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

Yes. StudyPug covers every strand in Manitoba's Grade 12 Pre-Calculus Mathematics (40S) course, so your child can find step-by-step help for the exact topics assigned in class and work through practice problems at their own pace.

How long are the video lessons?

Most video lessons run between 5 and 15 minutes, focusing on one concept at a time. Your child can pause, rewind, and rewatch as often as needed, making it easy to fit study sessions into any schedule.

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

Manitoba administers Provincial Assessments, and Grade 12 students may encounter province-wide assessments depending on the course. Check with your child's school or the Manitoba government for the most current assessment schedule for this course.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and desktop computers, so your child can study at home, at school, or on the go without needing to install any additional software.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can explore the content before committing. A 30-day money-back guarantee is also available, so there is no risk in getting started.

MB Grade 12 Math Curriculum

Help your child succeed in Grade 12 Pre-Calculus Mathematics (40S) with lessons and practice problems built around what Manitoba schools teach at this level.

MB Grade 12 Math Curriculum

GO_IDOutcomeStudyPug Topic

MB.GO.12P.T.1Demonstrate an understanding of angles in standard position, expressed in degrees and radians
- Angle in standard position
- Coterminal angles
- Reference angle
- Converting between degrees and radians
- Trigonometric ratios of angles in radians
MB.GO.12P.T.2Develop and apply the equation of the unit circle
- Unit circle
MB.GO.12P.T.3Solve problems using the six trigonometric ratios for angles expressed in radians and degrees
- Find the exact value of trigonometric ratios
- ASTC rule in trigonometry (All Students Take Calculus)
- Radian measure and arc length
MB.GO.12P.T.4Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems
- Sine graph: y = sin x
- Cosine graph: y = cos x
- Tangent graph: y = tan x
- Cotangent graph: y = cot x
- Secant graph: y = sec x
- Cosecant graph: y = csc x
- Graphing transformations of trigonometric functions
- Determining trigonometric functions given their graphs
MB.GO.12P.T.5Solve algebraically and graphically first and second degree trigonometric equations
- Solving first degree trigonometric equations
- Solving second degree trigonometric equations
- Solving trigonometric equations involving multiple angles
- Determining non-permissible values for trig expressions
- Solving trigonometric equations using pythagorean identities
- Solving trigonometric equations using sum and difference identities
- Solving trigonometric equations using double-angle identities
MB.GO.12P.T.6Prove trigonometric identities using various identities
- Quotient identities and reciprocal identities
- Pythagorean identities
- Sum and difference identities
- Double-angle identities
- Cofunction identities
MB.GO.12P.P.1Apply the fundamental counting principle to solve problems
- Fundamental counting principle
- Path counting problems
MB.GO.12P.P.2Determine the number of permutations of n elements taken r at a time to solve problems
- Factorial notation
- Permutations
MB.GO.12P.P.3Determine the number of combinations of n different elements taken r at a time to solve problems
- Combinations
- Problems involving both permutations and combinations
- Permutation vs. Combination
MB.GO.12P.P.4Expand powers of a binomial using the binomial theorem
- Pascal's triangle
- Binomial theorem
MB.GO.12P.R.1Demonstrate an understanding of operations on and compositions of functions
- Function notation (advanced)
- Composite functions
- Adding functions
- Subtracting functions
- Multiplying functions
- Dividing functions
- Operations with functions
- Inequalities of combined functions
- Difference quotient: applications of functions
MB.GO.12P.R.2Demonstrate an understanding of horizontal and vertical translations on function graphs and equations
- Transformations of functions: Horizontal translations
- Transformations of functions: Vertical translations
MB.GO.12P.R.3Demonstrate an understanding of horizontal and vertical compressions and stretches on function graphs
- Transformations of functions: Horizontal stretches
- Transformations of functions: Vertical stretches
MB.GO.12P.R.4Apply translations, compressions and stretches to the graphs and equations of functions
- Combining transformations of functions
- Even and odd functions
MB.GO.12P.R.5Demonstrate an understanding of reflections on function graphs and equations
- Reflection across the y-axis: y = f(-x)
- Reflection across the x-axis: y = -f(x)
MB.GO.12P.R.6Demonstrate an understanding of inverses of relations
- Inverse functions
- One to one functions
- Finding inverse trigonometric function from its graph
- Evaluating inverse trigonometric functions
- Finding inverse reciprocal trigonometric function from its graph
- Inverse reciprocal trigonometric function: finding the exact value
MB.GO.12P.R.7Demonstrate an understanding of logarithms
- What is a logarithm?
- Converting from logarithmic form to exponential form
- Evaluating logarithms without a calculator
- Common logarithms
- Natural log: ln
- Evaluating logarithms using change-of-base formula
MB.GO.12P.R.8Demonstrate an understanding of the product, quotient and power laws of logarithms
- Product rule of logarithms
- Quotient rule of logarithms
- Combining product rule and quotient rule in logarithms
- Power rule of logarithms
- Evaluating logarithms using logarithm rules
MB.GO.12P.R.9Graph and analyze exponential and logarithmic functions
- Graphing exponential functions
- Graphing transformations of exponential functions
- Finding an exponential function given its graph
- Graphing logarithmic functions
- Graphing transformations of logarithmic functions
- Finding a logarithmic function given its graph
MB.GO.12P.R.10Solve problems that involve exponential and logarithmic equations
- Solving logarithmic equations
- Converting from exponential form to logarithmic form
- Solving exponential equations with logarithms
- Solving exponential equations using exponent rules
MB.GO.12P.R.11Demonstrate an understanding of factoring polynomials of degree greater than 2
- Polynomial long division
- Polynomial synthetic division
- Remainder theorem
- Factor theorem
- Rational zero theorem
- Factor by taking out the greatest common factor
- Factor by grouping
- Factoring difference of squares: $x^2 - y^2$
- Factoring trinomials
- Fundamental theorem of algebra
- Factoring difference of cubes
- Factoring sum of cubes
- Descartes' rule of signs
MB.GO.12P.R.12Graph and analyze polynomial functions
- Polynomial functions
- Characteristics of polynomial graphs
- Determining the equation of a polynomial function
- Applications of polynomial functions
- Characteristics of quadratic functions
- Transformations of quadratic functions
- Quadratic function in general form: y = ax^2 + bx + c
- Graphing quadratic functions: General form VS. Vertex form
- Finding the quadratic functions for given parabolas
- Multiplicities of polynomials
- Imaginary zeros of polynomials
- Solving polynomial inequalities
MB.GO.12P.R.13Graph and analyze radical functions
- Radical functions and transformations
- Square root of a function
- Solving radical equations
- Operations with radicals
- Basic radical functions
MB.GO.12P.R.14Graph and analyze rational functions
- What is a rational function?
- Point of discontinuity
- Slant asymptote
- Solving rational equations
- Solving rational inequalities
- Graphing reciprocals of linear functions
- Vertical asymptote
- Horizontal asymptote
- Graphs of rational functions
- Graphing reciprocals of quadratic functions

Grade 12 Pre-Calculus Mathematics (40S)

About Grade 12 Manitoba math

Manitoba follows the Manitoba Curriculum Framework of Outcomes, which organizes Grade 12 Pre-Calculus Mathematics (40S) into strands covering topics such as trigonometry, relations and functions, permutations and combinations, and conics. Students at this level build the reasoning and algebraic skills needed for post-secondary mathematics. StudyPug provides step-by-step lessons, worked examples, and practice problems aligned to every strand of this course.

Strands: trigonometry, relations and functions, permutations and combinations, and conics
Step-by-step lessons and worked examples for every strand
Practice problems with guided solutions aligned to the Manitoba Curriculum Framework of Outcomes
Accessible on any device, any time, at your child's own pace

Curriculum topics by strand

Find lessons and practice problems for every strand in Grade 12 Pre-Calculus Mathematics (40S), aligned to the Manitoba Curriculum Framework of Outcomes.

Topic includes:

Practice

Video

Quiz

GO_ID

Outcome

StudyPug Topic

Manitoba Grade 12 Math Topics

Trigonometry: angles, identities, equations, and applications of trigonometric functions.
Relations and Functions: polynomial, rational, radical, exponential, logarithmic, and trigonometric functions and their graphs.
Permutations and Combinations: counting principles, permutations, combinations, and the binomial theorem.
Conics: circles, parabolas, ellipses, and hyperbolas and their equations in standard form.

How StudyPug Helps Manitoba Grade 12 Math Students

When a student gets stuck on a Pre-Calculus concept, StudyPug provides clear, step-by-step lessons that break each topic down into manageable parts. Practice problems with full solutions let students check their understanding and build confidence before tests.

Every lesson is available at any time, so students can revisit difficult strands like trigonometric identities or conic sections as many times as they need, working at a pace that fits their schedule.

Aligned to Manitoba Grade 12 Math Curriculum

All StudyPug content for Grade 12 Pre-Calculus Mathematics (40S) is organized to match the Manitoba Curriculum Framework of Outcomes, so students and parents can trust that the lessons and practice problems reflect exactly what is taught in Manitoba classrooms.

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Jump into practice questions for every MB Grade 12 topic - with instant feedback and step-by-step video solutions when you get stuck.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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