Listed below are topics in mathematics that are used in calculus. Some are essential for the development of the subject. They're marked with the symbol . Others are used incidently in applications of calculus. Most of them we assume that you know and we won't review them at all, but we'll remind you a bit about a few of them as we use them. Most of the topics are used in the first semester of calculus, but a few aren't used until later.

• Topics from arithmetic. We assume you know these:
  • Kinds of numbers. Fractions and decimals. We'll refer to integers (whole numbers, either positive, negative, or zero), rational and irrational numbers. The number line
  • Conventions for arithmetic notation including order of operations (precedence), proper use of parentheses
  • Expression manipulation. Distibutive laws, law of signs
  • Exponents and laws for exponents
  • Roots, laws for roots, rational exponents, rationalizing denominators
  • Absolute value, order (less than, etc.), and their properties
  • Factorials (e.g., 5! is the product of the integers from 1 through 5)
• Topics from geometry
  • Pythagorean theorem
  • Similar triangles
  • Areas of triangles, circles, and other simple plane figures
  • Perimeters of simple plane figures, circumference of circles
  • Volumes of spheres, cones, cylinders, pyramids
  • Surface areas of spheres and other simple solid figures
• Topics from algebra. We use algebra constantly. You've got to know algebra well. Topics:
  • Translating word problems into algebra
  • Expression manipulation. Addition, subtraction, and multiplication of polynomials
  • Rational functions and their domains, least common denominators
  • Techniques for simplifying algebraic expressions
  • Factoring quadratic polynomials and other simple polynomials
  • Techniques for solving linear equations in one unknown
  • Solving quadratic equations in one unknown, completing the square, quadratic formula
  • Solving linear equations in two or more unknowns
  • Techniques for solving inequalities and both equations and inequalities involving absolute value
  • The concept of function, functional notation and substitution, domain and range of a function
  • Composition of functions
• Uniform motion in a straight line. When objects move with constant velocity, the relation among distance, time, and velocity
• Notation and concepts from set theory. We only use a bit of the notation from set theory and only the most basic concepts
  • Sets, membership in sets, subsets, unions, intersections, empty set
  • Open and closed intervals and their notations
• Topics from analytic geometry. Mainly the basics, straight lines, circles, a little on quadratic functions
  • Coordinates of points in the plane
  • Linear equations. Slope-intercept form especially, but also other forms
  • Distance between two points
  • Equations of circles, especially the unit circle
  • Slopes of straight lines, parallel lines
  • Graphs of functions. Vertical line test
  • Symmetries of functions, even and odd functions. Transformation of functions
  • Graph of a quadratic function is a parabola
  • Graph of y = 1/x is a rectangular hyperbola
• Topics from trigonometry. For a review of trigonometry, see "Dave's Short Course in Trig" at http://www.clarku.edu/~djoyce/trig/
  • Angle measurement, both degrees and radians, but radians are more important in calculus. Negative angles.
  • Length of an arc of a circle
  • Understanding of trig functions of angles, especially sine, cosine, tangent, and secant. Trig functions and the unit circle
  • Right triangles, trig functions sine, cosine, and tangent of acute angles. Values of these trig functions for standard angles of 0, π/6, π/4, π/3, π/2
  • Solving right triangles
  • Obtuse triangles. Law of sines, law of cosines. Solving obtuse triangles
  • Basic trig identities. Pythagorean identities, trig functions in terms of sines and cosines
  • Other trig identities. Double angle formulas for sine and cosine, addition formulas for sine and cosine
• Exponential functions and logarithms. Although these are topics in algebra, they deserve to be separated for emphasis
  • Exponential functions. Growth of exponential functions
  • Laws for exponents. Manipulation of algebraic expressions involing exponents, solving equations involving exponents
  • Logarithms and their relation to exponential functions
  • Laws for logs. Manipulation of algebraic expressions involing logs, solving equations involving logs
• An understanding of mathematical proof. We'll develop more in calculus. You should be able to follow proofs like the ones you've already seen in geometry, algebra, and your other mathematics courses