 # Practice and Review for the Math Placement Assessment

### 1. To review and practice to place out of the 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,

your most important tool is the ALEKS Placement, Preparation and Learning program, which is part of the math placement program used by MIU.

A 12-month ALEKS PPL module is included with your math placement assessment package, and is covered by your tuition fees (free for prospective students who have applied to MIU). You are strongly advised to use this means of reviewing and practicing for your proctored math placement.

The initial assessment is not proctored and can be taken anywhere from a computer with Internet access. You are then given a personalized program of study based on your initial math placement assessment results. After studying in this program for some time, you are free to come for up to 4 proctored re-assessments within a year. Please see the Guide to ALEKS PPL Math Placement for complete details.

To gain access to the ALEKS PPL program, send an email to Connie Eyberg at mathadmin@miu.edu. State your reason for taking the assessment and your expected major or program at MIU (if you know).

### 2. To review and practice for the courses:

• Math 281 Calculus 1
• Math 282 Calculus 2

you will need to use other resources. We suggest you try one of the following books available on loan from the MIU Library or for a very low cost from Amazon.

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 assessment is to work problems, work problems, work problems.

Topics For Calculus 1:

• Limits
• Definition of the derivative
• Sum, product, and division rules for differentiation
• Chain rule
• Graph of a derivative function
• Equation of a tangent line
• Local linearization
• Definition of the integral, upper and lower sums
• Fundamental Theorem of Calculus
• Average value of a function
• Mean value theorem

References for Calculus 1 available in the MIU Library:

• Hughes-Hallett/Gleason: Calculus: Single Variable, Chapters 1 – 4. Preliminary edition: QA 303 .C155 1992; First edition QA303 .C155 1994; Second edition: QA 303 .C155 1998. (Note that the fifth edition of this book is the current textbook for the course. In the fifth edition Calculus 1 covers chapters 1 – 3 and 5.)
• 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.

Topics for Calculus 2:

• Topics of Calculus 1 and:
• Derivatives of trigonometric and inverse trigonometric functions
• Maxima and minima and modeling
• Hyperbolic functions
• Theorems about continuous and differentiable functions
• Implicit differentiation
• Constructing antiderivatives
• Second fundamental theorem of calculus
• Equations of motion
• Integration by substitution and by parts
• Integration by using tables
• Integration by trigonometric substitution
• Approximation methods
• Improper integrals
• L’Hospital’s rule
• Applications to geometry and physics

References for Calculus 2 available in the MIU Library:

• Hughes-Hallett/Gleason: Calculus Single Variable, Chapters 5 – 8 of the second edition. In the fifth edition (our current textbook) Calculus 2 covers chapters 4 and 6 – 8.

And all the books in the list above for Calculus 1 will have sections covering the topics for Calculus 2. You will find the topics in the table of contents and/or index of those books.

3. If you wish to use a book for studying for the ALEKS PPL assessment, we recommend the following:

For Basic Math, Elementary Algebra, or Intermediate Algebra:

• McKeague: Elementary Algebra, Fifth Edition, 1995, Chapters 1 – 5. QA152.2 .M32 1995. Other editions are also extremely useful. The first one or two chapters give a brief but very useful review of Basic Math.
• McKeague: Intermediate Algebra, Fifth Edition, 1995, Chapters 1 – 8. QA154.2 .M43 1995 Other editions are also extremely useful.

For Functions and Graphs 1:

• Connally/Hughes-Hallett/Gleason: Functions Modeling Change, First Edition, Chapters 1 – 5. QA331.3 .F86 2000 or Preliminary Edition, Chapters 1 – 4, 7. QA39.2 .C6 1998.

For Functions and Graphs 2:

• Connally/Hughes-Hallett/Gleason: Functions Modeling Change, First Edition, Chapters 1 – 9. QA331.3 .F86 2000 or Preliminary Edition, Chapters 1 – 7. QA39.2 .C6 1998

4. Online resources you may find useful for various levels are