By the time students graduate high school, they are expected to have a firm understanding of certain core mathematics concepts from their completed course of study in classes like Algebra II, Calculus, and Statistics.

From understanding the basic properties of functions and being able to graph ellipses and hyperbolas in given equations to comprehending the concepts of limits, continuity, and differentiation in Calculus assignments, students are expected to fully grasp these core concepts in order to continue their studies in college courses.

The following provides you with the basic concepts that should be attained by **the end** of the school year where mastery of the concepts of the previous grade is already assumed.

### Algebra II Concepts

In terms of studying Algebra, Algebra II is the highest level high school students will be expected to complete and should grasp all core concepts of this field of study by the time they graduate. Although this class is not always available depending on the jurisdiction of the school district, the topics are also included in precalculus and other math classes students would have to take if Algebra II were not offered.

Students should understand the properties of functions, the algebra of functions, matrices, and systems of equations as well as be able to identify functions as either linear, quadratic, exponential, logarithmic, polynomial or rational functions. They should also be able to identify and work with radical expressions and exponents as well as the binomial theorem.

In-depth graphing should also be understood including the ability to graph ellipses and hyperbolas of given equations as well as systems of linear equations and inequalities, quadratics functions and equations.

This can often include probability and statistics by using standard deviation measures to compare the scatter of sets of real-world data as well as permutations and combinations.

### Calculus and Pre-Calculus Concepts

For advanced math students who take a more challenging course load throughout their high school educations, understanding Calculus is essential to finishing off their mathematics curriculums. For other students on a slower learning track, Precalculus is also available.

In Calculus, students should be able to successfully review polynomial, algebraic, and transcendental functions as well as be able to define functions, graphs, and limits. Continuity, differentiation, integration, and applications using problem-solving as the context will also be a required skill for those expecting to graduate with a Calculus credit.

Understanding the derivatives of functions and real-life applications of derivatives will help students to investigate the relationship between the derivative of a function and the key features of its graph as well as understand the rates of change and their applications.

Precalculus students, on the other hand, will be required to understand more basic concepts of the field of study including being able to identify the properties of functions, logarithms, sequences and series, vectors polar coordinates, and complex numbers, and conic sections.

### Finite Math and Statistics Concepts

Some curricula also include an introduction to Finite Math, which combines many of the outcomes listed in other courses with topics which include finance, sets, permutations of n objects known as combinatorics, probability, statistics, matrix algebra, and linear equations. Although this course is typically offered in 11th grade, remedial students may only need to understand the concepts of Finite Math if they take the class their senior year.

Similarly, Statistics is offered in the 11th and 12th grades but contains a bit more specific data that students should familiarize themselves with before graduating high school, which include statistical analysis and summarizing and interpreting the data in meaningful ways.

Other core concepts of Statistics include probability, linear and non-linear regression, hypothesis testing using binomial, normal, Student-t, and Chi-square distributions, and the use of the fundamental counting principle, permutations, and combinations.

Additionally, students should be able to interpret and apply normal and binomial probability distributions as well as transformations to statistical data. Understanding and using the Central Limit Theorem and normal distribution patterns are also essential to fully comprehend the field of Statistics.