1-on-1 Mastery-Based Pre-Calculus · Taipei

Pre-Calculus, from algebra to calculus.

Pre-Calculus is the bridge between algebra and calculus thinking. Lessons build from the function-family fluency students bring toward the trigonometry and limit-thinking their next courses will require.

Audience
Pre-Calculus and equivalent pre-calculus content, international school students
Format
1-on-1, 1 to 1.5 hours per lesson
Duration
Typically 6 to 12 months per program
Begin
Complimentary consultation & assessment class

What Students Learn

Mastery-based Pre-Calculus at the level your child's school actually requires.

Pre-Calculus is for students who have completed Algebra II but are running into difficulty with the trigonometry and limit-thinking the course introduces. The program covers the core pre-calculus content high school mathematics builds on. Working with advanced function transformations, composition, and inverses. Reasoning through the unit circle and trigonometric functions. Manipulating trigonometric identities and solving trigonometric equations. Analyzing conic sections, polar coordinates, parametric equations, and vectors. Working with sequences, series, and summation patterns. Reasoning through limits and continuity as the entry to calculus. These are the topics AP Calculus, IB Higher Level Mathematics, and beyond assume.

Different pre-calculus content demands different approaches. Trigonometric functions work differently from polynomial functions, and a limit problem works differently from a sequence question. Students learn to recognize what kind of pre-calculus problem they're working with and to apply the strategies that fit. By the end of Pre-Calculus, this distinction is what separates students who think dynamically about functions from students who only memorize procedures.

Lessons follow Harland's Pre-Calculus curriculum, which is built to bring students to mastery of Pre-Calculus content and matches international school expectations. The program is structured into five units that follow the natural flow of Pre-Calculus content. Each unit closes in a deliverable that measures whether the student has reached mastery of the content before moving on. Lessons calibrate to your child's individual gaps and the topics they're working through at school. If a student is working through trigonometric identities at school, the teacher works through it with the student, applying the unit's analytical structure to the kinds of problems their class is currently doing. Harland's curriculum decides what gets taught. The student's school Pre-Calculus class is where the teaching happens.

Progress shows up in places parents can see. Your child stops freezing on trigonometric identity problems. They start moving comfortably between unit-circle reasoning and equation work. School feedback shifts from "losing the thread on multi-step problems" toward "thinks through complex problems systematically."

How We Teach It

Pre-Calculus taught through what students are working on.

Harland's pedagogy is content-based learning. Trigonometric reasoning, function analysis, and the introduction to calculus thinking develop through the topics, problem sets, and assignments your child is already working on at school. Assessments check whether the thinking holds up when the student moves to new content alone.

That means lessons that work directly with school material. A student working through advanced functions and inverses works on it with their teacher, applying the unit's analytical structure to the transformations and composition problems their school is asking for. A student moving into trigonometric identities and equations works on it with their teacher, applying the unit's reasoning structure to the trig manipulation their class is doing. A student working through sequences, series, and the introduction to limits works on it with their teacher, building the abstraction skills the next courses in the sequence will assume.

Pre-Calculus is also a question of engagement. Some students arrive having handled algebra and geometry well but hit a wall when trigonometry and limit-thinking begin. The unit circle feels arbitrary, the identities pile up, and what worked in earlier courses stops working. The 1-on-1 format gives teachers room to slow down where the new concepts are unfamiliar, and to keep the work rigorous without losing the student's interest. Skill and persistence develop together. Neither moves far in isolation.

The format also lets teachers calibrate within the program's structure. A student arriving with weak Algebra II foundations gets work calibrated to fill in those gaps before moving to trigonometric and limit content. They aren't held to a generic remediation script. A student fluent with procedural manipulation but uncomfortable with conceptual abstraction gets pushed toward the harder questions their school will eventually ask. What does this limit case reveal. Why does this trig identity work. How does this approach generalize to similar problems.

Curriculum and Alignment

A structured curriculum that aligns with your child's school.

Pre-Calculus at Harland follows a structured curriculum keyed to the typical Pre-Calculus content taught in international schools. A student who completes the program has demonstrated mastery of Pre-Calculus content.

Harland's curriculum runs five units. Most school Pre-Calculus courses spread across more. 1-on-1 lessons don't lose time to group pacing or mixed-ability instruction, so the same core content fits in fewer, more substantive units. The time saved goes into the functional reasoning Pre-Calculus rewards.

Lessons coordinate with whatever curriculum your child's school follows. The Pre-Calculus curriculum tracks against the Common Core State Standards for High School Algebra and Functions, extended to cover the trigonometric and limit content the program covers. Students from US-curriculum schools work through it as their school's Pre-Calculus course. Students at IB or Cambridge schools, where the pre-calculus content sits within an integrated G11–12 mathematics syllabus, use the program for targeted reinforcement calibrated to whatever their school is currently working on. Where a school uses its own internal curriculum, the Student Coordinator translates school expectations into lesson goals.

Standards
Harland's Pre-Calculus curriculum, with cross-references to Common Core State Standards for High School Algebra and Functions and school-specific expectations as relevant
Materials
Harland curriculum materials, with school texts, worksheets, and assignments integrated as ongoing input
Assessment
End-of-unit assessments, tracked against Pre-Calculus mastery and school-flagged skills
Reporting
Skill-level tracking against Harland's internal rubrics, matched to international school standards

Prerequisites and What Comes Next

Where Pre-Calculus fits in your child's learning.

Before starting

Pre-Calculus assumes Algebra II content fluency, including function-family thinking and the algebraic manipulation that supports it. Students with gaps in these areas typically work in Algebra II first or alongside Pre-Calculus, depending on how foundational the gaps are.

Some students at Pre-Calculus level still find that mathematical word problems read harder than the math itself, because the English vocabulary is doing more work than the math is. Where this is the case, Academic English (Grades 3–12) runs alongside as a parallel program. The Student Coordinator helps families judge whether the gap is in the math or in the language carrying the math.

The consultation and assessment class establishes whether Pre-Calculus is the right starting point and whether parallel work in another program would help. Some students arrive needing both Algebra II review and Pre-Calculus support, and the lesson plan covers what's most urgent first.

What comes after

Most students complete Pre-Calculus in 6 to 12 months, depending on starting position and lesson cadence. At completion, families have a clear decision point.

Most students who finish Pre-Calculus continue with AP Calculus AB or BC. Others step away from Harland once Pre-Calculus content is mastered, returning if Calculus becomes difficult.

Beyond AP Calculus, students continue with AP Statistics and other AP mathematics offerings on our AP Program. Students at IB schools continue through to IB Diploma Mathematics: Analysis and Approaches at Higher Level on the IB Diploma Programme. Some students prepare for the AP Pre-Calculus exam during the program, with targeted exam-style practice in the final weeks before the test.

The longer-term aim of Pre-Calculus is to make itself unnecessary. The program brings students to mastery of Pre-Calculus content. Some continue with AP Calculus, others don't need Harland until later in the sequence. A parent who's no longer worried about their child's math is the point of all of it.

Common Questions

Common questions about Pre-Calculus at Harland.

Who is Pre-Calculus at Harland for? +
Pre-Calculus at Harland is for students who have completed Algebra II and are now working through high school Pre-Calculus. Most of our students fall into one of three patterns. Some are at US-curriculum international schools where Pre-Calculus is the standard G11 or G12 course and they're falling behind their teacher's pace, particularly when trigonometry and limits enter the curriculum. Some are advanced students working through Pre-Calculus at G10 or earlier and want to deepen their mastery before AP Calculus. Some are at IB or Cambridge schools where the pre-calculus content within their integrated mathematics syllabus needs targeted reinforcement.
My child can do the algebra but trigonometry isn't clicking. Is this the right program? +
Yes, in most cases. The shift from Algebra II to Pre-Calculus is one of the most common difficulty points in international school mathematics. Algebra II built fluency with function families. Pre-Calculus introduces trigonometry and limit-thinking, which are new ways of thinking that don't map to algebra-style problem solving. The program addresses what makes that transition difficult. Reading the unit circle and recognizing how angles relate to coordinate values. Working with trigonometric identities and equations as algebraic objects. Building the conceptual scaffolding limits require. Building the persistence that pushing through new content demands.
Can my child begin Harland over the summer? +
Yes. Summer enrollment is available across most Harland programs. The summer block is a 4 to 8 week 1-on-1 program scheduled between late June and early August, typically two to three sessions per week, calibrated to what your child's school will be teaching later in the school year. See Summer Enrollment for full details.
What does Pre-Calculus at Harland cover? +
Pre-Calculus at Harland covers the core pre-calculus content typically taught in a high school Pre-Calculus course. Working with advanced function transformations, composition, and inverses. Reasoning through the unit circle and trigonometric functions. Manipulating trigonometric identities and solving trigonometric equations. Analyzing conic sections, polar coordinates, parametric equations, and vectors. Working with sequences, series, and summation patterns. Reasoning through limits and continuity as the entry to calculus. Working with applied problems and modeling. Lessons calibrate to whichever topics your child's school is emphasizing. If a teacher has flagged a specific skill, the lesson plan can focus on that skill rather than running through the whole program.
How long is each lesson and how often does my child attend? +
Lessons are 1-on-1 sessions of 1 to 1.5 hours, in person at our head office in Da'an or online. Most students attend one to three lessons per week. The Pre-Calculus program is structured around five units of work, each closing in a deliverable. At one or two lessons per week, the program typically takes a school year. At three lessons per week, a semester. The Student Coordinator helps you choose the cadence that fits.
How are lessons scheduled, and what if we need to reschedule? +
Lessons happen on a fixed weekly slot reserved with your child's primary teacher. This protects the teacher's time and keeps a consistent rhythm for your child. If you need to reschedule, give us at least 24 hours of notice and we'll find another time when your teacher is available. Many families add classes during summer or winter vacation, either to accelerate progress or to make up for a slower term. Once a unit has started, it should be completed within a defined window. The Student Coordinator walks through the details when you enroll.
How do you measure progress? +
Progress is measured through the curriculum's assessments. The Pre-Calculus program has five units, each closing in an assessment that measures conceptual understanding, procedural fluency, problem-solving, and mathematical reasoning across the unit's content. Parents receive updates after every lesson and formal progress reports when each unit ends. Skill-level tracking uses Harland's internal rubrics, which match international school standards. Where helpful, the Student Coordinator translates this into the expectations of your child's school.
How do we begin? +
Every Harland relationship begins with a consultation, followed by a 1-on-1 assessment class. The consultation is about your goals and your child's situation. The assessment class is about how your child works in the subject. Together they tell us where to start and what kind of teacher will fit best.

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