Summer University Prep: Calculus II

Course Description

Calculus II is one of the most challenging first-year university math courses—covering advanced integration techniques, sequences & series, Taylor polynomials, parametric calculus, and more. Many students struggle because they encounter these topics for the first time at full university speed. Our 32-hour Calculus II Summer Prep Course is designed to give students a strong early foundation before they enter university, making the real course significantly easier and less stressful. Class Options: • 8–15 Students: $50/hour • 2–6 Students (Small Group): $70/hour • Total: 32 hours (4 hours/week × 8 weeks) Who This Course Is For • Graduating Grade 12 students entering STEM or Math • Students who completed Calculus I but want a stronger foundation • Students entering competitive programs (UofT, Waterloo, McGill) • Anyone who wants university-level math to feel easy, not overwhelming Why Students Take This Course • University calculus becomes much easier, reducing stress • Students earn higher grades in their first year • Stronger foundation for STEM • Know what to expect before the real course begins • Build study habits & problem-solving skills early • A safer transition into the fast pace of university math University Course Equivalents This prep course directly supports the content of: • U of Toronto: MAT136 / MAT137 / MAT157 • U of Waterloo: MATH 138 • McMaster: MATH 1B03 • UBC: MATH 102 / 152 • McGill: MATH 141 • U of Alberta: MATH 115 Students walk into class already familiar with the major concepts—huge academic advantage. Course Modules Module 1 — Advanced Integration Techniques • Integration by parts • Trigonometric integrals • Partial fractions • Improper integrals Module 2 — Applications of Integration • Arc length • Surface area • Volumes (shell/disc methods) • Work & force problems Module 3 — Sequences & Convergence • Limits of sequences • Monotone sequences • Convergence tests (intro) Module 4 — Infinite Series & Convergence Tests • Geometric series • p-series • Ratio test • Root test • Alternating series Module 5 — Power Series & Taylor Series • Taylor polynomials • Maclaurin series • Error bounds • Convergence intervals Module 6 — Parametric & Polar Calculus • Parametric curves • Arc length • Polar area • Slope of polar curves Module 7 — Differential Equations (Intro) • Separable ODEs • Growth/decay models • Simple applications Module 8 — Full University-Style Review+Mock Exam • Exam-style problems • Timing strategies • Error analysis