Nova Scotia · Grade 11
Pre-Calculus 11
Nova Scotia’s Grade 11 math course, from Algebra and Number to Relations and Functions.
- Units
- 3
- Lessons
- 15
- Skills
- 28
- 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
Algebra and Number
Absolute value of real numbers
Understanding absolute value
I can interpret and compute absolute value as distance from zero.
Official code: AN01
Radicals and radical expressions
Simplifying and converting radical expressions
I can simplify radical expressions and convert between mixed and entire radicals.
Official code: AN02
Rationalizing denominators
I can rationalize a denominator containing a radical.
Official code: AN02
Radical equations
Solving radical equations
I can solve a radical equation and reject extraneous roots.
Official code: AN03
Rational expressions and equations
Equivalent forms of rational expressions
I can simplify rational expressions and state non-permissible values.
Official code: AN04
Operations on rational expressions
I can add, subtract, multiply, and divide rational expressions.
Official code: AN05
Solving rational equations
I can solve a rational equation and reject non-permissible solutions.
Official code: AN06
The official wording · 7 outcomes
- AN01
- Demonstrate an understanding of the absolute value of real numbers
- AN02
- Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands
- AN02
- Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands
- AN03
- Solve problems that involve radical equations (limited to square roots)
- AN04
- Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)
- AN05
- Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)
- AN06
- Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials)
Key ideas
The absolute value of a number is its distance from zero on the number line.
A radical simplifies by extracting perfect-power factors from the radicand.
Isolating the radical then squaring both sides removes the root.
A rational expression is a ratio of polynomials.
Absolute value is never negative.
Watch out for
- Thinking absolute value just removes a negative sign in every context.
- Adding unlike radicals as if they were like terms.
- Accepting every algebraic solution without checking it in the original equation.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 7 skills
Trigonometry
Angles in standard position
Sketching angles in standard position
I can sketch an angle in standard position and name its quadrant.
Official code: T01
Reference angles and reflections
I can find a reference angle and relate angles by reflection.
Official code: T01
Trig ratios for 0° to 360°
Trig ratios from a point on the terminal arm
I can find the trig ratios of an angle from a point on its terminal arm.
Official code: T02
Solving trigonometric equations and problems
I can solve a trig equation for angles from 0° to 360° and apply it.
Official code: T02
Radian measure
Radian measure and degree-radian conversion
I can convert between degrees and radians and sketch radian angles.
Official code: T03
Coterminal angles and arc length
I can find coterminal angles and relate radians to arc length.
Official code: T03
The unit circle
The equation of the unit circle
I can derive and apply the equation of the unit circle.
Official code: T04
The official wording · 7 outcomes
- T01
- Demonstrate an understanding of angles in standard position [0° to 360°]
- T01
- Demonstrate an understanding of angles in standard position [0° to 360°]
- T02
- Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position
- T02
- Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position
- T03
- Demonstrate an understanding of angles in standard position, expressed in degrees and radians
- T03
- Demonstrate an understanding of angles in standard position, expressed in degrees and radians
- T04
- Develop and apply the equation of the unit circle
Key ideas
An angle in standard position has its vertex at the origin and initial arm on the positive x-axis.
For a point (x, y) at distance r from the origin, sin θ = y/r, cos θ = x/r, tan θ = y/x.
One radian is the angle subtending an arc equal to the radius; 180° = π radians.
The unit circle has centre (0,0) and radius 1: x² + y² = 1.
The terminal arm is drawn by rotating counterclockwise for a positive angle.
Watch out for
- Confusing the terminal and initial arms.
- Ignoring the sign of x or y when computing a ratio.
- Using the wrong conversion factor direction.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 14 skills
Relations and Functions
Factoring polynomial expressions
Common factors and quadratic trinomials
I can factor out common factors and factor a quadratic trinomial.
Official code: RF01
Difference of squares
I can factor a difference of squares.
Official code: RF01
Quadratic-pattern factoring by substitution
I can factor an expression with a quadratic pattern using substitution.
Official code: RF01
Absolute value functions
Graphing absolute value functions
I can graph an absolute value function and write it in piecewise notation.
Official code: RF02
Solving absolute value equations
I can solve absolute value equations and problems.
Official code: RF02
Quadratic functions
Quadratic functions in vertex form
I can analyze a quadratic function in vertex form.
Official code: RF03
Quadratic functions in standard form
I can analyze a standard-form quadratic by completing the square.
Official code: RF04
Quadratic equations and systems
Solving quadratic equations by several methods
I can solve quadratic equations by several methods.
Official code: RF05
The discriminant and the roots-zeros-intercepts link
I can use the discriminant and relate roots, zeros, and intercepts.
Official code: RF05
Systems involving quadratics
I can solve systems of linear-quadratic and quadratic-quadratic equations.
Official code: RF06
Quadratic inequalities
Linear and quadratic inequalities
I can graph and solve linear and quadratic inequalities in two variables.
Official code: RF07
Sequences and series
Arithmetic sequences and series
I can find terms and sums of arithmetic sequences and series.
Official code: RF09
Geometric sequences and series
I can find terms and sums of geometric sequences and series.
Official code: RF10
Reciprocal functions
Graphing reciprocal functions
I can graph the reciprocal of a linear or quadratic function.
Official code: RF11
The official wording · 14 outcomes
- RF01
- Factor polynomial expressions of the form
- RF01
- Factor polynomial expressions of the form
- RF01
- Factor polynomial expressions of the form
- RF02
- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems
- RF02
- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems
- RF03
- Analyze quadratic functions of the form and determine the: ▪ vertex ▪ domain and range ▪ direction of opening ▪ axis of symmetry ▪ x- and y-intercepts
- RF04
- Analyze quadratic functions of the form
- RF05
- Solve problems that involve quadratic equations
- RF05
- Solve problems that involve quadratic equations
- RF06
- Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic- quadratic equations in two variables
- RF07
- Solve problems that involve linear and quadratic inequalities in two variables
- RF09
- Analyze arithmetic sequences and series to solve problems
- RF10
- Analyze geometric sequences and series to solve problems
- RF11
- Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions)
Key ideas
The greatest common factor comes out of every term first.
Taking |f(x)| reflects the part of the graph below the x-axis upward.
In y = a(x − p)² + q, the vertex is (p, q).
Quadratics can be solved by factoring, completing the square, or the quadratic formula.
The boundary curve splits the plane into regions.
Watch out for
- Skipping the common factor before factoring the trinomial.
- Reflecting the whole graph instead of only the part below the x-axis.
- Reading the vertex's x-coordinate with the wrong sign from (x − p).
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 3 math courses for Grade 11. Here they are side by side.
- Mathematics 114 units · 26 skillsNo provincial examWhat it coversGeometry · Logical Reasoning · Statistics · Relations and Functions
- Mathematics at Work 115 units · 25 skillsNo provincial examWhat it coversMeasurement · Geometry · Number · Algebra · Statistics
- Pre-Calculus 11This course3 units · 28 skillsNo provincial examWhat it coversAlgebra and Number · Trigonometry · 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 11.
Study it in MapleMind
MapleMind teaches Pre-Calculus 11 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 11 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
- 27
- Fillable fields
- 1,346
- Price
- $4.99
Questions about Pre-Calculus 11
What is Pre-Calculus 11?
Nova Scotia’s Grade 11 math course: 3 units and 28 skills, from Algebra and Number to Relations and Functions.
What units are in Pre-Calculus 11?
1. Algebra and Number, 2. Trigonometry and 3. Relations and Functions.
Is there a provincial exam for Pre-Calculus 11?
No. Nova Scotia gives no provincial exam for Pre-Calculus 11.
What comes after Pre-Calculus 11?
Mathematics 12, Pre-Calculus 12, Calculus 12 and Mathematics at Work 12.
Can MapleMind help with Pre-Calculus 11?
Yes. MapleMind teaches every skill of Pre-Calculus 11, 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 11
Practise every skill of Pre-Calculus 11 in MapleMind, free with daily limits.
