Ontario Grade 11 College Preparation math (MBF3C)

Quadratic and exponential relations in practical models.

• A1.1 · Build tables and graphs for applied quadratic relations (written lesson not published)
• A1.2 · Interpret meaningful values on applied quadratic graphs (written lesson not published)
• A1.3 · Investigate transformations of quadratic vertex form (written lesson not published)
• A1.4 · Sketch quadratic relations in vertex form (written lesson not published)
• A1.5 · Expand and simplify quadratic expressions (written lesson not published)
• A1.6 · Convert vertex form to standard form and verify equivalence (written lesson not published)
• A1.7 · Factor simple trinomials and common-factor quadratics (written lesson not published)
• A1.8 · Connect quadratic factors with x-intercepts (written lesson not published)
• A1.9 · Solve applied quadratic problems by factoring or graphing (written lesson not published)
• A2.1 · Explain zero and negative exponents (written lesson not published)
• A2.2 · Evaluate numerical expressions with integer exponents (written lesson not published)
• A2.3 · Develop exponent rules for products, quotients, and powers (written lesson not published)
• A2.4 · Graph simple exponential relations (written lesson not published)
• A2.5 · Connect tables, graphs, and equations of exponential relations (written lesson not published)
• A2.6 · Distinguish exponential, linear, and quadratic relations (written lesson not published)
• A3.1 · Collect and graph data modelled exponentially (written lesson not published)
• A3.2 · Describe characteristics of applied exponential relations (written lesson not published)
• A3.3 · Pose and solve exponential problems using graphs (written lesson not published)
• A3.4 · Solve applied exponential equations by substitution (written lesson not published)

Compound interest, financial services, credit, and vehicle costs.

• B1.1 · Compare simple and compound interest using tables and graphs (written lesson not published)
• B1.2 · Connect compound interest with exponential growth (written lesson not published)
• B1.3 · Calculate amount and principal in compound-interest problems (written lesson not published)
• B1.4 · Calculate total interest earned or paid (written lesson not published)
• B1.5 · Use technology to find interest rates or compounding periods (written lesson not published)
• B1.6 · Investigate how time, rate, and compounding affect future value (written lesson not published)
• B2.1 · Compare savings alternatives, services, and fees (written lesson not published)
• B2.2 · Compare investment risk and return (written lesson not published)
• B2.3 · Compare credit-card and debit-card costs and incentives (written lesson not published)
• B2.4 · Investigate the effect of delayed credit-card payments (written lesson not published)
• B2.5 · Calculate the compound-interest cost of credit purchases (written lesson not published)
• B3.1 · Compare vehicle insurance procedures, factors, and costs (written lesson not published)
• B3.2 · Compare buying new, leasing, and buying used vehicles (written lesson not published)
• B3.3 · Solve fixed and variable vehicle-cost problems (written lesson not published)

Design representations and acute-triangle applications.

• C1.1 · Recognize geometric shapes in practical design (written lesson not published)
• C1.2 · Represent three-dimensional objects in multiple ways (written lesson not published)
• C1.3 · Create nets, plans, and patterns with metric and imperial units (written lesson not published)
• C1.4 · Solve design problems under constraints and state assumptions (written lesson not published)
• C2.1 · Solve applied right-triangle problems (written lesson not published)
• C2.2 · Verify the sine law and cosine law using technology (written lesson not published)
• C2.3 · Choose and apply the sine law or cosine law in acute triangles (written lesson not published)
• C2.4 · Solve metric and imperial applications with sine or cosine law (written lesson not published)

One-variable data, sampling, statistics, and probability.

• D1.1 · Design ethical questionnaires or experiments for one-variable data (written lesson not published)
• D1.2 · Collect, organize, and store secondary one-variable data (written lesson not published)
• D1.3 · Distinguish populations and samples and explain good sampling (written lesson not published)
• D1.4 · Compare and apply sampling techniques (written lesson not published)
• D1.5 · Classify one-variable data and choose suitable displays (written lesson not published)
• D1.6 · Describe common distribution shapes (written lesson not published)
• D1.7 · Calculate and interpret measures of centre and spread (written lesson not published)
• D1.8 · Choose suitable measures of centre and spread (written lesson not published)
• D1.9 · Compare data sets using measures of centre and spread (written lesson not published)
• D1.10 · Solve problems by analysing secondary one-variable data (written lesson not published)
• D2.1 · Interpret probability representations in the media (written lesson not published)
• D2.2 · Calculate and represent theoretical probability (written lesson not published)
• D2.3 · Run experiments and determine experimental probability (written lesson not published)
• D2.4 · Compare theoretical and experimental probability (written lesson not published)
• D2.5 · Investigate long-run convergence of experimental probability (written lesson not published)
• D2.6 · Interpret probability and statistics claims in the media (written lesson not published)

A profit graph has vertex (80, 1200). What does it mean?

Worked method: If the parabola opens downward, the maximum profit is CAD 1200 when 80 items are produced.

A CAD 3000 loan is repaid with 24 payments of CAD 140. Find total interest.

Worked method: Total paid is 24 × 140 = CAD 3360. Interest is 3360 − 3000 = CAD 360.

A coin shows heads 27 times in 50 tosses. Find the experimental probability.

Worked method: The experimental probability is 27/50 = 0.54, or 54%.

Factor 3x² + 12x.

Find the mean of 4, 6, 7, 8, 10.