Quebec · Secondary 4
Mathematics, Secondary 4 (Cultural, Social and Technical)
- 563-414
Quebec’s Secondary 4 math course, from Arithmetic to Financial mathematics.
- Units
- 6
- Lessons
- 34
- Skills
- 44
- Provincial exam
- 50% of the final mark
- Official curriculum
- quebec.ca
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 2 skills
Arithmetic
Defines the concept of absolute value in context
Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
I can use absolute value to state the size of a difference or a distance in a real situation, whatever order the numbers come in.
Skill 1.1
Estimates the value of the power of an exponential expression
Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)
I can predict roughly how big a power will be from its base and its exponent, before I use a calculator.
Skill 1.2
The official wording · 2 outcomes
- 1.1
- Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
- 1.2
- Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)
Key ideas
The absolute value of a number is its distance from 0 on the number line, so it is never negative: |−7| = 7 and |7| = 7.
With a base greater than 1, a positive exponent gives a value greater than 1 that grows as the exponent grows, and a negative exponent gives a value between 0 and 1: 1.2^3 ≈ 1.73 and 1.2^(−3) ≈ 0.58.
The size of the difference between two numbers is |a − b|, and the order does not matter: |5 − (−8)| = |−8 − 5| = 13.
With a base between 0 and 1 the pattern reverses: a positive exponent gives a value between 0 and 1 that shrinks, and a negative exponent gives a value greater than 1: 0.8^3 = 0.512 and 0.8^(−3) ≈ 1.95.
Absolute value states a gap or a tolerance without saying which side it falls on: a bag sold as 500 g that may be off by 15 g is acceptable when |mass − 500| ≤ 15.
Watch out for
- Thinking absolute value removes every minus sign inside it, so |3 − 10| becomes 3 + 10 = 13 instead of 7.
- Thinking a negative exponent makes the value negative, so 2^(−3) = −8 instead of 1/8.
- Giving the gap between −8 °C and 5 °C as 3 degrees by subtracting 8 from 5, instead of the distance 13.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 11 skills
Algebra
Solves systems of first-degree equations in two variables
Solves systems of first-degree equations in two variables
I can solve a system of two first-degree equations by the method that suits it, and say what the solution means for the choice in the situation.
Skill 2.1
Represents and interprets the inverse of a function
I can represent the inverse of a relation by swapping its variables, and say what the inverse tells me in the situation.
Skill 2.2
Validates the solution, with or without technological tools
Validates the solution, with or without technological tools
I can check that the solution of a system is right, by substitution, with a graph or a table of values, and against the situation.
Skill 2.3
Constructs an algebraic expression using a register (type) of representation
I can write the algebraic rule of a situation from its description, its table of values or its graph, for first-degree, y = ax² and exponential situations.
Skill 2.4
Interprets the solution or makes decisions, depending on the context
Interprets the solution or makes decisions if necessary, depending on the context
I can explain what the solution of a system means in the situation and use it to make and justify a decision.
Skill 2.5
Determines values or data by solving equations and inequalities
I can find an unknown value in a situation by solving an equation or an inequality, with algebra, a table of values or a graph.
Skill 2.6
Analyzes a situation to be optimized using a system of inequalities
Analyzes a situation to be optimized using a system of first-degree inequalities
I can turn the constraints of a situation into a system of inequalities, draw its polygon of constraints and find the coordinates of its vertices.
Skill 2.7
Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot
I can represent a situation in words, with a table of values, a graph or a rule, and choose the family of functions that models it.
Skill 2.8
Analyzes exponential functions of the form f(x) = a·c^(bx)
Analyzes exponential functions of the form f(x) = a·c^(bx)
I can calculate values, draw the graph and describe the properties of an exponential function f(x) = a·c^(bx), and interpret it as growth or decay in a real situation.
Skill 2.9
Analyzes piecewise functions
Analyzes piecewise functions
I can read, evaluate and graph a piecewise function, using the right rule on each interval, and interpret it in a real situation.
Skill 2.10
Analyzes step functions
Analyzes step functions
I can graph and interpret a step function, reading which value applies on each interval and at each jump.
Skill 2.11
The official wording · 11 outcomes
- 2.1
- of first-degree equations in two variables
- 2.2
- Represents and interprets the inverse
- 2.3
- Validates the solution, with or without technological tools
- 2.4
- Constructs an algebraic expression using a register (type) of representation
- 2.5
- Interprets the solution or makes decisions if necessary, depending on the context
- 2.6
- Determines values or data by solving equations and inequalities
- 2.7
- Analyzes a situation to be optimized mathematizing the situation using a system of first-degree inequalities in two variables drawing a bounded or unbounded polygon of constraints to represent the situation determining the coordinates of the vertices of the bounded polygon (feasible region)
- 2.8
- Models a situation verbally, algebraically, graphically, using a table of values or a scatter
- 2.9
- f(x) = acbx
- 2.10
- Piecewise functions
- 2.11
- Step functions
Key ideas
A system of two first-degree equations asks for the pair (x, y) that makes both equations true at once; on a graph it is the point where the two lines cross.
A pair is a solution of a system only if it satisfies every equation: substitute it into each one, because passing one equation is not enough.
The solution of a system has a meaning in the context: in a comparison of two offers, x is the quantity at which they are equal and y is their common value.
Each constraint becomes a first-degree inequality in the two decision variables, including x ≥ 0 and y ≥ 0 when the quantities cannot be negative.
In f(x) = a·c^(bx), a is the initial value (f(0) = a), and each increase of 1 in x multiplies the output by c^b: the function grows when c^b > 1 and decays when 0 < c^b < 1.
Watch out for
- Solving for one variable and stopping, so the answer gives m = 10 months without the matching cost of $310.
- Checking the pair only in the equation it was solved from, which it always satisfies.
- Reporting the intersection point, '150 texts', as the answer without saying which plan to choose for the person's actual use.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 11 skills
Statistics
Interprets stem-and-leaf diagrams and the linear correlation coefficient
Constructs and interprets a stem-and-leaf diagram
I can organize data in a stem-and-leaf diagram and read the distribution's shape, centre and spread from it.
Skill 3.1
Approximates and interprets the linear correlation coefficient
I can estimate the linear correlation coefficient of a scatter plot with the rectangle method, check it with technology, and say what its value tells me.
Skill 3.2
Calculates measures of dispersion and position
Calculates and interprets the mean deviation
I can calculate the mean deviation of a distribution and use it to compare how spread out two sets of data are.
Skill 3.3
Determines and interprets percentiles
I can find the percentile rank of a value in a large set of data, find the value at a given percentile, and explain what each one means.
Skill 3.4
Represents data using a scatter plot or a two-variable distribution table
Represents data using a scatter plot or a double-entry (two-variable) distribution table
I can organize paired data in a scatter plot or a double-entry distribution table and describe the trend I see.
Skill 3.5
Models two-variable data using a first-degree polynomial function
Models two-variable data using a first-degree polynomial function
I can decide whether a scatter plot is best modelled by a first-degree function and explain what that model means in the situation.
Skill 3.6
Describes and interprets the relationship between two variables
Describes and interprets the relationship between two variables, if any
I can describe the relationship between two variables, its direction, form and strength, interpret it in context, and say when there is none.
Skill 3.7
Gives a qualitative assessment of a linear correlation
Gives a qualitative assessment of a linear correlation
I can judge a linear correlation in words: positive or negative, zero, weak or strong, perfect or imperfect.
Skill 3.8
Draws a curve associated with the chosen model
Draws a curve associated with the chosen model
I can draw the line or curve that fits a scatter plot, using the Mayer line or the median-median line when the trend is linear.
Skill 3.9
Interpolates or extrapolates values using a regression line
Interpolates or extrapolates values using a regression line
I can use a regression line to predict values inside and beyond the data, and judge how far each prediction can be trusted.
Skill 3.10
Compares two-variable distributions
Compares two-variable distributions
I can compare two two-variable distributions through their scatter plots, correlations and regression lines, and draw a conclusion about the two groups.
Skill 3.11
The official wording · 11 outcomes
- 3.1
- a stem-and-leaf diagram
- 3.2
- Approximates and interprets the linear correlation coefficient
- 3.3
- mean deviation
- 3.4
- percentile
- 3.5
- Represents data using a scatter plot or a double-entry (two-variable) distribution table
- 3.6
- first-degree polynomial function
- 3.7
- Describes and interprets the relationship between two variables, if any
- 3.8
- Gives a qualitative assessment of a linear correlation
- 3.9
- Draws a curve associated with the chosen model
- 3.10
- a regression line
- 3.11
- Compares two-variable distributions
Key ideas
In a stem-and-leaf diagram each value is split into a stem (the leading digit or digits) and a leaf (the last digit), and the leaves are written in increasing order beside their stem.
The mean deviation is the average distance between the data and their mean: MD = Σ|xᵢ − x̄| ÷ n.
Two-variable data pair each individual's values for two characteristics, such as each student's hours of sleep and test mark, and a scatter plot shows each pair as one point.
A scatter plot is modelled by a first-degree function when its points cluster around a straight band; when the band curves or levels off, or the points form no band, a line is not the right model.
A relationship is described by its direction (positive when both variables increase together, negative when one decreases as the other increases), its form (linear or curved) and its strength (how tightly the points follow the trend).
Watch out for
- Writing the leaves in the order the data were collected, so the median cannot be found by counting.
- Adding the signed deviations, getting 0, and concluding that the data have no spread.
- Putting the dependent variable on the horizontal axis, so the plot answers a different question.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 7 skills
Geometry
Determines the minimum conditions for congruent or similar triangles
Determines the minimum conditions required to conclude that triangles are congruent or similar
I can name the minimum conditions that make two triangles congruent (SSS, SAS, ASA) or similar (AA, SSS, SAS), and explain why fewer conditions are not enough.
Skill 4.1
Finds unknown measurements using metric or trigonometric relations
I can find an unknown length in a triangle with a metric or trigonometric relation and justify each step by naming the relation and why it applies.
Skill 4.2
Demonstrates congruence or similarity between triangles
Demonstrates the congruence or similarity between triangles or finds unknown measurements using minimum conditions
I can show that two triangles are congruent or similar by naming the minimum condition, and use the result to find an unknown measurement.
Skill 4.3
Determines metric relations associated with plane figures
Determines, through exploration or deduction, different metric relations associated with plane figures
I can discover the metric relations of a right triangle by showing that the altitude to the hypotenuse creates three similar triangles.
Skill 4.4
Finds unknown measurements using trigonometric ratios
Finds unknown measurements using the trigonometric ratios sine, cosine and tangent
I can use the sine, cosine and tangent ratios to find an unknown side or angle in a right triangle.
Skill 4.5
Calculates the area of a triangle using Hero’s formula
Calculates the area of a triangle using Hero’s formula
I can calculate the area of any triangle from its three side lengths with Hero's formula.
Skill 4.6
Calculates the area of a triangle from angle and side measurements
Calculates the area of a triangle given the measure of an angle and the lengths of two sides or given the measures of two angles and the length of one side
I can find the area of a triangle when I know two sides and the angle between them, or two angles and one side.
Skill 4.7
The official wording · 7 outcomes
- 4.1
- Determines the minimum conditions required to conclude that triangles are congruent or similar
- 4.2
- metric or trigonometric relations
- 4.3
- Demonstrates the congruence or similarity between triangles or finds unknown measurements using minimum conditions
- 4.4
- Determines, through exploration or deduction, different metric relations associated with plane figures
- 4.5
- trigonometric ratios: sine, cosine, tangent
- 4.6
- Hero’s formula
- 4.7
- Calculates the area of a triangle given the measure of an angle and the lengths of two sides or given the measures of two angles and the length of one side
Key ideas
Triangles are congruent when three pairs of sides are congruent (SSS), two sides and the contained angle are congruent (SAS), or two angles and the contained side are congruent (ASA).
A demonstration lists the corresponding parts that match, names the minimum condition (SSS, SAS or ASA for congruence; AA, SSS or SAS for similarity) and states the conclusion.
The altitude from the right angle to the hypotenuse splits a right triangle into two smaller right triangles, and all three triangles are similar, because each small one shares an acute angle with the large one.
In a right triangle each acute angle has three ratios, sin A = opposite ÷ hypotenuse, cos A = adjacent ÷ hypotenuse and tan A = opposite ÷ adjacent, and they depend only on the angle because all right triangles with that angle are similar.
Hero's formula gives a triangle's area from its three sides alone: A = √(p(p − a)(p − b)(p − c)), where p is the semi-perimeter (a + b + c) ÷ 2.
Watch out for
- Accepting AAA as a congruence condition, when three equal angles make triangles similar but not necessarily congruent.
- Matching sides that do not correspond, such as dividing the student's height by the flagpole's shadow.
- Assuming the altitude to the hypotenuse cuts it in half, which happens only when the two legs are equal.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 8 skills
Analytic Geometry
Calculates distances, points of division and slopes
Calculates the distance between two points
I can calculate the distance between two points in the Cartesian plane and use it on a real map or plan.
Skill 5.1
Determines the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)
I can find the coordinates of the point that divides a segment in a given ratio, including the midpoint.
Skill 5.2
Calculates and interprets a slope
I can calculate the slope between two points and interpret it as a rate of change with its units.
Skill 5.3
Determines the relative position of two straight lines using their slopes
Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident)
I can tell from their slopes and y-intercepts whether two lines intersect, are perpendicular, are parallel and distinct, or coincide.
Skill 5.4
Represents straight lines graphically and algebraically
Represents straight lines graphically and algebraically
I can model a situation with a straight line, writing its equation and drawing its graph, and switch between the functional form and the general form.
Skill 5.5
Represents parallel lines and perpendicular lines
I can model situations involving parallel or perpendicular lines and show them graphically and algebraically.
Skill 5.6
Determines the equation of a line using the slope and a point or two points
Determines the equation of a line using the slope and a point or using two points
I can find the equation of a line from its slope and one point, or from two points, and use it to describe a situation.
Skill 5.7
Determines the equation of a line parallel or perpendicular to another
Determines the equation of a line parallel or perpendicular to another
I can write the equation of a line parallel or perpendicular to a given line through a given point.
Skill 5.8
The official wording · 8 outcomes
- 5.1
- calculate the distance between two points
- 5.2
- determine the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)
- 5.3
- calculate and interpret a slope
- 5.4
- Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident)
- 5.5
- straight lines: graphically and algebraically
- 5.6
- parallel lines and perpendicular lines
- 5.7
- Determines the equation of a line using the slope and a point or using two points
- 5.8
- Determines the equation of a line parallel or perpendicular to another
Key ideas
The distance between A(x₁, y₁) and B(x₂, y₂) comes from the Pythagorean relation on the horizontal and vertical changes: d = √((x₂ − x₁)² + (y₂ − y₁)²).
Two lines with different slopes intersect at exactly one point, and if the product of their slopes is −1, they are perpendicular.
A straight-line situation has a constant rate of change; its functional form y = ax + b shows the rate a and the initial value b, and its graph is drawn from b and a.
From the slope a and a point (x₁, y₁), substitute the point into y = ax + b to find b.
A parallel line keeps the slope of the given line; a perpendicular line takes its negative reciprocal, so slope 2 gives −½.
Watch out for
- Adding the coordinate changes instead of using the Pythagorean relation, so the distance from (2, 3) to (8, 11) is given as 14.
- Reading the slope of 2x + 4y = 12 as 2 without isolating y.
- Taking the coefficient of x in the general form as the slope, so 3x + 4y − 24 = 0 is said to have slope 3.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 6 · 5 skills
Financial mathematics
Simple and compound interest
Simple and compound interest
I can calculate simple and compound interest and explain why compound interest grows faster.
Skill 6.1
Interest period
Interest period
I can find the rate per period and the number of periods from an annual rate and how often it is compounded, and see how the interest period changes the result.
Skill 6.2
Discounting (present value)
Discounting (present value)
I can find the present value of an amount I will receive or need in the future, at a given interest rate.
Skill 6.3
Compounding (future value)
Compounding (future value)
I can find the future value of an investment or a debt with Cₙ = C₀(1 + i)^n, and use a table, a graph or a calculator when the number of periods is the unknown.
Skill 6.4
Calculating, interpreting and analyzing financial situations
Calculating, interpreting and analyzing financial situations
I can analyze a personal-finance situation, such as a loan, a savings plan, a purchase or a car that loses value, by modelling it, calculating the key values and justifying a decision.
Skill 6.5
The official wording · 5 outcomes
- 6.1
- Simple and compound interest
- 6.2
- Interest period
- 6.3
- Discounting (present value)
- 6.4
- Compounding (future value)
- 6.5
- Calculating, interpreting and analyzing financial situations
Key ideas
Simple interest is paid on the original capital only: I = C × i × n, so the balance grows by the same amount each period (linear growth).
The interest period is how often interest is calculated and added: yearly, semi-annually, quarterly, monthly or daily.
Discounting answers 'how much must be invested today to have a given amount later?': the present value is C₀ = Cₙ(1 + i)^(−n), or Cₙ ÷ (1 + i)^n.
Compounding finds the future value of a present amount: Cₙ = C₀(1 + i)^n, where i is the rate per period and n the number of periods.
Analyzing a financial situation means modelling it (first-degree for simple interest or fixed costs, exponential for compound interest, depreciation or appreciation), calculating the values that matter, and interpreting them for the person involved.
Watch out for
- Adding the same amount of interest every year to an account that compounds, as if it paid simple interest.
- Using the annual rate with a monthly number of periods, such as 1.06^36 for 3 years compounded monthly.
- Treating an amount due in the future as if it were worth the same today, ignoring interest.
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.
The mark you need
Your class mark counts for 50% of the final mark, the exam for 50%. Quebec may moderate your class mark before it’s blended.
You need
65% on the exam
With 75% in class, your final mark lands between 37.5% (0 on the exam) and 87.5% (100% on it).
Which course?
Quebec has 3 math courses for Secondary 4. Here they are side by side.
- Mathematics, Secondary 4 (Cultural, Social and Technical)This course563-4146 units · 44 skillsMathematics, Secondary IV, Cultural, Social and Technical optionWhat it coversArithmetic · Algebra · Statistics · Geometry · Analytic Geometry · Financial mathematics
- Mathematics, Secondary 4 (Science)565-4065 units · 57 skillsMathematics, Secondary IV, Science optionWhat it coversArithmetic · Algebra · Statistics · Geometry · Analytic Geometry
- Mathematics, Secondary 4 (Technical and Scientific)564-4066 units · 76 skillsMathematics, Secondary IV, Technical and Scientific optionWhat it coversArithmetic · Algebra · Probability · Statistics · Geometry · Analytic Geometry
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 Quebec’s own curriculum for Mathematics, Secondary 4 (Cultural, Social and Technical).
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Questions about Mathematics, Secondary 4 (Cultural, Social and Technical)
What is Mathematics, Secondary 4 (Cultural, Social and Technical)?
Quebec’s Secondary 4 math course: 6 units and 44 skills, from Arithmetic to Financial mathematics.
What units are in Mathematics, Secondary 4 (Cultural, Social and Technical)?
1. Arithmetic, 2. Algebra, 3. Statistics, 4. Geometry, 5. Analytic Geometry and 6. Financial mathematics.
Is there a provincial exam for Mathematics, Secondary 4 (Cultural, Social and Technical)?
Yes. The Mathematics, Secondary IV, Cultural, Social and Technical option counts for 50% of the final mark. Next sitting: January 21, 2027.
What comes after Mathematics, Secondary 4 (Cultural, Social and Technical)?
Mathematics, Secondary 5 (Cultural, Social and Technical), Mathematics, Secondary 5 (Science) and Mathematics, Secondary 5 (Technical and Scientific).
Can MapleMind help with Mathematics, Secondary 4 (Cultural, Social and Technical)?
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