# 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.*