Nova Scotia · Grade 12
Pre-Calculus 12
Nova Scotia’s Grade 12 math course, from Trigonometry to Relations and Functions.
- Units
- 2
- Lessons
- 11
- Skills
- 26
- Provincial exam
- None
- Official curriculum
- Nova Scotia Department of Education and Early Childhood Development
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 7 skills
Trigonometry
The six trigonometric ratios
Exact and approximate values of the six ratios
I can find exact and approximate values of the six trig ratios.
Official code: T03
Finding the other ratios from one
I can find angles and the other ratios given one trig ratio.
Official code: T03
Graphing trigonometric functions
Graphing and characteristics of sine, cosine, and tangent
I can graph and describe the basic sine, cosine, and tangent functions.
Official code: T04
Transformations of trigonometric functions
I can transform trig functions and use them to model situations.
Official code: T04
Trigonometric equations
Solving trigonometric equations
I can solve first- and second-degree trigonometric equations.
Official code: T05
Trigonometric identities
Verifying and proving identities
I can verify and prove trigonometric identities.
Official code: T06
Sum, difference, and double-angle identities
I can use sum, difference, and double-angle identities.
Official code: T06
The official wording · 7 outcomes
- T03
- Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees
- 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
- 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
- T06
- sum or difference identities ▪ double-angle identities
Key ideas
The six ratios are sine, cosine, tangent and their reciprocals cosecant, secant, cotangent.
Sine and cosine oscillate between −1 and 1 with period 2π; tangent has period π and asymptotes.
A trig equation may have infinitely many solutions, repeating each period.
An identity holds for all permitted values; an equation holds only for some.
Exact values come from special angles and the unit circle.
Watch out for
- Taking the reciprocal of the angle instead of the ratio.
- Assigning an amplitude to the tangent function.
- Reporting only solutions in one period when a general solution is asked.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 19 skills
Relations and Functions
Operations and compositions of functions
Combining functions by operations
I can combine functions by adding, subtracting, multiplying, and dividing.
Official code: RF01
Composition of functions
I can compose functions and decompose a function into a composition.
Official code: RF01
Transformations of functions
Translations of functions
I can translate a function's graph horizontally and vertically.
Official code: RF02
Stretches of functions
I can stretch a function's graph horizontally and vertically.
Official code: RF03
Reflections of functions
I can reflect a function's graph in the axes and the line y = x.
Official code: RF05
Combining translations and stretches
I can apply combined translations and stretches to a function.
Official code: RF04
Inverses of relations
Finding the inverse of a relation
I can find the inverse of a relation graphically and algebraically.
Official code: RF06
When an inverse is a function
I can decide whether an inverse is a function and restrict a domain to make it one.
Official code: RF06
Logarithms
Understanding logarithms
I can convert between logarithmic and exponential form and evaluate logarithms.
Official code: RF07
The laws of logarithms
I can apply the product, quotient, and power laws of logarithms.
Official code: RF08
Exponential and logarithmic functions and equations
Graphing exponential functions
I can graph and analyze an exponential function.
Official code: RF09
Graphing logarithmic functions
I can graph and analyze a logarithmic function.
Official code: RF09
Solving exponential equations
I can solve exponential equations and growth/decay problems.
Official code: RF10
Solving logarithmic equations
I can solve logarithmic equations and logarithmic-scale problems.
Official code: RF10
Polynomial functions
Long and synthetic division of polynomials
I can divide a polynomial by a binomial and apply the remainder theorem.
Official code: RF11
Factoring with the factor theorem
I can factor a higher-degree polynomial using the factor theorem.
Official code: RF11
Graphing polynomial functions
I can graph a polynomial function and relate its zeros to the graph.
Official code: RF12
Radical and rational functions
Graphing radical functions
I can graph and analyze a radical function.
Official code: RF13
Graphing rational functions
I can graph and analyze a rational function.
Official code: RF14
The official wording · 19 outcomes
- RF01
- Demonstrate an understanding of operations on, and compositions of, functions
- 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
- 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
- RF09
- Graph and analyze exponential and logarithmic functions
- RF10
- Solve problems that involve exponential and logarithmic equations
- 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)
- 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)
Key ideas
Functions combine value-by-value: (f + g)(x) = f(x) + g(x).
Replacing y with y − k shifts the graph up by k; replacing x with x − h shifts right by h.
The inverse swaps the roles of x and y, reflecting the graph in y = x.
A logarithm is the inverse of an exponent: log_b x = y means b^y = x.
An exponential y = aˣ (a > 0) has a horizontal asymptote at y = 0.
Watch out for
- Combining functions but ignoring the shared domain.
- Shifting in the wrong direction for x − h (right, not left).
- Reflecting in an axis instead of the line y = x.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
Which course?
Nova Scotia has 4 math courses for Grade 12. Here they are side by side.
- Calculus 124 units · 42 skillsNo provincial examWhat it coversCalculus 12 — Rates of Change and the Derivative · Calculus 12 — Differentiation Rules and Applications · Calculus 12 — Curve Analysis, Tangents and Antiderivatives · Calculus 12 — Integration and Area
- Mathematics 124 units · 30 skillsNo provincial examWhat it coversFinancial Mathematics · Logical Reasoning · Probability · Relations and Functions
- Mathematics at Work 125 units · 22 skillsNo provincial examWhat it coversGeometry · Number · Algebra · Statistics · Probability
- Pre-Calculus 12This course2 units · 26 skillsNo provincial examWhat it coversTrigonometry · Relations and Functions
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Nova Scotia’s own curriculum for Pre-Calculus 12.
Study it in MapleMind
MapleMind teaches Pre-Calculus 12 one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Pre-Calculus 12 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 23
- Fillable fields
- 1,261
- Price
- $4.99
Questions about Pre-Calculus 12
What is Pre-Calculus 12?
Nova Scotia’s Grade 12 math course: 2 units and 26 skills, from Trigonometry to Relations and Functions.
What units are in Pre-Calculus 12?
1. Trigonometry and 2. Relations and Functions.
Is there a provincial exam for Pre-Calculus 12?
No. Nova Scotia gives no provincial exam for Pre-Calculus 12.
Can MapleMind help with Pre-Calculus 12?
Yes. MapleMind teaches every skill of Pre-Calculus 12, step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
Get ready for Pre-Calculus 12
Practise every skill of Pre-Calculus 12 in MapleMind, free with daily limits.
