$60
per sessionHigh School Pre Calculus/Trigonometry Tutor
Completed by 9 learners
Ages 13-17
Live 1-on-1 Lessons
Live video meetings
Meets on demand
55 min
What's included
Meets on Demand
schedule meetings as needed55 mins
per sessionTeacher support
Class Experience
US Grade 5 - 8
Precalculus serves as a bridge between Algebra, Geometry, and Calculus. It covers a broad range of topics that help students develop the skills needed for success in Calculus. Here are the standard topics typically covered in a Precalculus course: 1. Functions and Their Properties Types of Functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, inverse, and piecewise functions Domain and Range: Determining the domain and range of functions Operations on Functions: Addition, subtraction, multiplication, division, and composition of functions Inverse Functions: Definition and finding inverse functions Graphing Functions: Understanding transformations (translations, reflections, stretching, shrinking) 2. Polynomial and Rational Functions Polynomial Functions: Long division, synthetic division, zeros of polynomials (factoring, Rational Root Theorem) Graphing Polynomial Functions: End behavior, turning points, and identifying key characteristics of graphs Rational Functions: Asymptotes (vertical, horizontal, oblique), holes, and graphing rational functions Solving Polynomial and Rational Equations: Techniques for solving algebraically 3. Exponential and Logarithmic Functions Properties of Exponents: Growth and decay models Exponential Functions: Graphing and solving exponential equations Logarithmic Functions: Definition of logarithms, properties (product, quotient, power rules), and solving logarithmic equations Exponential and Logarithmic Applications: Compound interest, population growth, and decay models 4. Trigonometry Angles and Radian Measure: Degrees vs. radians, converting between them Trigonometric Functions: Definitions using the unit circle, sine, cosine, tangent, and their reciprocals (cosecant, secant, cotangent) Graphing Trigonometric Functions: Amplitude, period, phase shift, and vertical shift Inverse Trigonometric Functions: Understanding and solving inverse trig functions Trigonometric Identities: Pythagorean, sum and difference identities, double-angle, half-angle identities Solving Trigonometric Equations: Using identities and inverse functions Law of Sines and Cosines: Applications to solving triangles 5. Complex Numbers Definition and Operations: Addition, subtraction, multiplication, division of complex numbers Polar Form of Complex Numbers: Conversion between rectangular and polar forms, De Moivre's Theorem 6. Vectors Vector Operations: Addition, subtraction, dot product Magnitude and Direction: Representing vectors graphically, finding the magnitude and direction Applications of Vectors: Solving physics-related problems involving force, velocity, etc. 7. Sequences and Series Arithmetic Sequences and Series: Finding terms, sum formulas Geometric Sequences and Series: Finding terms, sum formulas, including infinite geometric series Mathematical Induction: Proving statements involving sequences or inequalities 8. Conic Sections Parabolas: Equations, vertex, focus, and directrix Ellipses: Equations, foci, major and minor axes Hyperbolas: Equations, foci, asymptotes Applications of Conic Sections: Real-world problems involving parabolas, ellipses, and hyperbolas 9. Polar Coordinates and Parametric Equations Polar Coordinates: Plotting points in the polar plane, converting between polar and rectangular coordinates Polar Equations: Graphing polar equations, finding symmetries, and analyzing polar curves Parametric Equations: Graphing and eliminating the parameter, applications to motion and curves 10. Limits (Introduction to Calculus) Concept of a Limit: Understanding limits intuitively, graphically, and algebraically Limits at Infinity: End behavior of functions and asymptotes Continuity: Defining continuity at a point, types of discontinuities Limit Laws: Basic properties and techniques for calculating limits 11. Additional Topics (Optional) Binomial Theorem: Expanding binomials, Pascal's Triangle Probability and Combinatorics: Permutations, combinations, and basic probability
Learning Goals
These topics form the foundation for Calculus and higher-level mathematics, helping students develop an understanding of functions, equations, and their applications in various mathematical contexts.
Other Details
External Resources
Learners will not need to use any apps or websites beyond the standard Outschool tools.
Meet the teacher
Teacher expertise and credentials
Hello! I am so excited to meet you! I currently tutor Chemistry, Algebra 1, Algebra 2 and Pre-Calculus. I have been teaching and tutoring these classes for the last 10 years. I graduated from Indiana University with my BS in Biochemistry and Minor in Mathematics. I also went to Purdue University for my MS in Biochemsitry. I love math and science! I enjoy helping students with these challenging classes to do their very best! I homeschool my own five children. I love to camp and hike with my family and play with my sweet bernedoodle, Daisy!
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