# Topics to Review

## TOPICS TO REVIEW

### 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.

**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.

**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.

**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.

**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.

**Calculus 1 MATH 281**

Limits, continuity. Definition of the derivative; sum, product, and division rules for differentiation; chain rule; graph of a derivative function; equation of a tangent line and local linearization. Definition of the integral in terms of upper and lower sums, fundamental theorem of calculus, average value of a function, mean value theorem.

### Calculus 2 MATH 282

Chain rule, derivatives of trigonometric and inverse trigonometric functions, implicit differentiation, maxima and minima, hyperbolic functions, antiderivatives, second fundamental theorem of calculus, integration by substitution, integration by parts, approximating integrals, improper integrals, L’Hospital’s rule, applications of integration to geometry and physics.