OntarioGrade 12 Math Courses - Ontario Curriculum
Explore Grade 12 Mathematics for College Technology (MCT4C) designed for students pursuing college programs in technology fields. This comprehensive courses covers essential mathematical concepts including exponential functions, polynomial functions, trigonometry, and geometric applications.
Ontario Grade 12 Math Curriculum - MCT4C CourseHelp
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
ON.OE.12CT.A1.1 | 12CT.A1.1: Determine, through investigation with technology, and describe the impact of changing the base and changing the sign of the exponent on the graph of an exponential function |
ON.OE.12CT.A1.2 | 12CT.A1.2: Solve simple exponential equations numerically and graphically, with technology, and recognize that the solutions may not be exact |
ON.OE.12CT.A1.4 | 12CT.A1.4: Pose problems based on real-world applications that can be modelled with exponential equations, 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 |
ON.OE.12CT.A2.1 | 12CT.A2.1: Simplify algebraic expressions containing integer and rational exponents using the laws of exponents |
ON.OE.12CT.A2.2 | 12CT.A2.2: Solve exponential equations in one variable by determining a common base |
ON.OE.12CT.A2.3 | 12CT.A2.3: Recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation of exponentiation, and evaluate simple logarithmic expressions |
ON.OE.12CT.A2.4 | 12CT.A2.4: Determine, with technology, the approximate logarithm of a number to any base, including base 10 |
ON.OE.12CT.A2.5 | 12CT.A2.5: Make connections between related logarithmic and exponential equations, and solve simple exponential equations by rewriting them in logarithmic form |
ON.OE.12CT.A2.6 | 12CT.A2.6: Pose problems based on real-world applications that can be modelled with given exponential equations, and solve these and other such problems algebraically by rewriting them in logarithmic form |
ON.OE.12CT.B1.1 | 12CT.B1.1: Recognize a polynomial expression and the equation of a polynomial function, give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions |
ON.OE.12CT.B1.2 | 12CT.B1.2: Compare, through investigation using graphing technology, the graphical and algebraic representations of polynomial functions |
ON.OE.12CT.B1.3 | 12CT.B1.3: Describe key features of the graphs of polynomial functions |
ON.OE.12CT.B1.4 | 12CT.B1.4: Distinguish polynomial functions from sinusoidal and exponential functions, and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions |
ON.OE.12CT.B1.5 | 12CT.B1.5: Substitute into and evaluate polynomial functions expressed in function notation, including functions arising from real-world applications |
ON.OE.12CT.B1.6 | 12CT.B1.6: Pose problems based on real-world applications that can be modelled with polynomial functions, 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 |
ON.OE.12CT.B1.7 | 12CT.B1.7: Recognize, using graphs, the limitations of modelling a real-world relationship using a polynomial function, and identify and explain any restrictions on the domain and range |
ON.OE.12CT.B2.1 | 12CT.B2.1: Factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies |
ON.OE.12CT.B2.2 | 12CT.B2.2: Make connections, through investigation using graphing technology, between a polynomial function given in factored form and the x-intercepts of its graph, and sketch the graph of a polynomial function given in factored form using its key features |
ON.OE.12CT.B2.3 | 12CT.B2.3: Determine, through investigation using technology, and describe the connection between the real roots of a polynomial equation and the x-intercepts of the graph of the corresponding polynomial function |
ON.OE.12CT.B3.1 | 12CT.B3.1: Solve polynomial equations in one variable, of degree no higher than four, by selecting and applying strategies, and verify solutions using technology |
ON.OE.12CT.B3.2 | 12CT.B3.2: Solve problems algebraically that involve polynomial functions and equations of degree no higher than four, including those arising from real-world applications |
ON.OE.12CT.B3.3 | 12CT.B3.3: Identify and explain the roles of constants and variables in a given formula |
ON.OE.12CT.B3.4 | 12CT.B3.4: Expand and simplify polynomial expressions involving more than one variable, including expressions arising from real-world applications |
ON.OE.12CT.B3.5 | 12CT.B3.5: Solve equations of the form x^n = a using rational exponents |
ON.OE.12CT.B3.6 | 12CT.B3.6: Determine the value of a variable of degree no higher than three, using a formula drawn from an application, by first substituting known values and then solving for the variable, and by first isolating the variable and then substituting known values |
ON.OE.12CT.B3.7 | 12CT.B3.7: Make connections between formulas and linear, quadratic, and exponential functions, using a variety of tools and strategies |
ON.OE.12CT.B3.8 | 12CT.B3.8: Solve multi-step problems requiring formulas arising from real-world applications |
ON.OE.12CT.C1.1 | 12CT.C1.1: Determine the exact values of the sine, cosine, and tangent of the special angles 0°, 30°, 45°, 60°, 90°, and their multiples |
ON.OE.12CT.C1.2 | 12CT.C1.2: Determine the values of the sine, cosine, and tangent of angles from 0° to 360°, through investigation using a variety of tools and strategies |
ON.OE.12CT.C1.3 | 12CT.C1.3: Determine the measures of two angles from 0° to 360° for which the value of a given trigonometric ratio is the same |
ON.OE.12CT.C1.4 | 12CT.C1.4: Solve multi-step problems in two and three dimensions, including those that arise from real-world applications, by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios |
ON.OE.12CT.C1.5 | 12CT.C1.5: Solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law and the cosine law |
ON.OE.12CT.C2.1 | 12CT.C2.1: Make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the relationship between angles from 0° to 360° and the corresponding sine ratios or cosine ratios |
ON.OE.12CT.C2.3 | 12CT.C2.3: Determine, through investigation using technology, the roles of the parameters d and c in functions of the form y = sin (x – d) + c and y = cos (x – d) + c, and describe these roles in terms of transformations on the graphs of f(x) = sin x and f(x) = cos x with angles expressed in degrees |
ON.OE.12CT.C2.6 | 12CT.C2.6: Represent a sinusoidal function with an equation, given its graph or its properties |
ON.OE.12CT.C3.1 | 12CT.C3.1: Collect data that can be modelled as a sinusoidal function, through investigation with and without technology, from primary sources, using a variety of tools, or from secondary sources, and graph the data |
ON.OE.12CT.D1.1 | 12CT.D1.1: Recognize a vector as a quantity with both magnitude and direction, and identify, gather, and interpret information about real-world applications of vectors |
ON.OE.12CT.D1.2 | 12CT.D1.2: Represent a vector as a directed line segment, with directions expressed in different ways, and recognize vectors with the same magnitude and direction but different positions as equal vectors |
ON.OE.12CT.D1.3 | 12CT.D1.3: Resolve a vector represented as a directed line segment into its vertical and horizontal components |
ON.OE.12CT.D1.4 | 12CT.D1.4: Represent a vector as a directed line segment, given its vertical and horizontal components |
ON.OE.12CT.D1.5 | 12CT.D1.5: Determine, through investigation using a variety of tools and strategies, the sum or difference of two vectors |
ON.OE.12CT.D1.6 | 12CT.D1.6: Solve problems involving the addition and subtraction of vectors, including problems arising from real-world applications |
ON.OE.12CT.D2.2 | 12CT.D2.2: Perform required conversions between the imperial system and the metric system using a variety of tools, as necessary within applications |
ON.OE.12CT.D2.3 | 12CT.D2.3: Solve problems involving the areas of rectangles, parallelograms, trapezoids, triangles, and circles, and of related composite shapes, in situations arising from real-world applications |
ON.OE.12CT.D2.4 | 12CT.D2.4: Solve problems involving the volumes and surface areas of spheres, right prisms, and cylinders, and of related composite figures, in situations arising from real-world applications |
ON.OE.12CT.D3.1 | 12CT.D3.1: Recognize and describe arcs, tangents, secants, chords, segments, sectors, central angles, and inscribed angles of circles, and some of their real-world applications |
ON.OE.12CT.D3.2 | 12CT.D3.2: Determine the length of an arc and the area of a sector or segment of a circle, and solve related problems |
ON.OE.12CT.D3.3 | 12CT.D3.3: Determine, through investigation using a variety of tools, properties of the circle associated with chords, central angles, inscribed angles, and tangents |