Here is the list of free online math exercises for he 11th Grade, junior year, year 12. Each corrected exercise is accompanied by indications, reminders of course, methodological advice which allows to practice independently.

34 exercises
• N°1601 (11th Grade) : The goal of this corrected exercise is to calculate the discriminant of a second degree polynomial from its algebraic form.

Exercise example :

Compute the discriminant of the following polynomial: 2*x^2+4*x.

• N°1602 (11th Grade) : The purpose of this corrected exercise is to find the number of solution of a second degree equation as a function of the discriminant.

Exercise example :

How many solutions does the following equation have: 2*x^2-x ?

• N°1603 (11th Grade) : The purpose of this corrected exercise is to use the discriminant of a second degree equation to find its roots.

Exercise example :

Give the roots of the following equation 4*x^2+x-2

• N°1604 (11th Grade) : The aim of this corrected maths exercise is to calculate the derivative number of a function.

Exercise example :

Calculate the derivative number of the function f(x) = 2+2*x^2 at point a = -2

• N°1605 (11th Grade) : The purpose of this exercise is to determine through the methods of algebraic calculations the derivative of a polynomial function.

Exercise example :

Let f be the function defined by f(x)= -x-2*x^2+x^3 , calculate the derivative of f, f'(x).

• N°1606 (11th Grade) : The purpose of this corrected math exercise is to calculate the derivative of a square root.

Exercise example :

Let f be the function defined by f(x)= 2*sqrt(x) , calculate the derivative of f, f'(x).

• N°1607 (11th Grade) : The purpose of this corrected math exercise is to calculate the derivative of a quotient.

Exercise example :

Let f be the function defined by f(x)= 1/(3*x^2) , calculate the derivative of f, f'(x).

• N°1608 (11th Grade) : The purpose of this corrected math exercise is to calculate the derivative of a quotient and a polynomial.

Exercise example :

Let f be the function defined by f(x)= 1/(4-2*x+x^2) , calculate the derivative of f, f'(x).

• N°1609 (11th Grade) : The goal of this corrected math exercise is to calculate the derivative of a polynomial and a square root.

Exercise example :

Let f be the function defined by f(x)= -3-3*x+2*x^2+x^3-5*sqrt(x) , calculate the derivative of f, f'(x).

• N°1610 (11th Grade) : The purpose of this corrected math exercise is to calculate the derivative of a function composed of a square root and a polynomial.

Exercise example :

Let f be the function defined by f(x)= sqrt(3*x) , calculate the derivative of f, f'(x).

• N°1611 (11th Grade) : The goal of this exercise on functions is to calculate the derivative of a quotient of polynomials.

Exercise example :

Let f be the function defined by f(x)= (4+2*x)/(1-4*x) , calculate the derivative of f, f'(x).

• N°1612 (11th Grade) : The purpose of this exercise on functions is to calculate the derivative of the product of a square root and a polynomial.

Exercise example :

Let f be the function defined by f(x)= 4*sqrt(x)*(1+2*x) , calculate the derivative of f, f'(x).

• N°1613 (11th Grade) : The purpose of this corrected math exercise is to calculate the derivative number of a function and derive the equation of a tangent to a curve.

Exercise example :

Let f be the function defined by f(x) = 5*x^2-2*x-4.
1. Calculate the derivative of the function f at the point of abscissa -2.
2. Deduce an equation of the tangent to the curve representing the function f at the point of abscissa -2.
• N°1614 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a rational fraction function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=(-5-4*n)/(4+3*n).
1. Compute u_(0)
2. Compute u_(1)

1614 numerical sequences 11th Grade sequence
• N°1615 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a linear function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=-4-4*n.
1. Compute u_(3)
2. Compute u_(7)

1615 numerical sequences 11th Grade sequence
• N°1616 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a power function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=(-1)^n*4^(n+1).
1. Compute u_(1)
2. Compute u_(2)

1616 numerical sequences 11th Grade sequence
• N°1617 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a fraction and a square root.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=sqrt(3+3*n)/(5+3*n).
1. Compute u_(4)
2. Compute u_(6)

1617 numerical sequences 11th Grade sequence
• N°1618 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a linear function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 2  and u_(n+1) = 1+u_(n).
1. Compute u_(3)
2. Compute u_(5)

1618 numerical sequences 11th Grade recursive_sequence
• N°1619 (11th Grade) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a quadratic function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 2  and u_(n+1) = -2+2*u_(n)^2.
1. Compute u_(2)
2. Compute u_(4)

1619 numerical sequences 11th Grade recursive_sequence
• N°1620 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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 (11th 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°1631 (11th Grade) : The purpose of this exercise is to practice developing a polynomial and determining its degree.

Exercise example :

1. Expand and reduce the following polynomial:(-6+x^2)*(-5-4*x).
2. What is its degree ?

• N°1632 (11th Grade) : The goal of this exercise is to practice developing a polynomial with remarkable identities and determining its degree.

Exercise example :

1. Expand and reduce the following polynomial:(7+x)^2-1-2*x+x^2+x^3.
2. What is its degree ?

• N°1633 (11th Grade) : The goal of this exercise of algebraic calculation is to factor a polynomial of degree 3 knowing one of its roots.

Exercise example :

P is the polynomial defined by P(x) =-4+8*x+3*x^2-x^3
1. Compute P(-2)
2. Find the polynomial Q such that for any real x, P(x)=(x+2)Q(x)

• N°1634 (11th 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 equation_solver

Themes associated with the 11th Grade : algebraic calculus, derivatives of functions, functions, polynomial functions, second degree polynomials, solving equations, numerical sequences.