Ontario Grade 12 Math for College Technology (MCT4C) curriculum and lessons

The course map includes Exponential Functions, Polynomial Functions, Trigonometric Functions, and 1 other section. Follow the complete section list above for the full study path.

درس ریاضی فناوری کالج پایه دوازدهم انتاریو (MCT4C) چه مباحثی دارد؟ از جمله مباحث این درس تابع‌های نمایی، تابع‌های چندجمله‌ای، تابع‌های مثلثاتی است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

The 57-topic course map is available now. Written lessons appear here only after they have been reviewed and published. Check the official Ontario curriculum for exact requirements.

درس‌ها و برنامهٔ درسی ریاضی فناوری کالج پایه دوازدهم انتاریو را از کجا پیدا کنم؟ نقشهٔ 57 موضوع این درس در دسترس است. درس‌های نوشتاری پس از بررسی و انتشار در همین صفحه نمایش داده می‌شوند. برای شرایط دقیق به برنامهٔ درسی رسمی انتاریو مراجعه کنید.

Graphs, equations, logarithms, and technology-based applications.

• A1.1 · Investigate exponential graphs with changing bases and signs (written lesson not published)
• A1.2 · Solve simple exponential equations numerically and graphically (written lesson not published)
• A1.3 · Solve intersections of exponential graphs (written lesson not published)
• A1.4 · Solve exponential applications using graphs and tables (written lesson not published)
• A2.1 · Apply exponent laws with integer and rational exponents (written lesson not published)
• A2.2 · Solve exponential equations using a common base (written lesson not published)
• A2.3 · Interpret logarithms as inverse operations (written lesson not published)
• A2.4 · Approximate logarithms in any base (written lesson not published)
• A2.5 · Convert logarithmic and exponential equations (written lesson not published)
• A2.6 · Solve real exponential equations using logarithms (written lesson not published)

Representations, factoring, equations, formulas, and applications.

• B1.1 · Recognize polynomial expressions and functions (written lesson not published)
• B1.2 · Compare polynomial representations (written lesson not published)
• B1.3 · Identify key polynomial graph features (written lesson not published)
• B1.4 · Distinguish polynomial functions from other families (written lesson not published)
• B1.5 · Evaluate polynomial functions and interpret notation (written lesson not published)
• B1.6 · Model applications with polynomial functions (written lesson not published)
• B1.7 · Apply contextual domain and range restrictions (written lesson not published)
• B2.1 · Factor polynomials up to degree four (written lesson not published)
• B2.2 · Connect factored form with graphs and intercepts (written lesson not published)
• B2.3 · Connect roots with x-intercepts (written lesson not published)
• B3.1 · Solve polynomial equations up to degree four (written lesson not published)
• B3.2 · Solve polynomial applications (written lesson not published)
• B3.3 · Distinguish constants and variables in formulas (written lesson not published)
• B3.4 · Expand multivariable polynomial expressions (written lesson not published)
• B3.5 · Solve power equations using rational exponents (written lesson not published)
• B3.6 · Solve formulas for a variable up to degree three (written lesson not published)
• B3.7 · Connect formulas with functions (written lesson not published)
• B3.8 · Solve multistep formula applications (written lesson not published)
• B3.9 · Investigate careers using polynomial models (written lesson not published)

Ratios, oblique triangles, sinusoidal models, and applications.

• C1.1 · Determine exact trigonometric ratios for special angles (written lesson not published)
• C1.2 · Determine trigonometric ratios from zero to 360 degrees (written lesson not published)
• C1.3 · Use related angles (written lesson not published)
• C1.4 · Solve two- and three-dimensional right triangles (written lesson not published)
• C1.5 · Apply the sine law and cosine law (written lesson not published)
• C2.1 · Connect trigonometric ratios with functions (written lesson not published)
• C2.2 · Graph sine and cosine functions in degrees (written lesson not published)
• C2.3 · Transform sinusoidal graphs vertically and horizontally (written lesson not published)
• C2.4 · Transform sinusoidal graphs with amplitude and period changes (written lesson not published)
• C2.5 · Interpret amplitude, period, and phase shift (written lesson not published)
• C2.6 · Determine an equation from a sinusoidal graph (written lesson not published)
• C3.1 · Collect and graph sinusoidal data (written lesson not published)
• C3.2 · Identify periodic models and restrictions (written lesson not published)
• C3.3 · Solve sinusoidal applications (written lesson not published)

Vectors, measurement, composite objects, and circles.

• D1.1 · Interpret vectors and their applications (written lesson not published)
• D1.2 · Represent vectors as directed segments (written lesson not published)
• D1.3 · Resolve a vector into components (written lesson not published)
• D1.4 · Construct a vector from components (written lesson not published)
• D1.5 · Add and subtract vectors graphically and algebraically (written lesson not published)
• D1.6 · Solve vector applications (written lesson not published)
• D2.1 · Investigate geometry applications in careers (written lesson not published)
• D2.2 · Convert imperial and metric measurements (written lesson not published)
• D2.3 · Calculate areas of composite figures (written lesson not published)
• D2.4 · Calculate volume and surface area of composite objects (written lesson not published)
• D3.1 · Identify circle elements and applications (written lesson not published)
• D3.2 · Calculate arc length and sector and segment area (written lesson not published)
• D3.3 · Apply circle properties (written lesson not published)
• D3.4 · Solve circle applications (written lesson not published)

Solve 4^(x + 1) = 32.

Worked method: Write both sides with base 2: 2^(2x + 2) = 2^5. Then 2x + 2 = 5, so x = 1.5.

Add the vectors (4, 1) and (−2, 3).

Worked method: Add components: (4 − 2, 1 + 3) = (2, 4).

Solve 10^x = 250 using logarithms.

Find the arc length for radius 6 cm and central angle 60°.