Corrected online math exercises for the 11th Grade, junior year, year 12.

Exercise example N°1601 :

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

second degree polynomials solving equations 11th Grade discriminant

The goal of this corrected exercise is to calculate the discriminant of a second degree polynomial from its algebraic form.

Exercise example N°1602 :

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

equations second degree polynomials solving equations 11th Grade discriminant

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 N°1603 :

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

equations second degree polynomials solving equations 11th Grade equation_solver

The purpose of this corrected exercise is to use the discriminant of a second degree equation to find its roots.

Exercise example N°1604 :

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

derivatives of functions functions 11th Grade derivative

The aim of this corrected maths exercise is to calculate the derivative number of a function.

Exercise example N°1605 :

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

derivatives of functions functions 11th Grade derivative

The purpose of this exercise is to determine through the methods of algebraic calculations the derivative of a polynomial function.

Exercise example N°1606 :

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

derivatives of functions functions 11th Grade derivative

The purpose of this corrected math exercise is to calculate the derivative of a square root.

Exercise example N°1607 :

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

derivatives of functions functions 11th Grade derivative

The purpose of this corrected math exercise is to calculate the derivative of a quotient.

Exercise example N°1608 :

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

derivatives of functions functions 11th Grade derivative

The purpose of this corrected math exercise is to calculate the derivative of a quotient and a polynomial.

Exercise example N°1609 :

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)`.

derivatives of functions functions 11th Grade derivative

The goal of this corrected math exercise is to calculate the derivative of a polynomial and a square root.

Exercise example N°1610 :

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

derivatives of functions functions 11th Grade derivative

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 N°1611 :

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

derivatives of functions functions 11th Grade derivative

The goal of this exercise on functions is to calculate the derivative of a quotient of polynomials.

Exercise example N°1612 :

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

derivatives of functions functions 11th Grade derivative

The purpose of this exercise on functions is to calculate the derivative of the product of a square root and a polynomial.

Exercise example N°1613 :

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.

derivatives of functions functions 11th Grade equation_tangent_line

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 N°1614 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a rational fraction function.

Exercise example N°1615 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a linear function.

Exercise example N°1616 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a power function.

Exercise example N°1617 :

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)`

numerical sequences 11th Grade sequence

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 N°1618 :

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)`

numerical sequences 11th Grade recursive_sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a linear function.

Exercise example N°1619 :

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)`

numerical sequences 11th Grade recursive_sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a quadratic function.

Exercise example N°1620 :

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)`.

numerical sequences 11th Grade 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 N°1621 :

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

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

numerical sequences 11th Grade 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 N°1622 :

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?

numerical sequences 11th Grade 12th Grade

Exercise on the direction of variation of a simple numerical sequence: constant sequences, increasing sequences and decreasing sequences.

Exercise example N°1623 :

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?

numerical sequences 11th Grade 12th Grade

Exercise on the direction of variation of a numerical sequence with a fraction: constant, increasing and decreasing sequences.

Exercise example N°1624 :

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.

numerical sequences 11th Grade 12th Grade

Exercise on arithmetic sequences, on geometric sequences and on common difference and on common ratio.

Exercise example N°1625 :

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.

numerical sequences 11th Grade 12th Grade

Exercise on geometric sequences, on arithmetic sequences and their reason.

Exercise example N°1626 :

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)`

numerical sequences 11th Grade 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 N°1627 :

"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. Compute `u_(5)`.

numerical sequences 11th Grade 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 N°1628 :

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.

numerical sequences 11th Grade 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 N°1629 :

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

numerical sequences 11th Grade 12th Grade

This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence.

Exercise example N°1630 :

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.

numerical sequences 11th Grade 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 N°1631 :

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

polynomial functions algebraic calculus 11th Grade degree

The purpose of this exercise is to practice developing a polynomial and determining its degree.

Exercise example N°1632 :

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

polynomial functions algebraic calculus 11th Grade degree

The goal of this exercise is to practice developing a polynomial with remarkable identities and determining its degree.

Exercise example N°1633 :

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)

polynomial functions factoring algebraic calculus 11th Grade factor

The goal of this exercise of algebraic calculation is to factor a polynomial of degree 3 knowing one of its roots.

Exercise example N°1634 :

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

polynomial functions algebraic calculus 11th Grade 12th Grade equation_solver

The goal of this exercise of algebraic calculation is to determine the values for which a polynomial of degree 3 is equal to 0.