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.

33 exercises
• N°1620 (12th Grade) : The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

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).

1620 numerical sequences
• N°1621 (12th Grade) : The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

Exercise example :

Let the sequence (u_(n)) defined by u_(n) = -3-3*n.

Express as a function of n the terms of u_(n+1).

1621 numerical sequences
• N°1622 (12th Grade) : Exercise on the direction of variation of a simple numerical sequence: constant sequences, increasing sequences and decreasing sequences.

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?

1622 numerical sequences
• N°1623 (12th Grade) : Exercise on the direction of variation of a numerical sequence with a fraction: constant, increasing and decreasing sequences.

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?

1623 numerical sequences
• N°1624 (12th Grade) : Exercise on arithmetic sequences, on geometric sequences and on common difference and on common ratio.

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.

1624 numerical sequences
• N°1625 (12th Grade) : Exercise on geometric sequences, on arithmetic sequences and their reason.

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.

1625 numerical sequences
• N°1626 (12th Grade) : This exercise allows you to practice the calculation of the terms of an arithmetic sequence from its common difference and its first term.

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)

1626 numerical sequences
• N°1627 (12th Grade) : This exercise allows you to practice the calculation of the terms of a geometric sequence from its common ratio and its first term.

Exercise example :

"Let (u_(n)) be a geometric sequence of reason 8, and of first term u_(0)= 2 .
1. Give the expression of u_(n) as a function of n
2. .
3. Compute u_(5).
"

1627 numerical sequences
• N°1628 (12th Grade) : This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence from its common difference and its first term.

Exercise example :

Let (u_(n)) be an arithmetic sequence of common difference 6, and of first term u_(0)= 1. Let S be the sum of u_(3) to u_(25). S=u_(3)+u_(4)+u_(5)+. . .+u_(25).
1. Compute the number of terms in S.
2. Compute S.

1628 numerical sequences
• N°1629 (12th Grade) : This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence.

Exercise example :

Let S be the sum defined by S = 1.
1. Compute the number of terms in S.
2. Compute S.

1629 numerical sequences
• N°1630 (12th Grade) : This exercise allows you to practice calculating the sum of the terms of a geometric sequence from its common ratio and its first term.

Exercise example :

Let (u_(n)) be a geometric sequence of common ratio -2, and of first term u_(0)= -2 . Let S be the sum of u_(2) to u_(14). S=u_(2)+u_(3)+u_(4)+. . .+u_(14).
1. Calculate u_(2)
2. Calculate u_(14).
3. Deduce S.

1630 numerical sequences
• N°1634 (12th Grade) : The goal of this exercise of algebraic calculation is to determine the values for which a polynomial of degree 3 is equal to 0.

Exercise example :

Compute the roots of P(x) =-4+8*x+3*x^2-x^3.

1634 polynomial functions equation_solver
• N°1701 (12th Grade) : The goal of this corrected exercise is to write a complex number in its algebraic form z=a+ib.

Exercise example :

Write in algebraic form the complex number Z = (-4-5*i)/(2+3*i)

1701 complex numbers 12th Grade complex_number
• N°1702 (12th Grade) : To succeed in this exercise, you must know how to determine the real part of a complex expression.

Exercise example :

Compute the real part of the complex number Z = (2-4*i)/(1+2*i)

1702 complex numbers 12th Grade real_part
• N°1703 (12th Grade) : The purpose of this exercise is to determine with the help of calculation, the imaginary part of a complex number.

Exercise example :

Calculate the imaginary part of the complex number Z = (1-3*i)/(5+i)

1703 complex numbers 12th Grade imaginary_part
• N°1704 (12th Grade) : This exercise allows to implement the techniques of calculation of the conjugate of a complex number.

Exercise example :

Compute the conjugate of the complex number Z = (5-2*i)/(1+i)

1704 complex numbers 12th Grade complex_conjugate
• N°1705 (12th Grade) : The purpose of this exercise is to find the result of arithmetic operations (sum, difference, product) that involve complex numbers.

Exercise example :

z = -3+2i
z' = 5-4i
Compute z*z'.

1705 complex numbers 12th Grade complex_number
• N°1706 (12th Grade) : The objective of this exercise is to find the imaginary part of a complex number from its algebraic form.

Exercise example :

Compute the imaginary part of the complex number, Z = -3+2*i

1706 complex numbers 12th Grade imaginary_part
• N°1707 (12th Grade) : The objective of this exercise is to find the real part of a complex number from its algebraic form.

Exercise example :

Compute the real part of the complex number, Z = -5+7*i

1707 complex numbers 12th Grade real_part
• N°1708 (12th Grade) : The purpose of this graphing exercise is to place in the plane the affix of a complex number.

Exercise example :

Represent in the complex plane, the point of affix 4+5i.

1708 complex numbers 12th Grade
• N°1709 (12th Grade) : The purpose of this corrected exercise is to simplify a neperian logarithm containing a power.

Exercise example :

Express ln(25) as a function of ln(5) .

1709 neperian logarithm 12th Grade
• N°1710 (12th Grade) : The goal of this corrected exercise is to simplify a neperian logarithm containing a quotient.

Exercise example :

Express ln(1/27) as a function of ln(3)

1710 neperian logarithm 12th Grade
• N°1711 (12th Grade) : The goal of this corrected exercise is to simplify the product of a fraction and a neperian logarithm containing a quotient.

Exercise example :

Express -3/8*ln(1/(27)) as a function of ln(3)

1711 neperian logarithm 12th Grade
• N°1712 (12th Grade) : The aim of this corrected exercise is to simplify the neperian logarithm of a square root.

Exercise example :

Express -5/8*ln(sqrt(2)) as a function of ln(2)

1712 neperian logarithm 12th Grade
• N°1713 (12th Grade) : The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation.

Exercise example :

Compute an antiderivative of the function f(x)=7/(9+7*x) on RR^+ .

1713 12th Grade antiderivative
• N°1714 (12th Grade) : The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation.

Exercise example :

Compute an antiderivative of the function f(x)=(8*x)/(1+4*x^2) on RR^+ .

1714 12th Grade antiderivative
• N°1715 (12th Grade) : The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.

Exercise example :

Calculate the derivative of the function ln(x)^5.

1715 12th Grade derivative
• N°1716 (12th Grade) : The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.

Exercise example :

Calculate the derivative of the function ln(9+9*x^2).

1716 12th Grade derivative
• N°1717 (12th Grade) : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.

Exercise example :

Simplify the following expression e^ln(3)+e^ln(4).

1717 exponential 12th Grade calculator
• N°1718 (12th Grade) : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.

Exercise example :

Simplify the following expression e^ln(8)/e^ln(4).

1718 exponential 12th Grade calculator
• N°1719 (12th Grade) : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.

Exercise example :

Simplify the following expression e^(ln(8)*ln(4)).

1719 exponential 12th Grade
• N°1731 (12th Grade) : The aim of this corrected exercise is to use the exponential for the calculation of derivatives.

Exercise example :

Calculate the derivative of the function e^(3+5*x^2).

1731 12th Grade derivative
• N°1740 (12th Grade) : The goal of this corrected exercise is to calculate a function primitive.

Exercise 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 integral

Themes associated with the 12th Grade : complex numbers, derivatives of functions, numerical sequences, neperian logarithm, exponential, antiderivatives.