Calculation methods

This EU is divided into two parts. 

The first aims to consolidate the secondary school knowledge that is essential for pursuing higher education in science: understanding proportionality and linearity, calculating with powers, manipulating fractions, and solving simple equations. 

The second part will be devoted to the study of real variable functions: the focus will be on common functions, the graphical representation of functions, and the mathematical concept of derivatives (or instantaneous rates of change). 

Most of the concepts discussed will be illustrated with concrete examples from biology. 

Provide the basic computational tools necessary for pursuing studies in life sciences.  

high school mathematics

Recommended prerequisites: specialization in mathematics in 11th grade

A CC grade for continuous assessment that will take into account: 

    - participation and investment in TD. 

    - the results of two interim evaluations (on each of the two parts)

A CT terminal control over the entire program. 

Max rule: the score is calculated using the formula Max(CT,Average(CT,CC))

• Basic mathematical techniques

1.a) Proportionality, linearity, and their different representations: 

• table of values, cross product, proportionality coefficient
• graphical representation (x-axis, y-axis, slope, and equation of a vector line)
• solving the equation ax=b

Examples of illustrations: conversion between units of measurement (joules vs. kilocalories, for example), voltage/current relationship, etc.

• linear variations: related concepts, y-intercept, equation y=ax+b

Examples of illustrations: determining bacterial concentration from calibration data, converting degrees Celsius to degrees Fahrenheit. 

• Linear regression

1.b) Fractions

• What is a fraction (ratio of proportionality between integers, simplification rule, concept of GCD)?
• calculation rules (sum and product, concept of GCD)
• inequalities (operations that preserve or reverse inequalities)

Examples of illustrations: concentration calculation after mixing, parallel resistance combinations, diagnostic tests (sensitivity, specificity, PPV, NPV, to be compared with prevalence)

1.c) Powers and orders of magnitude

• integer powers (calculation rules, domain of definition for negative powers, scientific notation)
• fractional powers and nth roots (domain of definition, equation x^n=c)
• orders of magnitude
• exponential growth

Examples of illustrations: dilution calculations, conversions (%, ‰, ppm, liters-cubic meters, etc.), Fermi estimation, reproduction number of an infectious disease. 

    2) Functions of a real variable

2.a) Vocabulary of functions through examples

• Basic concepts (function, domain, graph, image, antecedent). Examples from Part 1: linear functions, powers, polynomials. 
• The concept of bijection. Detailed study of logarithmic and exponential functions (logarithmic scale). 

Examples of illustrations: half-life, epidemiological models, allometry.

• the properties of functions and their visualization on graphs (parity, monotonicity, periodicity: trigonometric functions). 

2.b) Limitations and application

• concept of limits (examples using the usual functions already studied). 
• general results: gendarmes' theorem, comparative growth rates, rational fraction limits. 
• continuity of normal functions.

Examples of illustrations: predictive use of a functional model, Verhulst model, and carrying capacity.

2.c) Growth rate and derivative number

• Concept of derivative as instantaneous rate of change. Graphical representation and equation of the tangent. 
• instantaneous speed

Illustration examples: all kinds of speeds. 

N.B. The calculation of derivative functions is part of the optional EU program for the second semester.

Hourly volumes:

            CM: 12 p.m.

            TD: 9 p.m.

            TP:

            Land: