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The official Manitoba Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S) curriculum
Manitoba defines Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S) by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Manitoba's official curriculumRead it on the government site — edu.gov.mb.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand M | 4 | Measurement |
| Strand A | 5 | Algebra and Number |
| Strand R | 10 | Relations and Functions |
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How MapleMind teaches Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S) — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1MeasurementOfficial strand · Strand M
Linear measurement in SI and imperial units, unit conversion, surface area and volume of 3-D objects, and right-triangle trigonometry.
Linear Measurement and Conversion
- Referents and estimating linear measure10I.M.1 — Solve problems that involve linear measurement using SI and imperial referents and estimation strategies for millimetre, centimetre, metre, inch, foot, yard, and mile.
- Measuring with instruments10I.M.1 — Solve contextual linear-measurement problems using instruments such as rulers, tape measures, and calipers, and explain a personal measurement strategy.
- Converting within and between SI and imperial10I.M.2 — Apply proportional reasoning to convert measurements within and between the SI and imperial systems, and justify the reasonableness of a solution.
Surface Area, Volume, and Trigonometry
- Surface area and volume of solids10I.M.3 — Solve problems using SI and imperial units that involve the surface area and volume of right cones, cylinders, prisms, pyramids, and spheres.
- Composite solids and unknown dimensions10I.M.3 — Determine an unknown dimension of a solid given its surface area or volume, solve composite 3-D problems, and describe the relationship between the volumes of cones and cylinders and of pyramids and prisms with the same base and height.
- Primary trig ratios in right triangles10I.M.4 — Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems involving right triangles, including direct and indirect measurement.
The official wording — 4 outcomes in this unit
- 10I.M.1
Solve problems that involve linear measurement, using SI and imperial units of measure estimation strategies
- 10I.M.2
Apply proportional reasoning to problems that involve conversions within and between SI and imperial units of measure.
- 10I.M.3
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
- 10I.M.4
Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
Unit 2Algebra and NumberOfficial strand · Strand A
Factors of whole numbers, irrational numbers, powers with rational exponents, and multiplying and factoring polynomials.
Factors and Roots
- Prime factors, GCF, and LCM10I.A.1 — Demonstrate an understanding of factors of whole numbers by determining prime factors, the greatest common factor, and the least common multiple of a set of whole numbers.
- Square roots and cube roots10I.A.1 — Determine whether a whole number is a perfect square, a perfect cube, or neither, and find the square root of a perfect square and the cube root of a perfect cube.
- Understanding irrational numbers10I.A.2 — Demonstrate an understanding of irrational numbers by representing, identifying, and simplifying them, including expressing a radical as a mixed radical in simplest form and back.
- Ordering irrational numbers10I.A.2 — Order irrational numbers on a number line by approximating their values, and represent the relationship among the subsets of the real numbers.
Exponents and Polynomials
- Powers with rational exponents10I.A.3 — Demonstrate an understanding of powers with integral and rational exponents, applying the exponent laws and expressing powers with rational exponents as radicals.
- Multiplying polynomials10I.A.4 — Demonstrate an understanding of the multiplication of polynomial expressions (monomials, binomials, and trinomials) concretely, pictorially, and symbolically.
- Common factors and trinomial factoring10I.A.5 — Demonstrate an understanding of common factors and trinomial factoring by extracting common factors, factoring trinomials, and verifying by multiplication.
- Difference of squares10I.A.5 — Factor a polynomial that is a difference of squares, and explain why it is a special case of factoring a trinomial where b = 0.
The official wording — 5 outcomes in this unit
- 10I.A.1
Demonstrate an understanding of factors of whole numbers by determining prime factors greatest common factor least common multiple
- 10I.A.2
Demonstrate an understanding of irrational numbers by representing, identifying, and simplifying irrational numbers
- 10I.A.3
Demonstrate an understanding of powers with integral and rational exponents.
- 10I.A.4
Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials, and trinomials), concretely, pictorially, and symbolically.
- 10I.A.5
Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially, and symbolically.
Unit 3Relations and FunctionsOfficial strand · Strand R
Graphs and contexts, relations and functions, slope, linear relations across representations and forms, systems of linear equations, and distance and midpoint.
Graphs, Relations, and Functions
- Data, graphs, and contexts10I.R.1 — Interpret and explain the relationships among data, graphs, and contexts, including domain and range restrictions and whether points should be connected.
- Relations and functions10I.R.2 — Demonstrate an understanding of relations and functions, determining whether a set of ordered pairs or a graph represents a function and expressing domain and range.
- Slope as rise, run, and rate of change10I.R.3 — Demonstrate an understanding of slope as rise over run and as a rate of change, determining the slope of a line segment from any two points.
- Parallel and perpendicular slopes10I.R.3 — Apply a rule using slope to determine whether two lines are parallel or perpendicular.
Representing Linear Relations
- Linear relations in words and ordered pairs10I.R.4 — Describe and represent linear relations using words and ordered pairs, identifying independent and dependent variables in a context.
- Linear relations in tables and graphs10I.R.4 — Describe and represent linear relations using tables of values and graphs, and determine whether a table of values or graph represents a linear relation.
- Linear relations as equations10I.R.4 — Describe and represent linear relations using equations, determine whether an equation represents a linear relation, and match corresponding representations.
- Characteristics of linear graphs10I.R.5 — Determine the characteristics of the graphs of linear relations, including intercepts, slope, domain, and range.
Forms of a Line, Systems, and Distance
- Forms of a linear equation10I.R.6 — Relate linear relations expressed in slope-intercept form, general form, and slope-point form to their graphs.
- Equation of a line from a graph or point-slope10I.R.7 — Determine the equation of a linear relation given its graph or given a point and the slope, writing it in the form y = mx + b.
- Equation of a line from two points or a scatterplot10I.R.7 — Determine the equation of a linear relation given two points, given a point and a parallel or perpendicular line, or from a scatterplot's line of best fit.
- Function notation10I.R.8 — Represent a linear function using function notation, converting between function notation and a linear equation in two variables.
- Solving systems graphically10I.R.9 — Model a situation with a system of linear equations and solve it graphically, explaining the meaning of the point of intersection.
- Solving systems algebraically10I.R.9 — Determine and verify the solution of a system of linear equations algebraically, and explain why a system may have no, one, or an infinite number of solutions.
- Distance and midpoint10I.R.10 — Solve problems that involve the distance between two points and the midpoint of a line segment on the Cartesian plane.
The official wording — 10 outcomes in this unit
- 10I.R.1
Interpret and explain the relationships among data, graphs, and contexts.
- 10I.R.2
Demonstrate an understanding of relations and functions.
- 10I.R.3
Demonstrate an understanding of slope with respect to rise and run line segments and lines rate of change
- 10I.R.4
Describe and represent linear relations, using words ordered pairs
- 10I.R.5
Determine the characteristics of the graphs of linear relations, including the intercepts slope domain range
- 10I.R.6
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.
- 10I.R.7
Determine the equation of a linear relation, given a graph a point and the slope
- 10I.R.8
Represent a linear function, using function notation.
- 10I.R.9
Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
- 10I.R.10
Solve problems that involve the distance between two points and the midpoint of a line segment.
Printable workbook · A keepsake of the year
A Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S) workbook worth keeping
Built from the same official curriculum as this page. Before and after each skill above, your student colours in how sure they feel — so the two of you can see, on one page, what's clicking and what needs another look. It's a quiet way to follow how the year is really going.
By June it's full of their own handwriting: units worked through, confidence grown, a mid-year check-in, notes from parent-teacher night, and a certificate at the end. Less a worksheet, more a record of the year worth keeping on the shelf.
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Yes. Every skill in this course maps to an official outcome code from Manitoba's Grade 10 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
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Yes — 14 languages, including French. Both the app and the tutor's explanations switch to the language you choose.
Where can I see the official Manitoba curriculum for Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)?
The official source is linked on this page — Manitoba's official curriculum. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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