Math Remedial Course, Semester 2

This course unit is based on topics involving biological problems that require students to perform calculations and to understand or draw graphical representations (primarily curves). Motivated by these biological aspects, students must acquire a basic foundation that will enable them to continue their studies in biology.

Arithmetic, Algebra:

Counting, order of magnitude.

• Numerical calculations related to the principle of proportionality: conversion to a multiple or submultiple unit (from meters to centimeters or kilometers, for example), including for area or volume measurements (km²). Scale calculations.
• Using a spreadsheet to perform simple operations or repeat an operation.
• Digital implementation of a literal calculation.
• Simple operations on a fully numerical or fully algebraic calculation: adding or subtracting a constant from an equation, or multiplying or dividing an equation by a constant.
• Passage d’une grandeur dans une unité à une grandeur équivalente dans une autre unité par multiplication par une constante (pression <> énergie, concentration <> osmolarité). Calcul d’une grandeur physique résultant du produit ou de la somme de plusieurs grandeurs (de type loi de Fick).
• Physical quantities corresponding to an amount (which are added) or to a concentration (which are averaged). Breakdown of the numerical calculation corresponding to a dilution (determining the amount of substance and the volume of the container, converting amounts to concentrations, mixing two solutions).
• A situation in which the result and some of the parameters are known, and in which a parameter involved in calculating that result must be adjusted: the concept of an unknown.
• First-degree equations and their solutions.
• System of linear equations (up to 2 unknowns) and its solution by expressing one unknown in terms of the other.

Analysis:

• Understand how a phenomenon is represented by a curve. Be able to find f(x) given x, and vice versa.
• Using a curve, identify the regions of increasing and decreasing growth, as well as the optimal points. Pole, intersection with the axes, asymptote, inflection point.
• Rate of change, secant, tangent, derivative.
• Common functions and their analytical expressions: affine, quadratic, exponential, and logarithmic. Be able to graph these functions (notable points, shape of the curve between these points) or a function known numerically based on a few experimental points. Combinations in simple cases (e.g., logistic function). Variations and derivatives.
• Linear and exponential differential equations.
• Switching from a linear scale to a logarithmic scale and vice versa.

Recommended prerequisites*: middle school courses

Completion of a sample exercise that addresses several of the skills listed above (simple calculations in the context of a biological problem, plotting or analyzing a graph, etc.)

A series of biological problems will be presented, leading to the development of the listed skills. Lectures will serve to reinforce understanding of the various skills to be developed, after these skills have been applied to solve a problem (lectures thus follow the tutorials).

Hourly volumes*:

            CM: 12:00 p.m.

            TD: 9:00 p.m.

            Practical Work:

            Lot: