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Skills available for Ontario grade 11 math curriculum

Objectives are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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11.A Quadratic Functions

  • 11.A.1 expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph;

  • 11.A.2 demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions;

  • 11.A.3 solve problems involving quadratic functions, including problems arising from real-world applications.

    • 11.A.3.1 collect data that can be modelled as a quadratic function, through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials; measurement tools such as measuring tapes, electronic probes, motion sensors), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data

    • 11.A.3.2 determine, through investigation using a variety of strategies (e.g., applying properties of quadratic functions such as the x-intercepts and the vertex; using transformations), the equation of the quadratic function that best models a suitable data set graphed on a scatter plot, and compare this equation to the equation of a curve of best fit generated with technology (e.g., graphing software, graphing calculator)

    • 11.A.3.3 solve problems arising from real-world applications, given the algebraic representation of a quadratic function (e.g., given the equation of a quadratic function representing the height of a ball over elapsed time, answer questions that involve the maximum height of the ball, the length of time needed for the ball to touch the ground, and the time interval when the ball is higher than a given measurement)

11.B Exponential Functions

  • 11.B.1 simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions;

  • 11.B.2 identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications;

    • 11.B.2.1 collect data that can be modelled as an exponential function, through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials such as number cubes, coins; measurement tools such as electronic probes), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data

    • 11.B.2.2 identify exponential functions, including those that arise from real-world applications involving growth and decay (e.g., radioactive decay, population growth, cooling rates, pressure in a leaking tire), given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range (e.g., ambient temperature limits the range for a cooling curve)

    • 11.B.2.3 solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications (e.g., radioactive decay, population growth, height of a bouncing ball, compound interest) by interpreting the graphs or by substituting values for the exponent into the equations

  • 11.B.3 demonstrate an understanding of compound interest and annuities, and solve related problems.

    • 11.B.3.1 compare, using a table of values and graphs, the simple and compound interest earned for a given principal (i.e., investment) and a fixed interest rate over time

    • 11.B.3.2 solve problems, using a scientific calculator, that involve the calculation of the amount, A (also referred to as future value, FV), and the principal, P (also referred to as present value, PV), using the compound interest formula in the form A = P((1 + i) to the n power) [or FV = PV((1 + i) to the n power)]

    • 11.B.3.3 determine, through investigation (e.g., using spreadsheets and graphs), that compound interest is an example of exponential growth [e.g., the formulas for compound interest, A = P((1 + i) to the n power), and present value, PV = A((1 + i) to the -n power), are exponential functions, where the number of compounding periods, n, varies]

    • 11.B.3.4 solve problems, using a TVM Solver on a graphing calculator or on a website, that involve the calculation of the interest rate per compounding period, i, or the number of compounding periods, n, in the compound interest formula A = P((1 + i) to the n power) [or FV = PV((1 + i) to the n power)]

    • 11.B.3.5 explain the meaning of the term annuity, through investigation of numeric and graphical representations using technology

    • 11.B.3.6 determine, through investigation using technology (e.g., the TVM Solver on a graphing calculator, online tools), the effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of ordinary simple annuities (i.e., annuities in which payments are made at the end of each period, and the compounding period and the payment period are the same) (e.g., long-term savings plans, loans)

    • 11.B.3.7 solve problems, using technology (e.g., scientific calculator, spreadsheet, graphing calculator), that involve the amount, the present value, and the regular payment of an ordinary simple annuity (e.g., calculate the total interest paid over the life of a loan, using a spreadsheet, and compare the total interest with the original principal of the loan)

11.C Trigonometric Functions

  • 11.C.1 solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications;

  • 11.C.2 demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;

    • 11.C.2.1 describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications (e.g., natural gas consumption in Ontario, tides in the Bay of Fundy), given a numeric or graphical representation

    • 11.C.2.2 predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function (e.g., predicting hours of daylight on a particular date from previous measurements; predicting natural gas consumption in Ontario from previous consumption)

    • 11.C.2.3 make connections between the sine ratio and the sine function by graphing the relationship between angles from 0° to 360° and the corresponding sine ratios, with or without technology (e.g., by generating a table of values using a calculator; by unwrapping the unit circle), defining this relationship as the function f(x) = sinx, and explaining why the relationship is a function

    • 11.C.2.4 sketch the graph of f(x) = sinx for angle measures expressed in degrees, and determine and describe its key properties (i.e., cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/ decreasing intervals)

    • 11.C.2.5 make connections, through investigation with technology, between changes in a real-world situation that can be modelled using a periodic function and transformations of the corresponding graph (e.g., investigate the connection between variables for a swimmer swimming lengths of a pool and transformations of the graph of distance from the starting point versus time)

    • 11.C.2.6 determine, through investigation using technology, the roles of the parameters a, c, and d in functions in the form f(x) = a sinx, f(x) = sinx + c, and f(x) = sin(x – d), and describe these roles in terms of transformations on the graph of f(x) = sinx with angles expressed in degrees (i.e., translations; reflections in the x-axis; vertical stretches and compressions to and from the x-axis)

    • 11.C.2.7 sketch graphs of f(x) = a sinx, f(x) = sinx + c, and f(x) = sin(x – d) by applying transformations to the graph of f(x) = sinx, and state the domain and range of the transformed functions

  • 11.C.3 identify and represent sine functions, and solve problems involving sine functions, including problems arising from real-world applications.

    • 11.C.3.1 collect data that can be modelled as a sine function (e.g., voltage in an AC circuit, sound waves), through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials, measurement tools such as motion sensors), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data

    • 11.C.3.2 identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range

    • 11.C.3.3 pose problems based on applications involving a sine function, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation