New Brunswick · Grade 12
Pre-Calculus 120B
New Brunswick’s Grade 12 math course, from Relations and Functions to Limits.
- Units
- 3
- Lessons
- 9
- Skills
- 30
- Provincial exam
- None
- Official curriculum
- New Brunswick Department of Education and Early Childhood Development
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 16 skills
Relations and Functions
Arithmetic sequences and series
Arithmetic sequences
I can find any term of an arithmetic sequence.
Official code: RF1
Arithmetic series
I can find the sum of an arithmetic series.
Official code: RF1
Geometric sequences and series
Geometric sequences
I can find any term of a geometric sequence.
Official code: RF2
Geometric and infinite geometric series
I can find the sum of a geometric series, including an infinite one.
Official code: RF2
Polynomials of higher degree
Factoring higher-degree polynomials
I can factor a polynomial of degree greater than 2.
Official code: RF3
Factoring sums and differences of cubes
I can factor cubes and use grouping to factor polynomials.
Official code: RF3
Graphing polynomial functions
I can sketch a polynomial function from its zeros and degree.
Official code: RF4
Analyzing polynomial characteristics
I can read the key characteristics of a polynomial from its graph.
Official code: RF4
Reciprocal and rational functions
Graphing reciprocal functions
I can graph the reciprocal of a linear or quadratic function.
Official code: RF5
Reciprocal of a quadratic function
I can graph the reciprocal of a quadratic function.
Official code: RF5
Graphing rational functions
I can graph a rational function and tell asymptotes from holes.
Official code: RF6
Solving rational equations
I can solve a rational equation and reject extraneous roots.
Official code: RF6
Operations on and composition of functions
Operations on functions
I can add, subtract, multiply, and divide functions.
Official code: RF7
Composition of functions
I can compose two functions and evaluate the result.
Official code: RF7
A function toolkit: comparing function types
I can compare the main function families and their compositions.
Official code: RF8
Choosing a function to model a situation
I can pick the right function family for a model and decompose a composition.
Official code: RF8
The official wording · 16 outcomes
- RF1
- Analyze arithmetic sequences and series to solve problems
- RF1
- Analyze arithmetic sequences and series to solve problems
- RF2
- Analyze geometric sequences and series to solve problems
- RF2
- Analyze geometric sequences and series to solve problems
- RF3
- understanding of factoring polynomials of degree greater than 2
- RF3
- understanding of factoring polynomials of degree greater than 2
- RF4
- Graph and analyze polynomial functions (limited to polynomial functions of degree ≤5)
- RF4
- Graph and analyze polynomial functions (limited to polynomial functions of degree ≤5)
- RF5
- Graph and analyze reciprocal functions
- RF5
- Graph and analyze reciprocal functions
- RF6
- Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)
- RF6
- Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)
- RF7
- understanding of operations on, and compositions of, functions
- RF7
- understanding of operations on, and compositions of, functions
- RF8
- Assemble a function toolkit comparing various types of functions and compositions of them
- RF8
- Assemble a function toolkit comparing various types of functions and compositions of them
Key ideas
An arithmetic sequence adds a constant common difference d each step.
A geometric sequence multiplies by a constant common ratio r each step.
The factor theorem: (x − a) is a factor when P(a) = 0.
Where f(x) = 0, the reciprocal y = 1/f(x) has a vertical asymptote.
(f ± g)(x) = f(x) ± g(x), combined pointwise.
Watch out for
- Using n instead of (n − 1) in the general term.
- Using a common difference instead of a ratio.
- Testing candidates that do not divide the constant term.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 7 skills
Permutations, Combinations and Binomial Theorem
Counting principle and permutations
The fundamental counting principle
I can count outcomes by multiplying independent choices.
Official code: PCB1
Permutations of n objects taken r at a time
I can count ordered arrangements with permutations.
Official code: PCB2
Permutations with repetition and identical objects
I can count arrangements with identical objects or with repetition.
Official code: PCB2
Combinations and the binomial theorem
Combinations of n objects taken r at a time
I can count unordered selections with combinations.
Official code: PCB3
Combination problems with cases and conditions
I can solve combination problems that involve cases or conditions.
Official code: PCB3
Expanding binomials with the binomial theorem
I can expand (a + b)ⁿ with the binomial theorem.
Official code: PCB4
Finding a specific term of a binomial expansion
I can find one specific term of a binomial expansion.
Official code: PCB4
The official wording · 7 outcomes
- PCB1
- Apply the fundamental counting principle to solve problems
- PCB2
- Determine the number of permutations of n elements taken r at a time to solve problems
- PCB2
- Determine the number of permutations of n elements taken r at a time to solve problems
- PCB3
- Determine the number of combinations of n different elements taken r at a time to solve problems
- PCB3
- Determine the number of combinations of n different elements taken r at a time to solve problems
- PCB4
- Expand powers of a binomial in a variety of ways, including using the binomial theorem
- PCB4
- Expand powers of a binomial in a variety of ways, including using the binomial theorem
Key ideas
If one step has m outcomes and the next has n, together they have m·n outcomes.
A combination is an unordered selection; ₙCᵣ = n!/(r!(n − r)!).
The principle extends to any number of independent steps.
Order does not matter — {A, B, C} is one combination.
Restrictions (no repeats, a fixed first choice) change the count at each step.
Watch out for
- Adding the choices instead of multiplying them.
- Using a permutation when order does not matter.
- Ignoring a no-repeats restriction that reduces later choices.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 7 skills
Limits
The limit of a function at a point
Limits from a graph
I can find a limit by reading a graph.
Official code: L1
Limits analytically
I can compute a limit algebraically.
Official code: L1
One-sided limits
I can find one-sided limits and decide if the two-sided limit exists.
Official code: L2
Continuity and limits at infinity
Continuity of a function
I can decide where a function is continuous and name its discontinuities.
Official code: L3
Continuity on an interval and making a function continuous
I can decide continuity on an interval and repair a discontinuity.
Official code: L3
Limits involving infinity
I can evaluate limits at infinity and infinite limits.
Official code: L4
Indeterminate forms at infinity
I can resolve an indeterminate form in a limit at infinity.
Official code: L4
The official wording · 7 outcomes
- L1
- Determine the limit of a function at a point both graphically and analytically
- L1
- Determine the limit of a function at a point both graphically and analytically
- L2
- Explore one-sided limits graphically and analytically
- L3
- Analyze the continuity of a function
- L3
- Analyze the continuity of a function
- L4
- Explore limits which involve infinity
- L4
- Explore limits which involve infinity
Key ideas
lim(x→a) f(x) is the value the graph approaches near x = a.
A function is continuous at a if f(a) exists, the limit exists, and they are equal.
The limit can exist even where the function is undefined or has a hole.
A removable discontinuity is a hole; a jump has unequal one-sided limits.
The limit describes approach, not the value f(a) itself.
Watch out for
- Reporting f(a) instead of the value approached.
- Calling a function continuous where the limit and f(a) differ.
- Assuming a limit fails to exist just because there is a hole.
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?
New Brunswick has 5 math courses for Grade 12. Here they are side by side.
- Calculus 1201 units · 18 skillsNo provincial examWhat it coversCalculus
- Financial and Workplace Mathematics 1207 units · 30 skillsNo provincial examWhat it coversMeasurement · Geometry · Number · Algebra · Statistics · Probability · Mathematical Research Project
- Foundations of Mathematics 1204 units · 30 skillsNo provincial examWhat it coversStatistics · Logical Reasoning · Probability · Relations and Functions
- Pre-Calculus 120A2 units · 30 skillsNo provincial examWhat it coversRelations and Functions · Trigonometry
- Pre-Calculus 120BThis course3 units · 30 skillsNo provincial examWhat it coversRelations and Functions · Permutations, Combinations and Binomial Theorem · Limits
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 New Brunswick’s own curriculum for Pre-Calculus 120B.
Study it in MapleMind
MapleMind teaches Pre-Calculus 120B 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 120B 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
- 25
- Fillable fields
- 1,364
- Price
- $4.99
Questions about Pre-Calculus 120B
What is Pre-Calculus 120B?
New Brunswick’s Grade 12 math course: 3 units and 30 skills, from Relations and Functions to Limits.
What units are in Pre-Calculus 120B?
1. Relations and Functions, 2. Permutations, Combinations and Binomial Theorem and 3. Limits.
Is there a provincial exam for Pre-Calculus 120B?
No. New Brunswick gives no provincial exam for Pre-Calculus 120B.
Can MapleMind help with Pre-Calculus 120B?
Yes. MapleMind teaches every skill of Pre-Calculus 120B, 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 120B
Practise every skill of Pre-Calculus 120B in MapleMind, free with daily limits.
