Here is the list of mathematics exercises available online for free. Each corrected exercise is accompanied by indications, reminders of course, methodological advice which allows you to practice independently.
Exercise example :
Let the sequence (`u_(n)`) defined by `u_(n)` = `(2+n)/(2+5*n)`.
Express as a function of n the terms of `u_(n+3)`.
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Let the sequence (`u_(n)`) defined by `u_(n)` = `-3-3*n`.
Express as a function of n the terms of `u_(n+1)`.
Exercise example :
Let the sequence (`u_(n)`) be defined for any natural number n by `u_(0)= 3 ` and `u_(n+1)` = `-3+u_(n)`.
Is this sequence increasing or decreasing?
Exercise example :
Let the sequence (`u_(n)`) be defined for any natural number n by `u_(0)= 4 ` and `u_(n+1)` = `u_(n)/5`.
Is this sequence increasing or decreasing?
Exercise example :
Let the sequence (`u_(n)`) defined for any natural number n by `u_(0)= -3 ` and `u_(n+1)` = `-7+u_(n)`.
1. Is (`u_(n)`) an arithmetic or a geometric sequence ?
2. What is the reason of (`u_(n)`)
3. Give the expression of `u_(n)` as a function of n.
Exercise example :
Let the sequence (`u_(n)`) defined for any natural number n by `u_(0)= -1 ` and `u_(n+1)` = `-9*u_(n)`.
1. Is (`u_(n)`) an arithmetic or a geometric sequence?
2. What is the reason of (`u_(n)`).
3. Give the expression of `u_(n)` as a function of n.
Exercise example :
Let (`u_(n)`) be an arithmetic sequence of common difference -6, and of first term `u_(0)= 1 `.
1. Give the expression of `u_(n)` as a function of n.
2. Compute `u_(3)`
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Compute the roots of P(x) =`-4+8*x+3*x^2-x^3`.
1634 polynomial functions 11th Grade | 12th Grade equation_solverExercise example :
Write in algebraic form the complex number Z = `(-4-5*i)/(2+3*i)`
1701 complex numbers 12th Grade complex_numberExercise example :
Compute the real part of the complex number Z = `(2-4*i)/(1+2*i)`
1702 complex numbers 12th Grade real_partExercise example :
Calculate the imaginary part of the complex number Z = `(1-3*i)/(5+i)`
1703 complex numbers 12th Grade imaginary_partExercise example :
Compute the conjugate of the complex number Z = `(5-2*i)/(1+i)`
1704 complex numbers 12th Grade complex_conjugateExercise example :
z = `-3+2i`
z' = `5-4i`
Compute `z*z'`.
Exercise example :
Compute the imaginary part of the complex number, Z = `-3+2*i`
1706 complex numbers 12th Grade imaginary_partExercise example :
Compute the real part of the complex number, Z = `-5+7*i`
1707 complex numbers 12th Grade real_partExercise example :
Represent in the complex plane, the point of affix `4+5i`.
1708 complex numbers 12th GradeExercise example :
Express `-3/8*ln(1/(27))` as a function of ln(3)
1711 neperian logarithm 12th GradeExercise example :
Express `-5/8*ln(sqrt(2))` as a function of ln(2)
1712 neperian logarithm 12th GradeExercise example :
Compute an antiderivative of the function `f(x)=7/(9+7*x)` on `RR^+` .
1713 neperian logarithm | antiderivatives 12th Grade antiderivativeExercise example :
Compute an antiderivative of the function `f(x)=(8*x)/(1+4*x^2)` on `RR^+` .
1714 neperian logarithm | antiderivatives 12th Grade antiderivativeExercise example :
Calculate the derivative of the function `ln(x)^5`.
1715 neperian logarithm | derivatives of functions 12th Grade derivativeExercise example :
Calculate the derivative of the function `ln(9+9*x^2)`.
1716 neperian logarithm | derivatives of functions 12th Grade derivativeExercise example :
Simplify the following expression `e^ln(3)+e^ln(4)`.
1717 exponential 12th Grade calculatorExercise example :
Simplify the following expression `e^ln(8)/e^ln(4)`.
1718 exponential 12th Grade calculatorExercise example :
Calculate the derivative of the function `e^(3+5*x^2)`.
1731 exponential | derivatives of functions 12th Grade derivativeExercise example :
Let f be the function defined by f(x)= `3-2*x^2+x^3` ,compute an antiderivative of f, `F(x)`, with F(x)=0.
1740 antiderivatives 12th Grade integralThemes associated with the 12th Grade : derivatives of functions, exponential, neperian logarithm, complex numbers, antiderivatives, numerical sequences.
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