Ontario Grade 12 College Preparation math (MCT4C)

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°.