# Topics to Review for Math Placement Assessment and Waiver Exams

### Basic Mathematics MATH 051

Integers, prime numbers, factoring, least common multiple, greatest common divisor; operations with fractions and decimals; rules for exponents, roots, order of operations, simplifying expressions; ratios and solving proportions; converting between fraction, percent, and decimal; inequalities, absolute value; systems of units of measurement, unit conversion; significant figures and rounding; perimeter, circumference, area, length, volume, surface area of square, rectangle, circle, triangle, trapezoid, cube, sphere, cylinder; geometry of parallel lines and perpendicular lines; Pythagorean theorem.

To review these topics in preparation for taking the ALEKS PPL assessment with the aim of satisfying the prerequisite for Elementary Algebra MATH 152, send email to Connie Eyberg at mathadmin@miu.edu and request sign-up information for ALEKS PPL. Then take the preliminary test ALEKS gives you and choose the study module Prep for Beginning Algebra.

### Elementary Algebra MATH 152

**All topics of Basic Mathematics plus: **Accuracy and precision of measurements; mean, median, mode, dot plot, box-and-whisker plots, histogram; variables, simplifying algebraic expressions, distributive rule; functions, domain and range, table of values and graph; evaluating algebraic expressions and functions; graphing lines in the coordinate plane, slope, parallel and perpendicular lines, slope-intercept equation and point-slope equation of a line; solving equations and inequalities with one variable, literal equations; theory-driven linear modeling, creating an algebraic expression from a physical situation; data-driven linear modeling, scatter plots and fitting a line to data, evaluating the model; polynomials and their operations, factoring quadratics and other polynomials, solving equations involving polynomials by factoring.

To review these topics in preparation for the ALEKS PPL assessment with the aim of satisfying the prerequisite for Intermediate Algebra MATH 153 or for Statistics MGT 314, send email to Connie Eyberg at mathadmin@miu.edu and request sign-up information for ALEKS PPL. Then take the preliminary test ALEKS gives you and choose the study module Prep for Intermediate Algebra.

### Intermediate Algebra MATH 153

**All topics of Basic Mathematics and Elementary Algebra plus: **Graphing quadratic functions, solving quadratic equations exactly using factoring or quadratic formula, and approximately by graphing; simplifying variable expressions with roots and radicals and fractional exponents, rationalizing the denominator, solving equations with roots and radicals and fractional exponents; distance between two points in the plane, equation of a circle; graphing inequalities in the plane; operations with rational expressions, solving rational equations; solving systems of equations.

To review these topics in preparation for the ALEKS PPL assessment with the aim of satisfying the prerequisite for Functions and Graphs 1 MATH 161 or for other courses with prerequisite MATH 153, send email to Connie Eyberg at mathadmin@miu.edu and request sign-up information for ALEKS PPL. Then take the preliminary test ALEKS gives you and choose the study module Prep for College Algebra or Prep for Pre-Calculus.

### Functions and Graphs 1 MATH 161

**All topics of Basic Mathematics, Elementary Algebra, Intermediate Algebra plus: **Functions, rate of change of a function, domain and range of a function from graph and formula; concavity; absolute value functions, piecewise-defined functions; inverse functions; rules for exponents and logarithms, other bases, the number e and interest problems; solving equations involving logarithms and/or exponentials; applications of exponential and logarithmic functions; families of linear, quadratic, power, polynomial, rational, exponential, and logarithmic functions; average rate of change and comparison of rates of growth of these functions; transformations of functions and their graphs, shifts, reflections, symmetry, stretches, compressions.

To review these topics in preparation for the ALEKS PPL assessment with the aim of satisfying the prerequisite for Functions and Graphs 2 MATH 162 or for other courses with prerequisite MATH 161, send email to Connie Eyberg at mathadmin@miu.edu and request sign-up information for ALEKS PPL. Then take the preliminary test ALEKS gives you and choose the study module Prep for Calculus.

### Functions and Graphs 2 MATH 162

**All topics of Basic Mathematics, Elementary Algebra, Intermediate Algebra, and Functions and Graphs 1 plus: **Measuring angles in degrees and radians, reference angles, special angles; creating sine and cosine functions from circular motion; trigonometric functions and their graphs; trigonometric identities; inverse trigonometric functions and their graphs; solving equations involving trigonometric expressions; solving right triangles; solving general triangles using sine and cosine laws; applications of trigonometry; sums, products, inverses, and composition of functions; power functions; short run and long run behavior of polynomials and rational functions, applications of polynomials and rational functions; comparing power, exponential, and logarithmic functions; vectors in the plane and their components, dot product, applications of vectors.

To review these topics in preparation for the ALEKS PPL assessment with the aim of satisfying the prerequisite for Calculus 1 MATH 281 or Discrete Mathematics MATH 272 or for other courses with prerequisite MATH 162, send email to Connie Eyberg at mathadmin@miu.edu and request sign-up information for ALEKS PPL. Then take the preliminary test ALEKS gives you and choose the study module Prep for Calculus.

### Calculus 1 MATH 281

Limits, continuity. Definition of the derivative; sum, product, and division rules for differentiation; graph of a derivative function; equation of a tangent line and local linearization. Chain rule, derivatives of trigonometric and inverse trigonometric functions, implicit differentiation, maxima and minima, optimization, L’Hospital’s rule. Note that you need to understand how these work using formulas, graphs, tables, and words. Being able to apply memorized formulas and procedures is not sufficient.

Currently the waiver exam is based on the textbook used for our Calculus 1 and Calculus 2 courses. This is Hughes-Hallett et al: *Calculus Single Variable* 5th edition ISBN 978-0470-08915-6. Calculus 1 is roughly Chapters 1 – 4 but you can skip sections 3.8 and 4.5 and 4.8.

### Calculus 2 MATH 282

Definition of the integral in terms of upper and lower sums, fundamental theorem of calculus, average value of a function, mean value theorem, antiderivatives, second fundamental theorem of calculus, integration by substitution, integration by parts, approximating integrals, improper integrals, applications of integration to geometry and physics. Note that you need to understand how these work using formulas, graphs, tables, and words. Being able to apply memorized formulas and procedures is not sufficient.

Currently the assessment is based on the textbook used for our Calculus 1 and Calculus 2 courses. This is Hughes-Hallett et al: *Calculus Single Variable* 5th edition ISBN 978-0470-08915-6.Calculus 2 is roughly Chapters 5 – 8 but you can skip sections 8.3, 8.6, 8.7, 8.8.

Students wanting to take the waiver exam for MATH 282 Calculus 2 must first either waive or pass MATH 281 Calculus 1.

### Linear Algebra MATH 286

Linear systems of equations and how they are expressed by vector equations and matrix equations, properties of matrices, solution of linear systems, vector spaces and subspaces, linear independence, spanning sets, basis, linear transformations, kernel and range spaces, eigenvalues and eigenvectors, diagonalization of matrices.

Currently the waiver exam for linear algebra is based on the textbook used for MATH286 Linear Algebra. This is David Lay: *Linear Algebra and Its Applications*, **FOURTH** EDITION, Pearson/Addison-Wesley, 2012, ISBN-13: 978-0-321-38517-8 and ISBN-10: 0-321-38517-9. The sections covered are 1.1–1.10, 2.1–2.3, 2.6–2.9, 3.1–3.2, 5.1–5.3, 4.1–4.4.

Students wanting to take the waiver exam for MATH 286 Linear Algebra must first either waive or pass MATH 282 Calculus 2.

### Discrete Mathematics MATH 272

Logic and sets, relations and functions, vertex-edge graphs, recursion, combinatorics, boolean algebra.

Currently the waiver exam for discrete mathematics is based on the textbook used for MATH272 Discrete Math. This is Rosen: *Discrete Math and Its Applications* 7th edition, McGraw-Hill 2012, ISBN 978-0-07-338309-5. Sections covered are 1.1–1.5, 2.1–2.2, 5.1–5.3, 6.1–6.4, 10.1–10.6, 11.1–11.5, plus handouts on recursion.

Students wanting to take the waiver exam for MATH 272 Discrete Mathematics must first either waive or pass MATH 162 Functions and Graphs 2. One way to waive MATH 162 is to achieve a score of 76 or above on the ALEKS PPL assessment.

**Online resources you may find useful for various levels of mathematics are**

- Purple Math
- Khan Academy provides worked examples and lectures on all the topics.
- YouTube has a wide selection of videos on math topics.