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Resources for Practice and Review for Math Placement

For the following courses:

  • Math 051 Basic Mathematics
  • Math 152 Elementary Algebra
  • Math 153 Intermediate Algebra
  • Math 161 Functions and Graphs 1
  • Math 162 Functions and Graphs 2
  • Math 281 Calculus 1

You may need more than one source to cover all the topics listed for any one level. The information below provides guidelines, but you will need to check that all the topics listed for the courses above are covered.

Please send any corrections or suggestions to adow@mum.edu.

Websites with free practice tests:

  • http://www.gc.maricopa.edu/math/placement.htm Try any of the reviews: Numerical Skills (our Math 051), Elementary Algebra (our Math 152), Intermediate Algebra (our Math 153), College Algebra (our Math 161 and 162). You can also try the comprehensive test: Online Course Placement Test.
  • http://www.oaklandcc.edu/MathTest  Try the practice test. The other button tells you the solutions. Keep in mind that MUM does not permit a calculator to be used on a placement test. Also we do not require you to know about complex numbers.

 Website with free lessons:

  • www.purplemath.com  Click on Lessons index in the upper right hand corner. In the page you get next, click on Lessons in order in the top right hand corner. Make sure you are on the Lessons in order page or the following won’t make sense.
  • For our Basic Mathematics: All the topics under Preliminary Topics, under Beginning Algebra Topics: Exponents: basic rules, Radicals, Order of operations, Scientific notation, Canceling units; Under Appendix: Mean, Median, and Mode, Box-and-Whisker Plots, Stem-and-Leaf Plots. You’ll find some info about logarithms in the Logarithms and Log Rules sections of Advanced Algebra Topics.
  • For our Elementary Algebra: All the topics under Beginning Algebra Topics except the last two: Solving Radical Equations and Graphing Radical Equations; also Intermediate Algebra Topics: Factoring Quadratics, Special Factoring Formulas.
  • For our Intermediate Algebra: Start with Solving Radical Equations and Graphing Radical Equations from Beginning Algebra Topics; then go to Intermediate Algebra Topics – omit the first two items (Graphing systems of linear inequalities and Linear programming) and start with Inequalities: Absolute Value. Continue to the end of the Intermediate Algebra Topics, but skip Function Transformations and the last topic Sequences and Series. Then do the first few sections of Advanced Algebra Topics, namely, Complex Fractions, Rational Expressions: Simplifying, Adding Rational Expressions, and Multiplying Rational Expressions.  Also from “…and the beginnings of trig”. Everything up to Special Angle Values.  You will need to find the Law of Sines and the Law of Cosines in another trigonometry book.
  • For our Functions and Graphs 1: Start with Function Transformations from the Intermediate Algebra Topics. Then it won’t hurt to start Advanced Algebra Topics from the beginning. Omit Complex numbers and Partial-Fraction Decomposition. Work all the topics down to “Systems-of-equations word problems.” Omit the matrices and determinants and all the rest.
  • For our Functions and Graphs 2: Composition of functions and Inverse functions from Advanced Algebra Topics will be useful, but the rest of the course is not covered in Purplemath, namely trigonometry. You will need to look elsewhere for help with trigonometry.
  • Purplemath also has advice about what books would be helpful in reviewing (but not necessarily helpful for studying the topics from scratch). And lots of links to other helpful websites.
  • www.khanacademy.org You will find worked examples on all the topics.

Website with lessons on mathematics that you have to pay for:

  • www.aleks.com
 Click on course products. Note that Aleks.com provides a great analysis of where you are and what topics you need to study. You get a pie chart of the analysis and then you begin to fill in the areas you need to work on.
  • Our Elementary Algebra course corresponds to: Beginning Algebra  OR  Prep for Intermediate Algebra. It would also help to review the section called Descriptive Statistics in the course Prep for Statistics.
  • Our Intermediate Algebra: Intermediate Algebra  OR  Prep for College Algebra with Trigonometry  OR Prep for Pre-Calculus
  • Our Functions and Graphs 1: College Algebra (omit sequences, series, and probability)
  • Our Functions and Graphs 2: Pre-Calculus (omit sequences, series, and probability) OR College Algebra with Trigonometry

Books available from the MUM Library for review

Important Advice: Don’t just start reading a book! You won’t get very far if you do. First work through the relevant chapter reviews and chapter tests. Only then read the sections of the book pertaining to problems you had trouble with. The key to doing well on the test is to work problems, work problems, work problems. Note that you may need more than one book to cover all the topics listed in the “Topics to Review” page of the website www.mum.edu/mathplacement. Be sure to check that you have covered all the topics on that list.

Basic Mathematics:

  • Brown: Basic Arithmetic, Second edition, All chapters, Q107 .B75 1985.
  • Brumfiel: Principles of Arithmetic, Chapters 1 – 18, QA145 .B73
  • Fujii: Basic Skills in Mathematics, All chapters, QA106 .F77.
  • Fujii: Numbers and Arithmetic, Chapters 1 – 9, QA106 .F96.
  • Lay: Arithmetic: An Introduction to Mathematics, Chapters 1 – 20.2, QA145 .L27
  • Zuckerman: Basic Mathematics, Chapters 1, 6, 10, 11, QA39.2 .Z83 1980.

Elementary Algebra:

  • McKeague: Elementary Algebra, Fifth Edition, 1995, Chapters 1 – 5. QA152.2 .M32 1995. Other editions are also extremely useful.
  • Drooyan/Hadel: Elementary Algebra: Structure and Skills, 5th edition, QA152.2 .D75 1981
  • Drooyan/Wooton: Beginning Algebra: An Individualized Program, Chapters 1 – 6, . QA152.2 .D74 1978
  • Goodman: Concise Review of Algebra and Trigonometry,  Chapters 1 – 8, 9 (linear equations only), 12 (linear inequalities only) QA152.2 .G66
  • Hughes-Hallett: The Math Workshop: Algebra, Chapters 1 – 13, 17, 18. QA154.2 .H83 1980
  • Keedy/Bittinger: A Problem-Solving Approach to Introductory Algebra, Second Edition, Chapters 1 – 5, 7.1 – 7.2, 9, 10.1 – 10.5. QA152.2 .K44 1986
  • Larson/Hostetler/Heyd: Elementary Algebra, Third edition, Chapters 1 – 7. QA152.3 .L373 2001b.
  • Lial/Miller: Beginning Algebra, Chapters 1 – 5, 8. QA152.2 .L5 1980
  • Reigh and Hauck: Algebra Review Manual: A Program for Self-Instruction, Chapters 1 – 4, 7. QA152 .R35 1967
  • Rich: Schaum’s Principles and Problems of Elementary Algebra, Chapters 1 – 6, 10 – 12. QA152 .R5
  • Russell: Elementary Algebra, Chapters 1 – 8, 11. QA152 .R82 1968
  • Tobey/Slater: Beginning Algebra, Chapters 0 – 5, 8. QA152.2 .T6 1991
  • Wesner/Nustad: Elementary Algebra, with applications, Chapters 1 – 4, 6, 9. QA152.2 .W45 1983

Intermediate Algebra

  • McKeague: Intermediate Algebra, Fifth Edition, 1995, Chapters 1 – 8. QA154.2 .M43 1995 Other editions are also extremely useful.
  • Angel: Algebra for College Students. Chapters 1–8. Omit Sections 4.4, 4.5, 4.6, 7.7. QA152.2.A53 2000
  • Ashley: Introductory Algebra, Chapters 1 – 9. QA152.2 .A82 1979
  • Hughes-Hallett: The Math Workshop: Algebra, Chapters 1 – 21. QA 154.2 .H83 1980
  • Keedy/Bittinger: A Problem-Solving Approach to Introductory Algebra, Second Edition, Chapters 1 – 11. QA152.2 .K44 1986
  • Larson/Hostetler/Heyd: Elementary Algebra, Third edition, Chapters 1 – 10. QA152.3 .L373 2001b
  • Reigh and Hauck: Algebra Review Manual: A Program for Self-Instruction, Chapters 1 – 8, 11. QA152 .R35 1967
  • Russell: Intermediate Algebra, Chapters 1 – 8. QA152 .R83
  • Wesner/Nustad: Intermediate Algebra with Applications. Chapters 1–8 and Section 10.1. Omit Sections 6.6 and 8.6–8.8. QA154.2.W47 1985.
  • Wooton/Drooyan: Intermediate Algebra, Chapters 1 – 7, 9, 11. QA152.2 .W787

Functions and Graphs 1

  • Connally/Hughes-Hallett/Gleason: Functions Modeling Change, First Edition, Chapters 1 – 5. QA331.3 .F86 2000.
  • Connally/Hughes-Hallett/Gleason: Functions Modeling Change, Preliminary Edition, Chapters 1 – 4, 7. QA39.2 .C6 1998.
  • Hughes-Hallett: The Math Workshop: Elementary Functions, Chapters 1 – 12. QA331 .H795 1980
  • Ambrose: College Algebra and Trigonometry, Chapters 1 – 3, 5, 6, 11. QA 154.2 .A43 1977
  • Derrick: College Algebra and Trigonometry, Chapters 1 – 5, 8.1, 8.2. QA154.2 .D47 1982.
  • Foerster: Algebra and Trigonometry: Functions and Applications, Revised Edition, Chapters 1 – 3, 4.1 – 4.6, 5 – 7. QA 152.2 .F63 1984
Lial/Miller: Algebra and Trigonometry, Second Edition, 1980, Chapters 1 – 5, 9.1 – 9.2. QA154.2 .L49 1980.
  • Lial/Miller: Algebra and Trigonometry, Third edition, Chapters 1 – 5, 9.1 – 9.2. QA154.2 .L49 1983.
  • Munem/Foulis: Algebra and Trigonometry with Applications, Chapters 1 – 5, 9.1 – 9.2. QA 154.2 .M858 1982
  • Murphy/Oberhoff/Pierce/Rodriguez: Algebra and Trigonometry, 1983, Chapters 1 – 6. QA154.2 .A328 1983.
  • Novak: Intermediate Algebra, Second Edition, Chapters 1 – 8, 10, 11. QA152 .N7 1987.

Functions and Graphs 2

  • Connally/Hughes-Hallett/Gleason: Functions Modeling Change, First Edition, Chapters 1 – 9. QA331.3 .F86 2000.
  • Connally/Hughes-Hallett/Gleason: Functions Modeling Change, Preliminary Edition, 1998, Chapters 1 – 7. QA39.2 .C6 1998.
  • Hughes-Hallett: The Math Workshop: Elementary Functions, Chapters 1 – 19. QA 331 .H795 1980
  • Ambrose: College Algebra and Trigonometry, Chapters 1 – 3, 5 – 11, 13 – 15. QA 154.2 .A43 1977
  • Derrick: College Algebra and Trigonometry, Chapters 1 – 8.2. QA154.2 .D47 1982
  • Foerster: Algebra and Trigonometry: Functions and Applications, Revised Edition, Chapters 1 – 3, 4.1 – 4.6, 5 – 7. QA152.2 .F63 1984
  • Lial/Miller: Algebra and Trigonometry, Second Edition, Chapters 1 – 8.3, 9.1 – 9.2. QA154.2 .L49 1980
  • Lial/Miller: Algebra and Trigonometry, Third Edition, Chapters 1 – 8.3, 9.1 – 9.2. QA154.2 .L49 1983
  • Murphy/Oberhoff/Pierce/Rodriguez: Algebra and Trigonometry, 1983, Chapters 1 – 9.2. 
QA154.2 .A328 1983
  • Munem/Foulis: Algebra and Trigonometry with Applications, Chapters 1 – 7, 8.1 – 8.3, 9.1 – 9.2. QA 154.2 .M858 1982

Calculus 1

  • Hughes-Hallett/Gleason: Calculus, Chapters 1 – 4. Preliminary edition: QA 303 .C155 1992; First edition QA303 .C155 1994; Second edition: QA 303 .C155 1998.
  • Ayres: Schaum’s Outline of Theory and Problems of Differential and Integral Calculus, Chapters 1 – 7, 12 – 14, 21, 23, 24. QA303 .A9 1978
  • Ayres/Mendelson: Schaum’s Outline of Theory and Problems of Differential and Integral Calculus, Chapters 5 – 13, 17, 18, 21 – 24. QA303 .A96 1999
  • Clarke: Calculus and Analytic Geometry, 1974, Chapters 1 – 4, 7. QA303 .C6
  • Leithold: Essentials of Calculus for Business, Economics, Life Sciences, Social Sciences, Chapters 1 – 3, 7.1 – 7.5. QA303 .L4295 1984
  • Riddle: Calculus and Analytic Geometry. 1970, Chapters 5 – 6.3, 7.3 – 8.6, 11.1 – 11.2, 12.1 – 12.3. QA 303 .R53.
  • Taylor: Calculus, with Analytic Geometry, 1959, Chapters 1 – 3.6, 4.1 – 4.4, 5, 6. QA303 .T203
  • Thomas: Calculus and Analytic Geometry, Third edition. Chapters 1 – 3.4, 3.8, 4.1 –4.9. QA303 .T42 1960
  • Thomas/Finney: Calculus and Analytic Geometry, Fifth edition. Chapters 1 – 3.4, 3.8, 4. QA303 .T42 1979.

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