British Columbia · Grade 10
Foundations of Mathematics and Pre-calculus 10
- FMP 10
British Columbia’s Grade 10 math course, from Algebra & Number to Financial Literacy.
- Units
- 5
- Lessons
- 9
- Skills
- 23
- Provincial exam
- None
- Official curriculum
- BC Mathematics 10
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 3 skills
Algebra & Number
Powers & the Exponent Laws
Powers with positive and negative exponents
I can evaluate powers with positive, negative, and zero exponents.
Skill 1.1
The exponent laws with numerical and variable bases
I can simplify expressions using the exponent laws, including with variable bases.
Skill 1.2
Prime factorization, GCF, and LCM
I can write a number's prime factorization in power form and use it to find the GCF and LCM.
Skill 1.3
The official wording · 3 outcomes
- 1.1
- operations on powers with integral exponents
- 1.2
- operations on powers with integral exponents
- 1.3
- prime factorization
Key ideas
A negative exponent means reciprocal, not negative: 2^-3 = 1/2^3 = 1/8. The answer to a power with a negative exponent can still be positive.
Any nonzero base to the exponent 0 equals 1 — because the pattern of dividing by the base one step at a time lands there (2^2=4, 2^1=2, 2^0=1).
In mixed expressions, powers are evaluated before multiplying, dividing, adding, or subtracting.
Same base, multiplying: add the exponents (x^3 · x^4 = x^7). Same base, dividing: subtract (x^7 / x^2 = x^5).
Power of a power: multiply the exponents ((x^2)^3 = x^6) — a different move from the product law.
Watch out for
- Thinking a negative exponent makes the answer negative — 2^-3 is 1/8, a positive number.
- Reading -3^2 as (-3)^2 — without brackets the exponent applies before the negative, so -3^2 = -9.
- Multiplying the exponents when multiplying powers — x^3 · x^4 is x^7, not x^12.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 11 skills
Functions & Linear Relations
Relations, Functions & Function Notation
Is it a function? Relations and the function idea
I can decide whether a relation is a function and justify my answer.
Skill 2.1
Function notation, domain, and range
I can evaluate f(x) for a given input and state a function's domain and range, including in real contexts.
Skill 2.2
Connecting graphs, data, and situations
I can match graphs to situations and explain what the shape of a graph says about the story.
Skill 2.3
Linear Functions: Slope & Equations of Lines
Slope: positive, negative, zero, and undefined
I can calculate and interpret the slope of a line, including zero and undefined slopes.
Skill 2.4
Equations of lines: slope-intercept, point-slope, and general form
I can write the equation of a line in slope-intercept, point-slope, or general form, and convert between them.
Skill 2.5
Parallel, perpendicular, horizontal, and vertical lines
I can write equations of parallel, perpendicular, horizontal, and vertical lines through a given point.
Skill 2.6
Arithmetic Sequences
Common difference and the general term
I can find the general term of an arithmetic sequence and use it to compute any term.
Skill 2.7
Connecting sequences to linear functions
I can explain how an arithmetic sequence is a linear function evaluated at whole numbers.
Skill 2.8
Systems of Linear Equations
Solving systems graphically and reading the solution
I can solve a system of linear equations by graphing and explain what the intersection point means.
Skill 2.9
Substitution and elimination
I can solve a linear system by substitution or elimination and choose the efficient method.
Skill 2.10
Systems in situational contexts
I can set up a system of equations from a situation, solve it, and interpret the answer in context.
Skill 2.11
The official wording · 11 outcomes
- 2.1
- functions and relations
- 2.2
- functions and relations: connecting data, graphs, and situations
- 2.3
- connecting data, graphs, and situations
- 2.4
- linear functions: slope and equations of lines
- 2.5
- slope and equations of lines
- 2.6
- linear functions: slope and equations of lines
- 2.7
- arithmetic sequences
- 2.8
- arithmetic sequences
- 2.9
- systems of linear equations
- 2.10
- systems of linear equations
- 2.11
- systems of linear equations
Key ideas
A function assigns each input exactly one output. Repeating an OUTPUT is fine; repeating an INPUT with different outputs is not.
Slope = rise over run = (y2 - y1)/(x2 - x1): how much y changes for each step of 1 in x.
An arithmetic sequence adds the same common difference d each step; d can be negative for decreasing patterns.
The solution of a system is the point that satisfies BOTH equations — graphically, where the lines cross.
On a graph, the vertical line test: if any vertical line crosses twice, some input has two outputs — not a function.
Watch out for
- Thinking repeated OUTPUTS disqualify a function — {(1,2),(2,2)} is a perfectly good function.
- Calling a vertical line's slope 'zero' — zero belongs to horizontal lines; vertical is undefined because the run is 0.
- Writing t_n = t_1 + nd — forgetting the (n - 1) shifts every answer one step too far.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 4 skills
Polynomials: Multiplying & Factoring
Multiplying Polynomial Expressions
Multiplying binomials with the area model
I can multiply two binomials and connect the four products to the area model.
Skill 3.1
Products with trinomials
I can multiply a binomial by a trinomial and simplify by collecting like terms.
Skill 3.2
Polynomial Factoring
Greatest common factor of a polynomial
I can factor out the greatest common factor of a polynomial.
Skill 3.3
Factoring trinomials and the difference of squares
I can factor x^2 + bx + c trinomials and differences of squares, and verify by expanding.
Skill 3.4
The official wording · 4 outcomes
- 3.1
- multiplication of polynomial expressions
- 3.2
- multiplication of polynomial expressions
- 3.3
- polynomial factoring
- 3.4
- polynomial factoring
Key ideas
(a + b)(c + d) makes exactly four products — the four cells of a rectangle with sides a+b and c+d.
The GCF of terms takes the largest shared number AND the lowest shared power of each variable — 6x^3 and 9x has GCF 3x.
The two middle products usually combine: in (x+3)(x+5), 5x + 3x = 8x is the like-terms step.
Factoring out the GCF is the distributive property reversed: 6x^3 + 9x = 3x(2x^2 + 3).
Squaring a binomial is not distributing the square: (x + 4)^2 = x^2 + 8x + 16, never x^2 + 16.
Watch out for
- Distributing an exponent over addition: (x + 4)^2 = x^2 + 16 — the middle term 8x goes missing.
- Removing the GCF and leaving a term empty: 3x from 3x becomes 1, not 0 — 6x^2 + 3x = 3x(2x + 1).
- Multiplying only the firsts and lasts of two binomials and skipping the two middle products.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 3 skills
Trigonometry
The Primary Trigonometric Ratios
Sine, cosine, and tangent in right triangles
I can identify opposite, adjacent, and hypotenuse for an angle and write its sin, cos, and tan ratios.
Skill 4.1
Finding missing sides and angles
I can solve for unknown sides and angles in right triangles, choosing between trig ratios and the Pythagorean theorem.
Skill 4.2
Direct and indirect measurement
I can use trigonometry to calculate lengths that cannot be measured directly.
Skill 4.3
The official wording · 3 outcomes
- 4.1
- primary trigonometric ratios
- 4.2
- primary trigonometric ratios
- 4.3
- primary trigonometric ratios
Key ideas
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Opposite and adjacent depend on WHICH acute angle you stand at — swap angles and the labels swap.
The hypotenuse never changes: always the side across from the right angle, always the longest.
Choose the ratio by what you have and what you want: label the sides relative to the known angle, then pick the ratio linking them.
Finding an ANGLE from two sides uses the inverse function: angle = tan^-1(opposite/adjacent).
Watch out for
- Fixing 'opposite' to one side of the triangle regardless of the angle in question — the labels move with the angle.
- Treating sin as an operation to distribute or cancel — sin 30° is a single value, not 'sin times 30'.
- Using the calculator in radians — sin 30° should be 0.5; if it isn't, the mode is wrong.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 2 skills
Financial Literacy
Gross Pay, Deductions & Net Pay
Types of income and calculating gross pay
I can calculate gross pay from hourly, salary, commission, and overtime earnings.
Skill 5.1
Deductions and net pay
I can calculate net pay from gross pay by applying taxes and other deductions.
Skill 5.2
The official wording · 2 outcomes
- 5.1
- financial literacy
- 5.2
- financial literacy: gross and net pay
Key ideas
Gross pay is everything earned BEFORE deductions: rate × hours, salary ÷ pay periods, or sales × commission rate.
Overtime commonly pays 1.5× the regular rate for hours past the threshold — split the hours before multiplying.
Mixed income adds up: a base salary plus commission means computing each part, then summing.
Net pay = gross pay − all deductions: income tax, CPP, EI, and any union dues or benefit premiums.
Percentage deductions apply to gross: 5.95% CPP on $900 gross is $53.55, computed before anything else is removed.
Watch out for
- Paying all hours at the overtime rate once any overtime exists — only the hours past the threshold get 1.5×.
- Confusing gross with take-home — gross is before deductions; the bank deposit is net.
- Treating income tax as the only deduction — CPP and EI come off every eligible paycheque too.
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?
British Columbia has 2 math courses for Grade 10. Here they are side by side.
- Foundations of Mathematics and Pre-calculus 10This courseFMP 105 units · 23 skillsNo provincial examWhat it coversAlgebra & Number · Functions & Linear Relations · Polynomials: Multiplying & Factoring · Trigonometry · Financial Literacy
- Workplace Mathematics 10WPM 105 units · 11 skillsNo provincial examWhat it coversGraphs & Data · Right-Triangle Trigonometry · Measurement: Units, Surface Area & Volume · Central Tendency & Experimental Probability · Financial Literacy
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 British Columbia’s own curriculum for Foundations of Mathematics and Pre-calculus 10.
Textbooks
In British Columbia, each school district chooses its own textbooks: the ministry no longer recommends them. The ministry’s page
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Questions about Foundations of Mathematics and Pre-calculus 10
What is Foundations of Mathematics and Pre-calculus 10?
British Columbia’s Grade 10 math course: 5 units and 23 skills, from Algebra & Number to Financial Literacy.
What units are in Foundations of Mathematics and Pre-calculus 10?
1. Algebra & Number, 2. Functions & Linear Relations, 3. Polynomials: Multiplying & Factoring, 4. Trigonometry and 5. Financial Literacy.
Is there a provincial exam for Foundations of Mathematics and Pre-calculus 10?
No. British Columbia gives no provincial exam for Foundations of Mathematics and Pre-calculus 10.
What textbook does Foundations of Mathematics and Pre-calculus 10 use?
Each school district in British Columbia chooses its own textbooks, so ask your teacher which one your class uses.
What comes after Foundations of Mathematics and Pre-calculus 10?
Pre-calculus 11, Foundations of Mathematics 11 and Workplace Mathematics 11.
Can MapleMind help with Foundations of Mathematics and Pre-calculus 10?
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