Pre‑Calculus 12 Final Exam Review — Full Curriculum (Step‑by‑Step Solutions)

FINAL EXAM — PRE‑CALCULUS 12 (FULL CURRICULUM REVIEW, 8 SECTIONS) In this complete Pre‑Calculus 12 Final Exam Review, we walk through all major topics from the BC Curriculum (also aligned with Western Canada and overlapping with US Pre‑Calculus). This lesson from MathSupport, ‪@mathsupportnow‬ , includes transformations, inverses, polynomial functions, rational functions, exponential & logarithmic equations, sequences & series, and more — all explained slowly, clearly, and step‑by‑step. This is a calm, structured, confidence‑building review designed for students preparing for June final exams. ✅ What You’ll Learn in This Video 🔹 1. Transformations of Functions You’ll learn how to: • Identify reflections, stretches, compressions • Apply horizontal & vertical translations • Write mapping rules for each transformation • Interpret composite transformations 🔹 2. Inverse Functions You’ll learn how to: • Algebraically find the inverse of a function • Swap x and y and solve correctly • Determine domain & range of f(x) and f⁻¹(x) • Interpret inverse graphs 🔹 3. Polynomial Functions & Equations You’ll learn how to: • Use the Factor Theorem • Determine if (x – a) is a factor • Factor quartics using substitution • Find zeros & multiplicities • Describe end behaviour • Sketch polynomial graphs 🔹 4. Rational Functions You’ll learn how to: • Identify NPVs (non‑permissible values) • Find vertical asymptotes & holes • Determine horizontal asymptotes • Find x‑ and y‑intercepts • Sketch rational functions 🔹 5. Exponential Functions & Equations You’ll learn how to: • Solve exponential equations using exponent laws • Convert between exponential and continuous growth forms • Use natural logs to isolate variables • Interpret growth models 🔹 6. Logarithms You’ll learn how to: • Expand & condense logarithms • Apply log laws correctly • Solve logarithmic equations • Check for extraneous roots • Determine domain, range & vertical asymptotes 🔹 7. Geometric Sequences & Series You’ll learn how to: • Find common ratios • Determine missing terms • Find the first term • Write general term formulas 🔹 8. Combined Topics (Exam‑Style Problems) You’ll learn how to: • Apply multiple concepts in one question • Interpret functions graphically & algebraically • Solve mixed exponential/logarithmic/polynomial problems 00:00 – Introduction 00:07 – Overview of Topics (8 Sections) 00:33 – Section 1: Transformations 01:00 – Q1A: Reflection, Horizontal Shift, Vertical Shift 01:57 – Q1B: Vertical & Horizontal Compression 02:35 – Q1C: Reflection over y‑axis + Vertical Shift 02:58 – Section 2: Inverse Functions 03:06 – Finding f⁻¹(x) 04:25 – Domain & Range of f(x) and f⁻¹(x) 06:12 – Section 3: Polynomial Functions 06:20 – Factor Theorem Check 07:59 – Section 4: Polynomial Zeros & End Behaviour 08:07 – Factoring Quartic 09:22 – Zeros & Multiplicities 10:13 – End Behaviour & Sketch 11:39 – Section 5: Polynomial Equation (Grouping) 12:02 – Factoring by Grouping 13:23 – Section 6: Rational Functions 13:32 – Domain & NPVs 14:18 – Vertical Asymptote & Hole 16:01 – Horizontal Asymptote 16:43 – x‑ and y‑Intercepts 17:29 – Section 7: Exponential Equations 17:42 – Solving 4^(2x–1) = 8^(x+2) 19:12 – Bacteria Growth Model 20:00 – Solving for Time 21:10 – Continuous Growth Form (Find k) 23:04 – Section 8: Logarithms 23:12 – Condensing Logs 24:20 – Expanding Logs 26:04 – Solving Log Equation + Extraneous Root 28:01 – Log Function: Domain, Range, Asymptote 29:23 – x‑Intercept (Exact Value) 30:25 – Sketching the Log Graph 32:13 – Section 9: Geometric Sequences 32:31 – Finding r 33:26 – Finding First Term 34:02 – General Term Formula 🎯 This Video Is Ideal For: • Pre‑Calculus 12 (BC Curriculum) • Western Canada Grade 12 Math • US Pre‑Calculus (overlapping topics) • Homeschool learners • Adult learners returning to math • Teachers needing a classroom‑ready final exam review 👍 Like if this helped you 🔔 Subscribe for more clear, step‑by‑step math lessons 💬 Comment with topics you want next 📤 Share with classmates or study groups #precalculus12 #finalexam #mathreview #bcmathcurriculum #mathsupport #studywithme #grade12math #precalculus