Category: Rational Epressions Math 0960 C. + 11 D. + 16 E. + 8 Solution: Since cannot equal -4 the denominator will not equal zero. Therefore, the fraction is defined for all values in its domain. See if the numerator and/or denominator are factorable. The numerator is factorable as shown: ( + )( + ) ( ) + 1+ 3 4 8 + 4 + 4 The fraction can now be simplified by reducing the common factor in the numerator and denominator: This fraction can now be simplified to give: + 1+ 3 4 + 4 ( + ) ( + 8) ( + 4) + 1+ 3 + 4 + 8 The answer is B. Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 004 by ACT, Inc. Mathematics Preparation Guide 7/15/013 8

Mathematics Sample Test Questions Work out these sample questions and return this packet to an Assessment Center before taking the placement tests. (1) 1 3 4 5 +? 3 4 5 6 A. B. C. D. E. 1 16 17 7 13 18 7 9 5 6 () What value of solves the following proportion? A. 1 5 3 9 6 8 B. 3 6 4 C. 1 10 D. 11 E. 1 (3) On a math test, 1 students earned an A. This number is eactly 5% of the total number of students in the class. How many students are in the class? A. 15 B. 16 C. 1 D. 30 E. 48 Mathematics Preparation Guide 7/15/013 9

Mathematics Sample Test Questions (4) If 3, what is the value of A. 4 B. C. 1 1 +? D. 3 3 E. 5 (5) Which of the following is equivalent to 3a 4b ( 6a 3b) A. 16ab B. 3a+ b C. 3a+ 7b D. 9a + b E. 9a+ 7b +? (6) If ( 5) 11, then? A. 1 B. 8 C. 11 D. 3 E. 1 Mathematics Preparation Guide 7/15/013 10