Online Pre-Calculus Help | K-12 Math Curriculum

Pre-Calculus Is Where Every Gap From the Past Few Years Shows Up at Once

Students who coasted through algebra or scraped through geometry tend to feel it most in pre-calculus. That's not a coincidence. Pre-calculus draws on practically everything a student has covered since Grade 6: functions from algebra, geometric reasoning, trigonometry, exponentials, logarithms and coordinate geometry. It pulls all of it together, often quickly, and expects students to move between topics fluidly.

For a student whose foundations are solid, pre-calculus is demanding but manageable. For a student with unresolved gaps from earlier years, it can feel like the wheels come off completely.

The good news is that pre-calculus gaps almost always trace back to something specific and fixable. The Math Doctor assessment is particularly useful at this level because it finds exactly where the understanding breaks down, whether that's in algebraic manipulation, trigonometric ratios or the concept of a function.

Pre-Calculus Is Part of Our Full K-12 Math Curriculum

Pre-calculus is covered within our full K-12 math curriculum, as part of the personalized plan we build around each student.

When your child joins, the Math Doctor assessment maps their math understanding across the full curriculum. If the gaps are in pre-calculus topics, the weekly plan targets those. If the difficulty actually traces back to algebra or geometry concepts from earlier years, the plan addresses those first. Progress is faster when it starts in the right place.

What We Cover in Pre-Calculus

Our pre-calculus curriculum is fully aligned to Common Core Standards and covers every major topic in a high school pre-calculus course, from linear functions and coordinate geometry through to the foundational calculus concepts that come next.

Linear Functions and Coordinate Geometry

The algebraic foundations that run through everything else in pre-calculus.

Transposing a linear equation
Gradient of a line
Equation of a straight line in gradient form
Equation of a straight line using two points
Solutions of simultaneous equations
Distance formula and midpoint of a line
Gradient of a perpendicular line
Angle between two lines

Matrices

An area many students encounter for the first time in pre-calculus.

Matrix basics
Scalar multiplication of matrices
Multiplication of matrices
Matrices and powers
Inverse of a matrix

Polynomials and Quadratics

Building on algebra foundations to work with more complex expressions and equations.

Elementary algebra and substitution
Factorization
The cross sword method of factoring
Graphing factored quadratic and polynomial functions
Polynomial division
Remainder and factor theorems
Solution of quadratic equations
The discriminant
Solutions of linear and quadratic equations

Functions and Relations

One of the most conceptually demanding parts of pre-calculus, and one of the most important for calculus.

Functions and relations
The hyperbola
Circles and other curves
Domain and range of a function
Curve sketching using translation and dilation
Inverse functions
Rate of change of non-linear functions
Absolute value and inequations
Rate of change of linear functions
Relating gradient function to original function
Displacement and velocity graphs
Continuity and hybrid functions
Direct, inverse and joint variation

Trigonometry

Where the trigonometry from geometry gets extended into a full set of functions and identities.

Trig revision and exact values
Relations between radians and degrees
Allied angles and trig identities
The trigonometric functions
Finding angles from sine and cosine
Arc length and sector area

Exponentials and Logarithms

Topics that connect to both algebra and the calculus that follows.

Basic and advanced exponent laws
Graphing exponential functions
Logarithms
Solving exponential equations

Introduction to Calculus

The calculus content here provides a genuine foundation for AP Calculus rather than just a preview.

Limits
Derivative from first principles
Differentiating x to the power of n
Negative values of n
Differentiating roots of x
The product rule
The quotient rule
Stationary points
The second derivative
Maxima and minima
Tangents and normals
Anti-differentiation
The definite integral
Area under a curve

How Our Tutoring Works

Step 1: Math Doctor Assessment

Every student starts with the Math Doctor assessment. At pre-calculus level this is particularly valuable because it identifies whether the difficulty is in the pre-calculus content itself or in earlier algebra, geometry or trigonometry concepts that pre-calculus relies on.

Step 2: A Weekly Lesson Plan Built Around Your Child

Every Monday the plan is updated with lessons targeting the specific areas that need work. Your child works through each lesson at their own pace, with step-by-step solutions built in for every question.

Step 3: Self-Paced Learning

Pre-calculus covers a lot of ground and moves quickly in a classroom. Working at their own pace means your child can spend as long as they need on any concept, revisit worked solutions and go back to earlier material when something from algebra or geometry needs consolidating. No pressure to keep up with anyone else.

Step 4: Tutor Support When They Need It

Pre-calculus is one of those subjects where a student can follow every step of a worked solution and still not feel like they understand what just happened. When that's the case, talking it through with a real person makes a meaningful difference. Your child can call our tutor line, up to 10 hours per week. A tutor works through the specific concept with them using screen sharing and an interactive whiteboard. No extra charge.

Why Pre-Calculus Matters for What Comes Next

Pre-calculus sits directly before calculus in the high school math sequence, and the connection between the two is closer than in most subject transitions. The concept of a limit introduced in pre-calculus is the foundation on which differentiation and integration in calculus are built. The trigonometric functions covered in pre-calculus appear again in calculus in more complex forms. The algebraic manipulation skills required throughout pre-calculus are used constantly in calculus problem solving.

A student who moves into AP Calculus with a weak pre-calculus foundation will spend most of their calculus course firefighting algebra and trig difficulties rather than learning the new content. Getting pre-calculus right makes the calculus course that follows significantly more manageable.

Pre-calculus skills also appear in standardized assessments. The SAT and ACT include functions, coordinate geometry and trigonometry, all core pre-calculus topics. We're a curriculum service, not a test prep service, but a student who has genuinely worked through the pre-calculus curriculum will be drawing on those skills directly when they sit those assessments.

Pricing

Math tutoring starts from $24 per week, covering the full K-12 curriculum, the Math Doctor assessment, a personalized weekly lesson plan, access to the tutor helpline and weekly progress reports. New students get their first two weeks free.

$24 / week

Full K-12 math curriculum (pre-calculus included)
Math Doctor diagnostic
Personalized weekly lesson plan
Tutor helpline up to 10 hrs/week
Weekly progress reports

Start Your 2 Weeks Free

Frequently Asked Questions

What grade is pre-calculus typically taken?

Pre-calculus is usually taken in Grade 11, though some students take it in Grade 10 or Grade 12 depending on their school's math sequence. The personalized plan meets your child wherever they are in that sequence.

My child is struggling in pre-calculus. Is the problem likely pre-calculus itself or something earlier?

Often it's something earlier. Pre-calculus draws heavily on algebra, geometry and trigonometry from previous years. A student who found those subjects manageable but not fully understood will frequently find that difficulty catches up with them in pre-calculus. The Math Doctor assessment identifies whether the gaps are in the current content or in the foundations it relies on.

How does pre-calculus connect to AP Calculus?

Pre-calculus builds the foundational concepts that AP Calculus requires, particularly functions, limits, trigonometry and algebraic manipulation. Our pre-calculus curriculum includes an introduction to calculus covering limits, differentiation and integration at a foundational level, so the transition into AP Calculus is a continuation rather than a fresh start.

Does pre-calculus help with the SAT or ACT?

We're a curriculum service, not a test prep service. But functions, coordinate geometry and trigonometry all appear regularly in the math sections of the SAT and ACT. A student who has genuinely worked through the pre-calculus curriculum will be using those skills when they sit those assessments.

What comes before and after pre-calculus in the curriculum?

Pre-calculus typically follows Algebra 2. After pre-calculus, the curriculum covers AP Calculus and Probability and Statistics. The personalized plan moves with your child through the full high school math sequence.

Does the pre-calculus curriculum work for students with ADHD or learning differences?

Yes. APLUS America can support students with ADHD, dyscalculia, and other learning differences. Pre-calculus can feel challenging because it brings together a lot of earlier math skills, including algebra, functions, trigonometry, and problem solving. If there are gaps in these foundations, students may find it harder to keep up or feel confident with new concepts. When your child gets started, they complete our Math Doctor assessment. This helps identify what they already understand, where there may be gaps in their learning, and which skills need more support. From there, your child's personalized weekly learning plan can target the right skills in the right order. The self-paced format of our curriculum is particularly valuable here. Your child can spend as long as needed on functions before moving to trigonometry, and as long as needed on trigonometry before moving to exponentials. Nothing moves forward until your child is ready to. If your child needs extra support, our online tutors are available to explain pre-calculus concepts in another way and answer questions.

Online Pre-Calculus Help: Functions, Trigonometry and Calculus Foundations