Newfoundland & Labrador · Grade 11
Mathematics 2201 (Academic)
Newfoundland & Labrador’s Grade 11 math course, from Radical Expressions and Equations to Statistical Reasoning.
- Units
- 7
- Lessons
- 15
- Skills
- 34
- Provincial exam
- None
- Official curriculum
- gov.nl.ca
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 5 skills
Radical Expressions and Equations
Simplifying Radical Expressions
Mixed and entire radicals
I can convert between mixed and entire radicals.
Skill 1.1
Comparing and operating with radicals
I can compare, order, and combine radical expressions.
Skill 1.2
Rationalizing a denominator
I can rationalize a monomial radical denominator.
Skill 1.3
Solving Radical Equations
Solving radical equations algebraically
I can solve a radical equation algebraically.
Skill 1.4
Verifying roots and extraneous solutions
I can verify roots and identify extraneous solutions.
Skill 1.5
The official wording · 5 outcomes
- 1.1
- Express a mixed radical with a numerical radicans as an entire radical.
- 1.2
- Perform one or more operations to simplify radical expressions with numerical or variable radicands
- 1.3
- Rationalize the monomial denominator of a radical expression
- 1.4
- Determine, algebraically, the roots of a radical equation, and explain the process used to solve the equation
- 1.5
- Verify, by substitution, that the values determined in solving a radical equation are roots of the equation
Key ideas
A coefficient moves inside a radical by raising it to the index.
Isolate the radical, then raise both sides to the index to remove it.
A radical simplifies to mixed form by removing the largest perfect-power factor.
Restrictions on the variable come from requiring the radicand to be non-negative.
A radical with a variable radicand is defined only where the radicand is non-negative (for even indices).
Watch out for
- Adding the coefficient inside instead of squaring it.
- Squaring before isolating the radical.
- Ignoring restrictions on a variable radicand.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 4 skills
Inductive and Deductive Reasoning
Conjectures and Counterexamples
Making conjectures inductively
I can make and justify a conjecture from a pattern.
Skill 2.1
Counterexamples
I can disprove a conjecture with a counterexample.
Skill 2.2
Deductive Proof
Proving with deductive reasoning
I can prove a relationship using deductive reasoning.
Skill 2.3
Comparing reasoning and finding proof errors
I can compare inductive and deductive reasoning and spot flawed proofs.
Skill 2.4
The official wording · 4 outcomes
- 2.1
- Make conjectures by observing patterns and identifying properties, and justify the reasoning
- 2.2
- Provide and explain a counterexample to disprove a given conjecture
- 2.3
- Prove a conjecture, using deductive reasoning (not limited to two column proofs)
- 2.4
- Compare, using examples, inductive and deductive reasoning
Key ideas
Inductive reasoning generalizes a rule from observed cases.
A deductive proof starts from accepted facts and reasons step by step to the conclusion.
A conjecture is only a claim until proven; patterns can mislead.
Representing a general number algebraically lets you prove a rule for all cases.
One counterexample is enough to disprove a general conjecture.
Watch out for
- Treating a conjecture as proven fact.
- Proving with examples instead of a general argument.
- Testing too few cases.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 6 skills
Quadratic Functions and Equations
Quadratic Equations and Their Roots
Roots, zeros and intercepts
I can connect the roots, zeros, and x-intercepts of a quadratic.
Skill 3.1
Solving quadratics by factoring
I can solve a quadratic equation by factoring.
Skill 3.2
Solving with the quadratic formula
I can solve any quadratic equation with the quadratic formula.
Skill 3.3
Graphs of Quadratic Functions
Characteristics of a quadratic function
I can find the domain, range, and intercepts of a quadratic function.
Skill 3.4
Vertex and axis of symmetry
I can find the vertex and axis of symmetry of a parabola.
Skill 3.5
Sketching from standard and vertex form
I can sketch a parabola from standard or vertex form.
Skill 3.6
The official wording · 6 outcomes
- 3.1
- Explain the relationships among the roots of an equation, the zeros of the corresponding function, and the x -intercepts of the graph of the function
- 3.2
- Determine, by factoring, the roots of a quadratic equation, and verify by substitution
- 3.3
- Determine, using the quadratic formula, the roots of a quadratic equation
- 3.4
- Determine the domain and range of a quadratic function
- 3.5
- Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function
- 3.6
- Determine the characteristics of a quadratic function
Key ideas
The roots of a quadratic equation are the zeros of the function and the x-intercepts of its graph - three names for the same values.
A quadratic's domain is all real numbers; its range depends on the vertex and whether it opens up or down.
A parabola can cross the x-axis zero, one, or two times.
The y-intercept is the constant term; x-intercepts are the zeros.
If a product is zero, at least one factor is zero (the zero-product property).
Watch out for
- Thinking zeros and the y-intercept are the same.
- Giving a restricted domain for a plain quadratic.
- Assuming every quadratic has two real roots.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 4 skills
Angles, Triangles and Proof
Parallel Lines and Angle Relationships
Angle relationships from transversals
I can generalize the angle relationships from parallel lines and a transversal.
Skill 4.1
Proving angle properties
I can prove angle properties and the triangle angle sum.
Skill 4.2
Congruence and Angle Problems
Proving triangles congruent
I can prove two triangles are congruent.
Skill 4.3
Solving angle problems and checking solutions
I can solve multi-step angle problems and justify each step.
Skill 4.4
The official wording · 4 outcomes
- 4.1
- Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology
- 4.2
- Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle
- 4.3
- Prove, using deductive reasoning, that two triangles are congruent
- 4.4
- Determine the measures of angles in a diagram that includes parallel lines, angles and triangles, and justify the reasoning
Key ideas
A transversal creates corresponding, alternate, and co-interior angle pairs.
Congruent triangles have all corresponding sides and angles equal.
These relationships hold only when the lines are parallel.
A congruence condition (such as side-angle-side) guarantees congruence from limited information.
Deductive proof chains known angle relationships to a new result.
Watch out for
- Applying parallel-line angle rules to non-parallel lines.
- Using a non-congruence condition (such as angle-side-side).
- Confusing alternate and co-interior pairs.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 7 skills
Proportional Reasoning: Scale and Rates
Scale Diagrams of 2-D Shapes
Scale factor and 2-D dimensions
I can use a scale factor to find dimensions and draw scale diagrams.
Skill 5.1
Scale factor and area
I can predict how a scale factor changes area.
Skill 5.2
Scale and 3-D Objects
Scale diagrams of 3-D objects
I can find scale factors and dimensions for 3-D objects.
Skill 5.3
Scale factor, surface area and volume
I can predict how a scale factor changes surface area and volume.
Skill 5.4
Rates and Unit Rates
Interpreting and comparing rates
I can interpret and compare rates and unit rates.
Skill 5.5
Graphing rates and slope
I can represent a rate with a graph and connect slope to rate.
Skill 5.6
Solving rate problems
I can solve real problems using rates.
Skill 5.7
The official wording · 7 outcomes
- 5.1
- Determine, using proportional reasoning, an unknown dimension of a 2-D shape, given a scale diagram or model
- 5.2
- Explain, using examples, the effect of a change in the scale factor on the area of a 2-D shape
- 5.3
- Determine, using proportional reasoning, the scale factor, given one dimension of a 3-D object, and its representation
- 5.4
- Explain, using examples, the effect of a change in the scale factor on the surface area and volume of a 3-D object
- 5.5
- Determine and compare rates and unit rates
- 5.6
- Draw a graph to represent a rate
- 5.7
- Solve a contextual problem that involves rates or unit rates
Key ideas
A scale factor is the ratio of a diagram length to the real length.
A 3-D scale model scales every linear dimension by the same factor.
A rate compares two quantities with different units; a unit rate has a denominator of one.
Proportional reasoning scales any dimension by the same factor.
The scale factor is recovered from any matching pair of dimensions.
Watch out for
- Using the reciprocal of the scale factor.
- Applying a 2-D idea of scale incorrectly to volume.
- Comparing rates with different denominators directly.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 6 · 2 skills
Acute Triangle Trigonometry
The Sine Law and the Cosine Law
Applying the sine and cosine laws
I can solve acute triangles with the sine law and the cosine law.
Skill 6.1
Problems with more than one triangle
I can solve problems that involve more than one triangle.
Skill 6.2
The official wording · 2 outcomes
- 6.1
- Solve a contextual problem that requires the use of the sine law (excluding the ambiguous case) or the cosine law, and explain the reasoning
- 6.2
- Solve a contextual problem that involves more than one triangle
Key ideas
The sine law relates each side to the sine of its opposite angle.
The cosine law generalizes the Pythagorean theorem to any triangle.
A labelled diagram shows which law fits the given information.
A shared side or angle links two triangles so a result from one feeds the next.
Solving in the right order keeps each step to known values.
Watch out for
- Choosing the sine law when only sides and an included angle are known.
- Mislabelling opposite sides and angles.
- Trying to solve both triangles at once.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 7 · 6 skills
Statistical Reasoning
Data Collection and Dispersion
Collecting and assessing data
I can collect data and judge its reliability.
Skill 7.1
Standard deviation and dispersion
I can calculate and interpret standard deviation.
Skill 7.2
The Normal Distribution
Properties of the normal curve
I can describe and recognize a normal distribution.
Skill 7.3
z-scores and normal problems
I can use z-scores to solve normal-distribution problems.
Skill 7.4
Confidence Intervals and Margin of Error
Confidence intervals and margin of error
I can interpret confidence intervals and margin of error.
Skill 7.5
Statistics in the media
I can analyze statistics presented in the media.
Skill 7.6
The official wording · 6 outcomes
- 7.1
- Assess the accuracy, reliability and relevance of the primary or secondary data collected by: identifying examples of bias and points of view identifying and describing the data collection methods determining if the data is relevant determining if the data is consistent with information obtained from other sources on the same topic
- 7.2
- Explain, using examples, the meaning of standard deviation
- 7.3
- Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve
- 7.4
- Determine, with or without technology, and explain the z -score for a given value in a normally distributed data set
- 7.5
- Explain, using examples, the significance of a confidence interval, margin of error or confidence level
- 7.6
- Interpret and explain confidence intervals and margin of error, using examples found in print or electronic media
Key ideas
Primary data is gathered first-hand; secondary data comes from existing sources.
A normal curve is symmetric with mean, median, and mode at the centre.
A confidence interval is a range likely to contain the true population value.
Reliable data is unbiased, relevant, and consistent with other sources.
About 68 percent of data lies within one standard deviation of the mean.
Watch out for
- Ignoring how the data was collected.
- Assuming any single-peaked data is normal.
- Reading the margin of error as a certainty.
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?
Newfoundland & Labrador has 3 math courses for Grade 11. Here they are side by side.
- Mathematics 22004 units · 43 skillsNo provincial examWhat it coversRadicals and Absolute Value · Rational Expressions and Factoring · Relations and Functions · Trigonometry
- Mathematics 2201 (Academic)This course7 units · 34 skillsNo provincial examWhat it coversRadical Expressions and Equations · Inductive and Deductive Reasoning · Quadratic Functions and Equations · Angles, Triangles and Proof · Proportional Reasoning: Scale and Rates · Acute Triangle Trigonometry · Statistical Reasoning
- Mathematics 22026 units · 28 skillsNo provincial examWhat it coversPersonal Finance · Formulas · Surface Area, Volume, and 3-D Views · Slope, Rate of Change, and Scale · Trigonometry · Graphs and Data
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 Newfoundland & Labrador’s own curriculum for Mathematics 2201 (Academic).
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Course Companion
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Questions about Mathematics 2201 (Academic)
What is Mathematics 2201 (Academic)?
Newfoundland & Labrador’s Grade 11 math course: 7 units and 34 skills, from Radical Expressions and Equations to Statistical Reasoning.
What units are in Mathematics 2201 (Academic)?
1. Radical Expressions and Equations, 2. Inductive and Deductive Reasoning, 3. Quadratic Functions and Equations, 4. Angles, Triangles and Proof, 5. Proportional Reasoning: Scale and Rates, 6. Acute Triangle Trigonometry and 7. Statistical Reasoning.
Is there a provincial exam for Mathematics 2201 (Academic)?
No. Newfoundland & Labrador gives no provincial exam for Mathematics 2201 (Academic).
What comes after Mathematics 2201 (Academic)?
Mathematics 3200, Mathematics 3201 (Academic), Mathematics 3202 and Mathematics 3208 (Calculus).
Can MapleMind help with Mathematics 2201 (Academic)?
Yes. MapleMind teaches every skill of Mathematics 2201 (Academic), 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.
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