Get help with Pre-Calculus 12
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The official Nova Scotia Pre-Calculus 12 curriculum
Nova Scotia defines Pre-Calculus 12 by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Nova Scotia's official curriculumRead it on the government site — curriculum.novascotia.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand T | 4 | Trigonometry |
| Strand RF | 14 | Relations and Functions |
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How MapleMind teaches Pre-Calculus 12 — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1TrigonometryOfficial strand · Strand T
The six trigonometric ratios in radians and degrees, graphing and analyzing trigonometric functions, solving trigonometric equations, and proving trigonometric identities.
The six trigonometric ratios
- Exact and approximate values of the six ratiosT03 — Determine exact and approximate values of the six trigonometric ratios for angles expressed in radians and degrees.
- Finding the other ratios from oneT03 — Determine the measures of angles in a domain given a trigonometric ratio and find the exact values of the other ratios given one ratio, and solve problems.
Graphing trigonometric functions
- Graphing and characteristics of sine, cosine, and tangentT04 — Sketch and determine the characteristics — amplitude, period, domain, range, asymptotes, and zeros — of the graphs of sine, cosine, and tangent functions.
- Transformations of trigonometric functionsT04 — Determine how the parameters a, b, c, and d transform sine and cosine graphs, sketch transformed graphs, and model a situation with a trigonometric function.
Trigonometric equations
- Solving trigonometric equationsT05 — Solve first- and second-degree trigonometric equations algebraically and graphically with the domain expressed in degrees and radians, including general solutions.
Trigonometric identities
- Verifying and proving identitiesT06 — Distinguish an identity from an equation, verify identities numerically and graphically, and prove trigonometric identities algebraically using reciprocal, quotient, and Pythagorean identities.
- Sum, difference, and double-angle identitiesT06 — Apply the sum, difference, and double-angle identities to determine the exact value of a trigonometric ratio.
The official wording — 4 outcomes in this unit
- T03
Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees
- T04
Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems
- T05
Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians
- T06
Prove trigonometric identities, using: ▪ reciprocal identities ▪ quotient identities ▪ Pythagorean identities
Unit 2Relations and FunctionsOfficial strand · Strand RF
Operations and compositions of functions, transformations and inverses of functions, logarithms and exponential/logarithmic functions and equations, and polynomial, radical, and rational functions.
Operations and compositions of functions
- Combining functions by operationsRF01 — Determine the sum, difference, product, and quotient of functions from their graphs or equations and find the domain and range of the result.
- Composition of functionsRF01 — Determine and sketch the composition of functions, evaluate compositions at a point, and decompose a function into a composition.
Transformations of functions
- Translations of functionsRF02 — Determine the effects of horizontal and vertical translations on the graphs of functions and their equations, and sketch and write translated functions.
- Stretches of functionsRF03 — Determine the effects of horizontal and vertical stretches on the graphs of functions and their equations, and sketch and write stretched functions.
- Reflections of functionsRF05 — Determine the effects of reflections in the x-axis, y-axis, and the line y = x on graphs of functions, and sketch and write reflected functions.
- Combining translations and stretchesRF04 — Apply combined translations and stretches to the graphs and equations of functions.
Inverses of relations
- Finding the inverse of a relationRF06 — Sketch and determine the inverse of a relation graphically and algebraically, using the reflection in the line y = x and the coordinate swap.
- When an inverse is a functionRF06 — Determine whether a relation and its inverse are functions and find restrictions on a domain so that an inverse is a function.
Logarithms
- Understanding logarithmsRF07 — Explain the relationship between logarithms and exponents, convert between logarithmic and exponential form, and evaluate or estimate logarithms.
- The laws of logarithmsRF08 — Develop, derive, and apply the product, quotient, and power laws of logarithms to rewrite and evaluate logarithmic expressions.
Exponential and logarithmic functions and equations
- Graphing exponential functionsRF09 — Graph and analyze exponential functions, including domain, range, horizontal asymptote, and intercepts, and apply transformations.
- Graphing logarithmic functionsRF09 — Graph and analyze logarithmic functions, including domain, range, vertical asymptote, and intercepts, and show they are inverses of exponential functions.
- Solving exponential equationsRF10 — Solve exponential equations by matching bases or taking logarithms, and solve problems involving exponential growth and decay.
- Solving logarithmic equationsRF10 — Solve logarithmic equations, verify solutions and reject extraneous roots, and solve problems involving logarithmic scales such as pH and the Richter scale.
Polynomial functions
- Long and synthetic division of polynomialsRF11 — Divide a polynomial by a binomial of the form x − a using long division and synthetic division and relate the remainder to the remainder theorem.
- Factoring with the factor theoremRF11 — Use the factor theorem to express a polynomial of degree greater than 2 as a product of factors, relating factors to zeros.
- Graphing polynomial functionsRF12 — Graph and analyze polynomial functions of degree at most 5, relating zeros, roots, x-intercepts, and multiplicity to the graph.
Radical and rational functions
- Graphing radical functionsRF13 — Graph and analyze radical functions involving one radical, applying transformations to the square-root parent function and stating domain and range.
- Graphing rational functionsRF14 — Graph and analyze rational functions with monomial, binomial, or trinomial numerators and denominators, identifying asymptotes and holes.
The official wording — 14 outcomes in this unit
- RF01
Demonstrate an understanding of operations on, and compositions of, functions
- RF02
Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations
- RF03
Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations
- RF05
Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections in the: x-axis, y-axis, and the line
- RF04
Apply translations and stretches to the graphs and equations of functions
- RF06
Demonstrate an understanding of inverses of relations
- RF07
Demonstrate an understanding of logarithms
- RF08
Demonstrate an understanding of the product, quotient and power laws of logarithms
- RF09
Graph and analyze exponential and logarithmic functions
- RF10
Solve problems that involve exponential and logarithmic equations
- RF11
Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients)
- RF12
Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5)
- RF13
Graph and analyze radical functions (limited to functions involving one radical)
- RF14
Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)
Printable workbook · A keepsake of the year
A Pre-Calculus 12 workbook worth keeping
Built from the same official curriculum as this page. Before and after each skill above, your student colours in how sure they feel — so the two of you can see, on one page, what's clicking and what needs another look. It's a quiet way to follow how the year is really going.
By June it's full of their own handwriting: units worked through, confidence grown, a mid-year check-in, notes from parent-teacher night, and a certificate at the end. Less a worksheet, more a record of the year worth keeping on the shelf.
Instant download · see every page, reviews and the full description · five or more workbooks are $2.99 each
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Common questions
Can MapleMind help me with Pre-Calculus 12?
Yes. MapleMind's AI tutor covers all 26 skills in Nova Scotia's Pre-Calculus 12 — you pick the exact skill, and the tutor teaches it step by step: a short lesson, a worked example, solving together, then a skill check to show it stuck.
Is MapleMind aligned to Nova Scotia's official curriculum?
Yes. Every skill in this course maps to an official outcome code from Nova Scotia's Grade 12 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
What does MapleMind cost?
It's free to start — 5 tutoring chats and a practice quiz every day, no credit card. A Pro subscription ($9.99/month or $49.99/year CAD, 7-day free trial) unlocks unlimited tutoring, practice, and exam simulations.
What if I'm stuck on just one topic?
That's the point of skill-level tutoring: open Pre-Calculus 12 in the app, tap the exact skill from the list on this page, and the tutor teaches just that — no wading through lessons you don't need.
Does MapleMind work in French or other languages?
Yes — 14 languages, including French. Both the app and the tutor's explanations switch to the language you choose.
Where can I see the official Nova Scotia curriculum for Pre-Calculus 12?
The official source is linked on this page — Nova Scotia's official curriculum. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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