Precalculus
Encyclopedia
In American mathematics education
, precalculus (or Algebra 3 in some areas), an advanced form of secondary school algebra
, is a foundational mathematical
discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra
and Trigonometry
. Precalculus prepares students for calculus
the same way as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus
. Some precalculus courses might differ with others in terms of content. For example, an honors level course might spend more time on topics such as conic sections, vectors, and other topics needed for calculus. A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices, which are used in business.
In detail, precalculus deals with:
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
, precalculus (or Algebra 3 in some areas), an advanced form of secondary school algebra
Elementary algebra
Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. It is typically taught in secondary school under the term algebra. The major difference between algebra and...
, is a foundational mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and Trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
. Precalculus prepares students for calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
the same way as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
. Some precalculus courses might differ with others in terms of content. For example, an honors level course might spend more time on topics such as conic sections, vectors, and other topics needed for calculus. A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices, which are used in business.
In detail, precalculus deals with:
- Sets
- Real numberReal numberIn mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s - Complex numberComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s - Solving inequalities and equationEquationAn equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s - Properties of functionFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
s - Composite functions
- Polynomial functions
- Rational functionRational functionIn mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational.-Definitions:...
s - TrigonometryTrigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
- Trigonometric functionTrigonometric functionIn mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...
s and their inverses - Trigonometric identities
- Conic sectionConic sectionIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...
s - Exponential functionExponential functionIn mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
s - Logarithmic functions
- SequenceSequenceIn mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...
s and seriesSeries (mathematics)A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.... - Binomial theoremBinomial theoremIn elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...
- Vectors
- Parametric equationParametric equationIn mathematics, parametric equation is a method of defining a relation using parameters. A simple kinematic example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion....
s - Polar coordinates
- MatricesMatrix (mathematics)In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
- Mathematical inductionMathematical inductionMathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers...
- LimitsLimit (mathematics)In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...