High School Math Milestones

Our high school math tutoring program can provide support in key areas of algebraic, geometric, calculus, trigonometry and more.

Algebraic Concepts Students will be able to:

  • understand symbolic reasoning and calculations with symbols
  • understand function
  • understand linear and quadratic equations
  • understand Algebra of Polynomials, including division
  • understand probability

Geometric Concepts Students will be able to:

  • understand the construction of formal, logical arguments and proofs in geometry
  • understand lines and angles
  • understand the principle of volume and surface area
  • understand the Pythagorean theorem
  • understand triangles and quadrilaterals
  • understand circles and three-dimensional figures
  • understand inductive and deductive reasoning
  • understand basic trigonometric functions defined by angles of a right triangle

Trigonometry Students will be able to:

  • understand trigonometric functions
  • graph trigonometric functions
  • understand the notion of angles and how to measure it, in both degrees and radians
  • understand right triangle trigonometry and basic identities
  • understand oblique triangles
  • understand trigonometric identities (e.g., cos2 (x) + sin2 (x) = 1).
  • understand inverse trigonometric functions
  • exponential and logarithmic functions

Pre-Calculus Students will be able to:

  • understand theorems evaluating limits, products, quotients, and composition of functions
  • understand sets, sequences, series, number systems, exponents and factoring
  • understand linear and non-linear equations and inequalities
  • understand Rolle’s theorem, the mean value, and L’Hôpital’s rule
  • understand the Cartesian coordinate system
  • understand quadratic, linear, polynomial and rational functions
  • understand logarithms and exponential functions

Calculus Students will be able to:

  • demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions
  • prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions
  • demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
  • demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability
  • apply Rolle’s theorem, the mean value theorem, and L’Hôpital’s rule
  • demonstrate Newton’s method for approximating the zeros of a function

Probability and Statistics Students will be able to:

  • understand the study of probability, interpretation of data, and fundamental statistical problem solving
  • understand and know the definitions of independent events and can use the rules for addition, multiplication, and completion to solve for probabilities
  • understand the notion of discrete random variables by using them to solve for probabilities of outcomes, such as the probability of the occurrences of five heads in 14 coin tosses
  • understand the definition of mean, median, and mode
  • demonstrate an understanding of the standard distributions, e.g. normal, binomial, and exponential; and can use the distributions to solve for events in problems in which the distribution belongs to those families

This information has been adapted from the California State Board of Education’s web site and was adopted by the California State Board of Education, December 1997.