Revision of the differential calculus program

To help you succeed in your differential calculus course, it’s important to master certain essential concepts. This page will give you access to the key concepts of the differential calculus program. This knowledge is in line with program 201 – NYA – 05, differential calculus.

 

 

What is decisive knowledge (learning)?

 

 

It corresponds to what you need to know, be able to do or understand to succeed in the course in which you are enrolled. For learning to be decisive, it must be prior, transferable and lasting.

 

Prerequisite: Does it prepare your child for other essential learning in the field in question?

 

Transferable: Is it useful for your child in other school subjects or disciplines?

 

Durable: Is it useful for your child throughout his or her life?

 

  

Key skills for the program

 

 

Differential calculus

 

The following knowledge is essential for successful completion of the differential calculus course.

 

 

 

Algebraic concepts and functions

 

 

 

 

Number sets and intervals

 

Allô prof – Sets of numbers

Simple intervals – Numerical Calculation – Maths seconde – Les Bons Profs

 

 

 

Exponents

 

Exponent theory

Fractional exponents

 

 

Operations on polynomials

 

Operations on polynomials – Addition, subtraction, product and division

Addition and subtraction of rational fractions

Division of rational fractions

 

 

 

Factoring

 

Simple highlighting

Double highlighting

Difference of squares

Allô prof – Factoring by completing a square

Sum product

Sum and difference of cubes – Factorization technique

 

Algebraic functions and functions defined by parts

 

Composition of functions

Affine functions

Constant functions

Allô prof – Equation of degree 2 polynomial function (zeros)

Solving quadratic equations

Polynomial functions of degree n

The rational function, p.1 of 2

Function defined by parts

 

 

Exponential and logarithmic functions

 

Find the rule of an exponential function

Logarithmic function

 

 

 

Trigonometry

Radians and the trigonometric circle 1

Radians and the trigonometric circle 2

The sine function

The cosine function

 

Limits and continuities

 

Limits of a function

Limit at a point – Functions defined by parts

Limit at a point – Indeterminate form 0 on 0 – Algebraic function

Limits to infinity – Algebraic functions

Continuity of a function

 

 

Derivative of algebraic functions

 

Derivative of a constant function

Derivative of the product of a constant and a function

Derivative of a sum of two functions

Derivative of a compound function

Implicit derivation

Demonstrate that implicit and explicit derivation give the same result

 

 

 

Rate of change

 

 

Calculating an instantaneous rate of change – Using an alternative definition

Differential calculus: chapter 4, related rates

 

 

Algebraic function analysis

 

Differential calculus: complete analysis step 1

Differential calculus: complete analysis, step 2

Differential calculus: complete analysis, steps 3-4

Differential calculus: complete analysis step 5

Differential calculus: complete analysis, step 6

 

Exponential and logarithmic functions

 

Derivative of exponential functions

Derivative of logarithmic functions

 

 

 

Trigonometric functions

 

Derivative of sine functions

Derivative of cosine functions

Derivative of tan, cot, sec and cosec functions

Derivative of inverse trigonometric functions

 

 

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