Jump Start to Precalculus

Precalculus doesn't have to feel like a wall you run into — Jump Start to Precalculus turns it into a launching pad. This intensive course is designed for high school students who want to sharpen their algebra skills, tackle brand-new concepts, and walk into precalculus (or calculus) feeling genuinely prepared. Over multiple sessions, students work through everything from graphing linear equations and solving absolute value problems to mastering function transformations, complex numbers, factoring, and trigonometry. Whether you're reviewing material that's gone rusty or encountering these ideas for the first time, this course meets you where you are and pushes you forward. By the end, you won't just recognize these concepts — you'll be able to use them fluently and confidently.

What This Course Is — and Who It's For

Jump Start to Precalculus is a focused, fast-paced intensive built for students heading into precalculus or calculus who want to show up ready. Whether you're shaking off summer rust, filling in gaps from Algebra 2, or getting a head start on new material, this course gives you the tools to engage with higher-level math from day one. The pacing is active and the instruction is direct — expect to work problems, ask questions, and leave each session with skills you can actually use.

Algebra Foundations That Actually Matter

The course opens with the algebraic building blocks that show up constantly in precalculus and calculus. Students learn to graph linear equations efficiently using x- and y-intercepts, write equations of lines in multiple forms, and tackle absolute value equations — including the cases that trip most students up, like equations with no solution or variables on both sides. These aren't just review topics; they're the scaffolding for everything that comes next.

Functions: The Core of Precalculus

A huge portion of the course centers on functions — understanding them, manipulating them, and seeing how they behave. Students evaluate functions using proper notation, determine domain and range, and analyze behavior like increasing/decreasing intervals and intercepts. From there, the course goes deeper: students work with composite and nested functions (solving from the inside out), explore inverse functions (how to find them algebraically, verify them with composition, and know when they exist), and apply transformations — horizontal and vertical shifts, stretches, and compressions — across linear, quadratic, absolute value, and other function families. A key insight students develop: transformations inside the function move the graph in the opposite direction you'd expect, and understanding why makes the whole concept click.

Complex Numbers and Factoring

Students dive into imaginary and complex numbers — starting with the definition of i as the square root of −1 and the cyclical pattern of its powers (1, i, −1, −i, repeat), then moving into operations like addition, subtraction, multiplication, and division with complex numbers. They learn to use complex conjugates to simplify expressions and connect complex solutions to the geometry of parabolas that don't cross the x-axis. On the factoring side, students work through difference of squares, perfect square trinomials, and grouping — and apply those techniques to higher-degree polynomials, setting them up for the algebraic manipulation precalculus and calculus demand.

Trigonometry: Right Triangles and the Six Functions

Depending on the cohort, students also get a solid introduction to trigonometry. Using SOH CAH TOA as a foundation, they apply all six trig functions — sine, cosine, tangent, cosecant, secant, and cotangent — to solve right triangle problems. Students practice sketching triangles from given trig ratios, using the Pythagorean theorem to find missing sides, and working with inverse trig functions. This section bridges the algebraic work of the course into one of the most important new topics students encounter in precalculus.

What You'll Walk Away With

By the end of Jump Start to Precalculus, students have a working command of the skills that separate students who struggle in precalculus from those who thrive: clean algebraic technique, fluency with functions, comfort with complex numbers, and a solid first look at trigonometry. More than any single topic, students leave with the confidence that comes from actually solving hard problems — which is exactly the mindset precalculus rewards.