Will this help with my child's Grade 12 math homework?

Yes. StudyPug covers every MCT4C strand, so your child can find step-by-step explanations for the exact topic causing trouble, work through practice problems, and build the skills needed to complete their homework with confidence.

How long are the video lessons?

Most video lessons run between 5 and 15 minutes, keeping each concept focused and easy to revisit. Your child can pause, rewind, and rewatch as many times as needed until the topic clicks.

Is there a provincial test for Grade 12 math in Ontario?

MCT4C is a College Preparation course and is not one of the EQAO assessment years. EQAO assessments in Ontario cover Grades 3, 6, and 9, and the OSSLT at Grade 10, so Grade 12 students are not assessed through EQAO.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and computers, so your child can practice MCT4C topics at home, on the bus, or anywhere else. No app download is required - just open a browser and start learning.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can explore the content before committing. If you subscribe and are not satisfied, a 30-day money-back guarantee means you can get a full refund - no questions asked.

ON Grade 12 Math Curriculum

Support your child through MCT4C with lessons and practice problems covering every strand in the Ontario Grade 12 Mathematics for College Technology curriculum.

ON Grade 12 Math Curriculum

OE_IDExpectationsStudyPug Topic

ON.OE.12CT.A1.1Determine, 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
- Graphing exponential functions
- Graphing transformations of exponential functions
ON.OE.12CT.A1.2Solve simple exponential equations numerically and graphically, with technology, and recognize that the solutions may not be exact
- Solving exponential equations with logarithms
ON.OE.12CT.A1.4Pose 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
- Exponential growth and decay by a factor
- Exponential decay: Half-life
- Exponential growth and decay by percentage
- Finance: Compound interest
- Continuous growth and decay
ON.OE.12CT.A2.1Simplify algebraic expressions containing integer and rational exponents using the laws of exponents
- Quotient rule of exponents
- Power of a product rule
- Power of a quotient rule
- Power of a power rule
- Negative exponent rule
- Combining the exponent rules
- Product rule of exponents
- Exponents: Product rule (a^x)(a^y) = a^(x+y)
- Exponents: Division rule: a^x / a^y = a^(x-y)
- Exponents: Power rule: (a^x)^y = a^(xy)
ON.OE.12CT.A2.2Solve exponential equations in one variable by determining a common base
- Solving exponential equations using exponent rules
ON.OE.12CT.A2.3Recognize 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
- What is a logarithm?
- Converting from logarithmic form to exponential form
- Evaluating logarithms without a calculator
ON.OE.12CT.A2.4Determine, with technology, the approximate logarithm of a number to any base, including base 10
- Common logarithms
- Natural log: ln
ON.OE.12CT.A2.5Make connections between related logarithmic and exponential equations, and solve simple exponential equations by rewriting them in logarithmic form
- Evaluating logarithms using change-of-base formula
- Converting from exponential form to logarithmic form
- Product rule of logarithms
ON.OE.12CT.A2.6Pose 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
- Logarithmic scale: Richter scale (earthquake)
- Logarithmic scale: pH scale
- Logarithmic scale: dB scale
ON.OE.12CT.B1.1Recognize 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
- What is a polynomial?
- Polynomial components
ON.OE.12CT.B1.2Compare, through investigation using graphing technology, the graphical and algebraic representations of polynomial functions
- Polynomial functions
ON.OE.12CT.B1.3Describe key features of the graphs of polynomial functions
- Characteristics of polynomial graphs
- Determining the equation of a polynomial function
ON.OE.12CT.B1.4Distinguish 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
- Applications of polynomial functions
ON.OE.12CT.B1.5Substitute into and evaluate polynomial functions expressed in function notation, including functions arising from real-world applications
- Function notation (advanced)
- Function notation
ON.OE.12CT.B1.6Pose 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
- Applications of polynomials
ON.OE.12CT.B1.7Recognize, 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
- Domain and range of a function
ON.OE.12CT.B2.1Factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies
- Factor by taking out the greatest common factor
- Factor by grouping
- Factoring difference of squares: $x^2 - y^2$
- Factoring trinomials
- Factoring difference of cubes
- Factoring sum of cubes
ON.OE.12CT.B2.2Make 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
- Factor theorem
- Multiplicities of polynomials
- Imaginary zeros of polynomials
ON.OE.12CT.B2.3Determine, 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
- Fundamental theorem of algebra
ON.OE.12CT.B3.1Solve polynomial equations in one variable, of degree no higher than four, by selecting and applying strategies, and verify solutions using technology
- Descartes' rule of signs
ON.OE.12CT.B3.2Solve problems algebraically that involve polynomial functions and equations of degree no higher than four, including those arising from real-world applications
- Solving polynomial inequalities
ON.OE.12CT.B3.3Identify and explain the roles of constants and variables in a given formula
- Applications of linear equations
- Evaluating algebraic expressions
ON.OE.12CT.B3.4Expand and simplify polynomial expressions involving more than one variable, including expressions arising from real-world applications
- Multiplying monomial by monomial
- Multiplying monomial by binomial
- Multiplying binomial by binomial
- Multiplying polynomial by polynomial
ON.OE.12CT.B3.5Solve equations of the form x^n = a using rational exponents
- Convert between radicals and rational exponents
- Exponents: Rational exponents
ON.OE.12CT.B3.6Determine 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
- Solving literal equations
ON.OE.12CT.B3.7Make connections between formulas and linear, quadratic, and exponential functions, using a variety of tools and strategies
- Relationship between two variables
ON.OE.12CT.B3.8Solve multi-step problems requiring formulas arising from real-world applications
- Understand relations between x- and y-intercepts
ON.OE.12CT.C1.1Determine the exact values of the sine, cosine, and tangent of the special angles 0Â°, 30Â°, 45Â°, 60Â°, 90Â°, and their multiples
- Find the exact value of trigonometric ratios
ON.OE.12CT.C1.2Determine the values of the sine, cosine, and tangent of angles from 0Â° to 360Â°, through investigation using a variety of tools and strategies
- ASTC rule in trigonometry (All Students Take Calculus)
ON.OE.12CT.C1.3Determine the measures of two angles from 0Â° to 360Â° for which the value of a given trigonometric ratio is the same
- Unit circle
ON.OE.12CT.C1.4Solve 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
- Use sine ratio to calculate angles and sides (Sin = o / h)
- Use cosine ratio to calculate angles and sides (Cos = a / h)
- Combination of SohCahToa questions
- Use tangent ratio to calculate angles and sides (Tan = o / a)
ON.OE.12CT.C1.5Solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law and the cosine law
- Law of sines
- Law of cosines
- Applications of the sine law and cosine law
ON.OE.12CT.C2.1Make 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 0Â° to 360Â° and the corresponding sine ratios or cosine ratios
- Sine graph: y = sin x
- Cosine graph: y = cos x
ON.OE.12CT.C2.3Determine, through investigation using technology, the roles of the parameters d and c in functions of the form y = sin (x â€“ d) + c and y = cos (x â€“ 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
- Graphing transformations of trigonometric functions
ON.OE.12CT.C2.6Represent a sinusoidal function with an equation, given its graph or its properties
- Determining trigonometric functions given their graphs
ON.OE.12CT.C3.1Collect 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
- Ferris wheel trig problems
- Tides and water depth trig problems
- Spring (simple harmonic motion) trig problems
ON.OE.12CT.D1.1Recognize a vector as a quantity with both magnitude and direction, and identify, gather, and interpret information about real-world applications of vectors
- Introduction to vectors
ON.OE.12CT.D1.2Represent 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
- Magnitude of a vector
ON.OE.12CT.D1.3Resolve a vector represented as a directed line segment into its vertical and horizontal components
- Direction angle of a vector
ON.OE.12CT.D1.4Represent a vector as a directed line segment, given its vertical and horizontal components
- Scalar multiplication of vectors
ON.OE.12CT.D1.5Determine, through investigation using a variety of tools and strategies, the sum or difference of two vectors
- Equivalent vectors
- Adding and subtracting vectors in component form
- Operations on vectors in magnitude and direction form
ON.OE.12CT.D1.6Solve problems involving the addition and subtraction of vectors, including problems arising from real-world applications
- Unit vector
- Word problems on vectors
ON.OE.12CT.D2.2Perform required conversions between the imperial system and the metric system using a variety of tools, as necessary within applications
- Conversions between metric and imperial systems
- Conversions involving squares and cubic
ON.OE.12CT.D2.3Solve problems involving the areas of rectangles, parallelograms, trapezoids, triangles, and circles, and of related composite shapes, in situations arising from real-world applications
- Surface area of 3-dimensional shapes
ON.OE.12CT.D2.4Solve 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
- Surface area and volume of prisms
- Surface area and volume of pyramids
- Surface area and volume of cylinders
- Surface area and volume of cones
- Surface area and volume of spheres
ON.OE.12CT.D3.1Recognize and describe arcs, tangents, secants, chords, segments, sectors, central angles, and inscribed angles of circles, and some of their real-world applications
- Circles and circumference
- Arcs of a circle
- Areas and sectors of circles
ON.OE.12CT.D3.2Determine the length of an arc and the area of a sector or segment of a circle, and solve related problems
- Radian measure and arc length
ON.OE.12CT.D3.3Determine, through investigation using a variety of tools, properties of the circle associated with chords, central angles, inscribed angles, and tangents
- Angles in a circle

Grade 12 Mathematics for College Technology (MCT4C)

About Grade 12 Ontario math

Ontario follows The Ontario Curriculum, organized into strands that build on one another across the grade. MCT4C covers exponential and logarithmic functions, polynomial functions, applications of geometry, trigonometric functions, and vectors. StudyPug provides step-by-step lessons and practice problems aligned to every strand, giving students the support they need to keep pace with what their teacher is covering in class.

Strands: exponential and logarithmic functions, polynomial functions, trigonometric functions, vectors, and applications of geometry
Step-by-step lessons and worked examples for every MCT4C topic
Practice problems with guided solutions to build confidence before tests
Content aligned to The Ontario Curriculum for Grade 12 College Preparation math

Curriculum topics by strand

Find lessons and practice problems for every MCT4C strand, aligned to The Ontario Curriculum.

Topic includes:

Practice

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OE_ID

Expectations

StudyPug Topic

Ontario Grade 12 Math Topics

Exponential Functions: Investigating graphs by changing the base and sign of the exponent, solving exponential equations numerically, graphically, and algebraically by finding a common base, and modelling real-world applications with exponential equations.
Logarithmic Functions: Recognizing logarithms as inverse operations of exponentiation, evaluating logarithmic expressions, connecting logarithmic and exponential forms, and solving applied problems by rewriting equations in logarithmic form.
Polynomial Functions: Identifying and comparing polynomial functions, describing key graph features, factoring polynomial expressions of degree up to four, determining real roots, and solving polynomial equations arising from real-world applications.
Applications of Geometry: Converting between imperial and metric units, solving problems involving areas of plane figures and composite shapes, calculating volumes and surface areas of spheres, prisms, and cylinders, and applying properties of circles including arcs, chords, tangents, and inscribed angles.
Trigonometric Functions: Determining exact and approximate values of trigonometric ratios, solving problems in two and three dimensions using primary ratios, the sine law, and the cosine law, and graphing sinusoidal functions while identifying amplitude, period, and phase shift.
Vectors: Representing vectors as directed line segments, resolving vectors into horizontal and vertical components, and solving problems involving addition and subtraction of vectors from real-world contexts.
Formulas and Mathematical Modelling: Expanding and simplifying polynomial expressions with multiple variables, solving equations using rational exponents, applying formulas from real-world contexts, and connecting formulas to linear, quadratic, and exponential functions.

How StudyPug Helps Ontario Grade 12 Math Students

When a student gets stuck on a concept like factoring a degree-four polynomial or sketching a sinusoidal function, StudyPug lets them go back to the exact lesson they need, watch a clear explanation, and work through practice problems with step-by-step solutions. This means less frustration and more time building the skills that matter for college technology programs.

Because the content is organized by strand and aligned to The Ontario Curriculum, students can move through MCT4C topics in the same order their class does, or jump directly to a specific concept they need to review before a test or assignment.

Aligned to Ontario Grade 12 Math Curriculum

Every lesson and practice problem in StudyPug's MCT4C coverage is built to match The Ontario Curriculum expectations for Grade 12 Mathematics for College Technology, College Preparation. Whether the topic is vector operations, logarithmic equations, or circle properties, the content follows the same learning expectations Ontario teachers use in the classroom.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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