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Master Grade 12 Math MCT4C

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Exponential functions made no sense. The video lessons broke down logs and bases perfectly. Went from C to A- in 6 weeks.

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Find the right Ontario Grade 12 course

Grade 12 Advanced Functions, University Preparation (MHF4U)

Grade 12 Calculus and Vectors, University Preparation (MCV4U)

Grade 12 Mathematics of Data Management, University Preparation (MDM4U)

Grade 12 Mathematics for College Technology, College Preparation (MCT4C)

Grade 12 Foundations for College Mathematics, College Preparation (MAP4C)

Grade 12 Mathematics for Work and Everyday Life, Workplace Preparation (MEL4E)

Grade 12 Math MCT4C Help: Master Concepts FastHelp

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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.A2.2

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
Complete Ontario Grade 12 Mathematics for College Technology Coverage

MCT4C Lessons

102

Video Explanations

534

Practice Problems

1065

Ontario Standards

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Ontario Grade 12 Mathematics for College Technology, College Preparation (MCT4C) Math FAQ

We’ve got answers to some popular questions.

What are the main topics covered in Grade 1 math in Alberta?

Grade 1 math in Alberta covers counting to 100, basic addition and subtraction within 20, introduction to fractions (halves), shape recognition, and simple data representation through concrete graphs.

How can I help my child transition from kindergarten to Grade 1 math?

Encourage counting during daily activities, practice simple addition with objects, and explore shapes in your environment. Maintaining a positive attitude towards math is crucial for a smooth transition.

Are there specific math skills my child should master by the end of Grade 1?

By the end of Grade 1, children should confidently count to 100, add and subtract within 20, recognize basic shapes, understand the concept of half, and create simple concrete graphs.

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