Remediation in mathematics S2

This course unit focuses on topics involving biological problems, for which it is essential to perform calculations and understand or draw graphical representations (mainly curves). Motivated by these biological aspects, students must acquire a minimum level of knowledge to enable them to continue their studies in biology.

Calculus, algebra:

Counting, order of magnitude.

• Numerical calculations related to the principle of proportionality: conversion to a multiple or sub-multiple unit (from m to cm or km, for example), including for surface area or volume measurements (km²). Scale calculation.
• Using a spreadsheet to perform simple operations or repeat an operation.
• Digital application of a literal calculation.
• Simple operations on a fully numerical or fully literal calculation: adding or subtracting a constant from an equation, 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 a quantity (which are added together) or a concentration (which are averaged). Breakdown of the numerical calculation corresponding to a dilution (identification of the quantity of material and the quantity of container, conversion of quantities to concentrations, mixing of two solutions).
• A situation where the result and some of the parameters are known, and where a parameter involved in calculating this result must be adjusted: the concept of the unknown.
• First-degree equation and its solution.
• System of linear equations (max. 2 unknowns) and its solution by expressing one unknown as a function of the other.

Analysis:

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

Recommended prerequisites: middle school programs

Completion of a typical exercise corresponding to several of the skills listed above (simple calculation in the context of a biological problem, construction or analysis of a curve, etc.).

A series of biological problems will be established, leading to the development of the skills listed. Lectures will be used to reinforce ideas about the different skills to be developed, after these have been used to solve a problem (lectures therefore come after tutorials).

Hourly volumes:

            CM: 12 p.m.

            TD: 9 p.m.

            TP:

            Land: