NYC PRECALCULUS TUTOR

1:1 NYC Precalculus Tutoring, All Ages, All Learners

Why is Precalculus Difficult? 

Precalculus, which combines trigonometry and mathematical analysis, bridges the conceptual gap between trigonometry and calculus. Students are suddenly expected to memorize a large amount of information and remember diverse ideas from their prior math courses.

Why is precalculus required for students, and how does it apply to real life?

Though it is regarded as one of the difficult subjects, like trigonometry and geometry, calculus is an important branch of mathematics, so learning the basics at hand will make all other concepts easier.

Since most things in the natural world are continually changing, calculus is a branch of mathematics that analyzes rate of change. Calculus is necessary to understand fields like engineering, statistics, physics, economics, computer science, and even medicine.

Therefore, as a student, learning this subject by heart will ultimately advance your future career.

Here Are the Precalculus Key Concepts:

Fundamental Skills

Sets, functions, and their inverses, rational functions, linear, quadratic, cubic, and quartic equations, trigonometry, exponential and logarithmic functions, changing number bases, complex numbers, graphing, and word problems are some of the subjects that will be studied.

Functions and their Graphs

The graph of a function f in mathematics is the set of ordered pairs where f(x)=y. In the typical example, when x and f(x) are real numbers, these pairs represent the Cartesian coordinates of points in two-dimensional space and constitute a subset of this plane.

Polynomial and Rational Functions

Any function expressed as the ratio of the two polynomials P(x) and Q (x)is said to be rational. We will look at a graph to better understand these functions.

Exponential and Logarithmic Functions

Examples of exponential functions include 2x, 10x, and ex; they have the form ax, where a is a constant. 

Trigonometric Functions

Trigonometry deals with particular angles’ functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant.

Trigonometric Identities and Equations

The reciprocal trigonometric identities are: Sin θ = 1/Csc θ or Csc θ = 1/Sin θ Cos θ = 1/Sec θ or Sec θ = 1/Cos θ Tan θ = 1/Cot θ or Cot θ = 1/Tan θ.

Polar and Parametric Equations

Circles and spirals are simple to express mathematically using polar equations. Two functions that are each dependent on the same third variable make up a set of parametric equations.

Vectors

An object with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector—the vector points in a direction from its tail to its head.

Conic Sections

Any curve created by the intersection of a plane and a right circular cone is known in geometry as a conic section, sometimes a conic. The intersection can be an ellipse, a circle, a hyperbola, or a parabola, depending on the plane’s angle with the cone.

Systems of Equations and Matrices

An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system.

Sequences and Series

A grouping of numbers in a specific order is known as a sequence. However, a series is defined as the collection of elements of a sequence.

Introduction to Calculus

Calculus is the branch of mathematics that explains how functions change. Integral calculus and differential calculus are the fundamental applications of calculus.

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