Alberta · Grade 10
Mathematics 10C
- MAT1791
Alberta’s Grade 10 math course, from Measurement to Relations and Functions.
- Units
- 3
- Lessons
- 18
- Skills
- 41
- Provincial exam
- None
- Official curriculum
- Alberta Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 10 skills
Measurement
Linear Measurement
SI and imperial units
I can solve linear measurement problems in both SI and imperial units.
Skill 1.1
Estimation and measurement strategies
I can estimate lengths with referents and apply measurement strategies to real problems.
Skill 1.2
Converting Between Measurement Systems
Converting within and between systems
I can convert measurements within and between SI and imperial systems using proportional reasoning.
Skill 1.3
Conversion problem solving
I can solve multi-step real problems that hinge on unit conversions.
Skill 1.4
Surface Area and Volume of 3-D Objects
Prisms and cylinders
I can find surface area and volume of right prisms and cylinders.
Skill 1.5
Pyramids and cones
I can find surface area and volume of right pyramids and cones, using slant height correctly.
Skill 1.6
Spheres and mixed problems
I can find surface area and volume of spheres and solve problems combining 3-D objects.
Skill 1.7
Right-Triangle Trigonometry
The three primary ratios
I can define the sine, cosine and tangent ratios from a right triangle's sides.
Skill 1.8
Finding missing sides
I can find unknown side lengths with the primary trig ratios.
Skill 1.9
Finding angles and solving problems
I can find unknown angles with inverse ratios and solve elevation/depression problems.
Skill 1.10
The official wording · 10 outcomes
- 1.1
- Solve problems that involve linear measurement, using: SI and imperial units of measure; estimation strategies; measurement strategies.
- 1.3
- Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
- 1.5
- Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including: right cones; right cylinders; right prisms; right pyramids; spheres.
- 1.8
- Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
Key ideas
SI runs on powers of ten (mm, cm, m, km); imperial uses inches, feet, yards and miles with mixed factors (12 in = 1 ft, 3 ft = 1 yd, 5280 ft = 1 mi).
A conversion factor is a ratio equal to one (2.54 cm / 1 in) — multiplying by it changes the units without changing the quantity.
Prisms and cylinders share one structure: Volume = base area × height; a cylinder is just a prism with a circular base (V = πr²h).
Label sides RELATIVE to the chosen acute angle: opposite, adjacent, hypotenuse. Then sin = opp/hyp, cos = adj/hyp, tan = opp/adj (SOH CAH TOA).
Choose the unit AND the instrument that fit the job: callipers for machine parts, tape measure for framing, odometer for road distance.
Watch out for
- Treating imperial like base ten (writing 5 ft 12 in instead of 6 ft).
- Multiplying when you should divide (using the conversion factor upside-down) — the units tell you which way.
- Using the diameter as the radius in πr²h.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 11 skills
Algebra and Number
Factors of Whole Numbers
Prime factors, GCF and LCM
I can find prime factorizations and use them for GCF and LCM.
Skill 2.1
Square roots and cube roots
I can find square roots of perfect squares and cube roots of perfect cubes using prime factors.
Skill 2.2
Irrational Numbers and Radicals
Identifying and simplifying radicals
I can identify irrational numbers and simplify radicals between mixed and entire forms.
Skill 2.3
Ordering irrational numbers
I can order irrational numbers with rationals on a number line.
Skill 2.4
Powers with Integral and Rational Exponents
Integral exponents and exponent laws
I can apply the exponent laws with integral exponents, including negatives.
Skill 2.5
Rational exponents
I can interpret rational exponents as roots and move between radical and exponent forms.
Skill 2.6
Multiplying Polynomials
Multiplying binomials
I can multiply binomials with area models and the distributive property.
Skill 2.7
Multiplying larger polynomials
I can multiply any mix of monomials, binomials and trinomials.
Skill 2.8
Factoring
Common factors
I can factor out the greatest common factor from a polynomial.
Skill 2.9
Factoring trinomials
I can factor trinomials of the forms x² + bx + c and ax² + bx + c.
Skill 2.10
Difference of squares and perfect-square trinomials
I can recognize and factor differences of squares and perfect-square trinomials.
Skill 2.11
The official wording · 11 outcomes
- 2.1
- Demonstrate an understanding of factors of whole numbers by determining the: prime factors; greatest common factor; least common multiple; square root; cube root.
- 2.3
- Demonstrate an understanding of irrational numbers by: representing, identifying and simplifying irrational numbers; ordering irrational numbers.
- 2.5
- Demonstrate an understanding of powers with integral and rational exponents.
- 2.7
- Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.
- 2.9
- Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.
Key ideas
Every whole number has one prime factorization (24 = 2³ × 3). The GCF takes the LOWEST power of each shared prime; the LCM takes the HIGHEST power of every prime present.
An irrational number can't be written as a fraction — its decimal never ends and never repeats (√2, √10, π). Roots of perfect squares are RATIONAL (√25 = 5).
The laws: product adds exponents, quotient subtracts, power multiplies — for ANY integral exponents.
Every term of the first binomial multiplies every term of the second — the area model's four cells ARE those four products.
Find the GCF of the coefficients AND the lowest power of each shared variable, then divide it out: 6x² + 9x = 3x(2x + 3).
Watch out for
- Swapping the rules (highest powers for GCF).
- Calling every square root irrational (√25 is rational).
- Treating a negative exponent as a negative RESULT (5⁻² = −25).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 20 skills
Relations and Functions
Graphs and Situations
Interpreting graphs in context
I can interpret the relationship between a graph and the situation it describes.
Skill 3.1
Graphs from descriptions
I can sketch a possible graph from a description, and describe a situation for a given graph.
Skill 3.2
Relations and Functions
Relations and how to represent them
I can represent relations between quantities in multiple ways.
Skill 3.3
Functions as special relations
I can decide whether a relation is a function, including with the vertical line test.
Skill 3.4
Slope
Slope as rise over run
I can compute slope from graphs and coordinates, including the special cases.
Skill 3.5
Slope as rate of change
I can interpret slope as a rate of change in context.
Skill 3.6
Parallel and perpendicular slopes
I can use the slope relationships of parallel and perpendicular lines.
Skill 3.7
Representing Linear Relations
Five representations
I can represent a linear relation in words, ordered pairs, tables, graphs and equations.
Skill 3.8
Moving between representations
I can match equivalent representations and spot when two disagree.
Skill 3.9
Characteristics of Linear Graphs
Intercepts
I can find and interpret the intercepts of a linear relation.
Skill 3.10
Slope, domain and range
I can determine the slope, domain and range of a linear relation, with contextual restrictions.
Skill 3.11
Forms of Linear Equations
Slope–intercept form
I can relate y = mx + b to its graph.
Skill 3.12
General and slope–point forms
I can relate general form and slope–point form to their graphs and convert among all three forms.
Skill 3.13
Finding the Equation of a Line
From a graph, or a point and slope
I can find a line's equation from its graph, or from a point and the slope.
Skill 3.14
From two points, or a parallel/perpendicular line
I can find a line's equation from two points, or through a point parallel/perpendicular to a given line.
Skill 3.15
Function Notation
Reading and writing f(x)
I can evaluate f(a) and solve f(x) = b in function notation.
Skill 3.16
Function notation and graphs
I can connect function notation to graphs.
Skill 3.17
Systems of Linear Equations
Solving systems graphically
I can solve a system of two linear equations by graphing.
Skill 3.18
Substitution and elimination
I can solve systems by substitution and elimination, including special cases.
Skill 3.19
Problem solving with systems
I can model real problems as systems and choose an efficient solving method.
Skill 3.20
The official wording · 20 outcomes
- 3.1
- Interpret and explain the relationships among data, graphs and situations.
- 3.3
- Demonstrate an understanding of relations and functions.
- 3.5
- Demonstrate an understanding of slope with respect to: rise and run; line segments and lines; rate of change; parallel lines; perpendicular lines.
- 3.8
- Describe and represent linear relations, using: words; ordered pairs; tables of values; graphs; equations.
- 3.10
- Determine the characteristics of the graphs of linear relations, including the: intercepts; slope; domain; range.
- 3.12
- Relate linear relations expressed in: slope-intercept form (y = mx + b); general form (Ax + By + C = 0); slope-point form (y - y1 = m(x - x1)) to their graphs.
- 3.14
- Determine the equation of a linear relation, given: a graph; a point and the slope; two points; a point and the equation of a parallel or perpendicular line to solve problems.
- 3.16
- Represent a linear function, using function notation.
- 3.18
- Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
Key ideas
Read the AXES first — what quantities, what units. Then read segments as events: steepness is rate, flat is no change, falling is decrease.
A relation is ANY association between two quantities — shown as ordered pairs, a table, a mapping diagram, or a graph.
Slope = rise/run = (y₂ − y₁)/(x₂ − x₁) — subtract in the SAME order top and bottom.
Every representation encodes the same two facts: the constant rate of change and a starting value.
The y-intercept is where x = 0 (the start); the x-intercept is where y = 0 (the break-even/zero point) — set the OTHER variable to zero and solve.
Watch out for
- Reading a distance-time graph as a picture of the path (a downhill segment isn't a downhill road).
- Thinking a relation must follow a formula (any set of pairs is a relation).
- Computing run over rise.
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?
Alberta has 2 math courses for Grade 10. Here they are side by side.
- Mathematics 10-3MAT17934 units · 29 skillsNo provincial examWhat it coversMeasurement · Geometry · Number · Algebra
- Mathematics 10CThis courseMAT17913 units · 41 skillsNo provincial examWhat it coversMeasurement · Algebra and Number · 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 Alberta’s own curriculum for Mathematics 10C.
Study it in MapleMind
MapleMind teaches Mathematics 10C 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 Mathematics 10C 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
- 29
- Fillable fields
- 1,547
- Price
- $4.99
Questions about Mathematics 10C
What is Mathematics 10C?
Alberta’s Grade 10 math course: 3 units and 41 skills, from Measurement to Relations and Functions.
What units are in Mathematics 10C?
1. Measurement, 2. Algebra and Number and 3. Relations and Functions.
Is there a provincial exam for Mathematics 10C?
No. Alberta gives no provincial exam for Mathematics 10C.
What comes after Mathematics 10C?
Mathematics 20-1, Mathematics 20-2 and Mathematics 20-3.
Can MapleMind help with Mathematics 10C?
Yes. MapleMind teaches every skill of Mathematics 10C, 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 Mathematics 10C
Practise every skill of Mathematics 10C in MapleMind, free with daily limits.
