This site offers many math exercises to review the main high school concepts. It uses the calculator to display a detailed correction.

88 exercises
• N°1438 (High School) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

Consider the expression E=(8*x+4)^2-(8*x+4)*(7*x-5).
1. Expand and reduce E.
2. Factor E.
3. Solve the equation (9+x)*(4+8*x)=0.

1438 expand_and_simplify
• N°1439 (High School) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

Consider the expression E=(2*x+10)^2-(2*x+10)*(5*x-4).
1. Expand and reduce E.
2. Factor E.
3. Solve the equation (14-3*x)*(10+2*x)=0.

1439 expand_and_simplify
• N°1501 (High School) : This corrected exercise allows to practice solving linear equations with one unknown of the form ax+b=0.

Exercise example :

Solve the following equation: x/2-3=0.

• N°1502 (High School) : The purpose of this exercise on quadratic equations is to practice solving 2nd degree equations and null product equations.

Exercise example :

Solve the following equation: z^2+1-2*z=0.

• N°1503 (High School) : The purpose of this exercise is to solve a second degree equation by reducing it to solving a first degree equation.

Exercise example :

Solve the following equation: y^2-16=0.

• N°1504 (High School) : The goal of this exercise is to solve a null product equation of the type a*b=0, with a=0 or b=0.

Exercise example :

Solve the following equation: z^2+1-2*z=0.

• N°1505 (High School) : The purpose of this corrected exercise is to determine the parity of a function (specify whether the function is even or odd).

Exercise example :

Specify if the function f:x->7-3*x^2 is even, odd, neither even nor odd.

• N°1506 (High School) : The purpose of this corrected exercise is to determine graphically the parity of a function (specify whether the function is even or odd).

Exercise example :

With the help of the graphical representation of the function shown below in an orthogonal reference, indicate if the function is even, odd, neither even nor odd.

• N°1507 (High School) : The aim of this corrected exercise is to recognize from their graphical representations the square and inverse functions.

Exercise example :

To which type of curve corresponds the following plot ?

• N°1508 (High School) : The purpose of this exercise is to solve graphically an equation.

Exercise example :

The representative curve of the function f is given below. Find graphically one or more integer values of x on the interval [-5,5[ which verify the equation f(x)=1. You can use the red cursor to read the coordinates of the points.

• N°1509 (High School) : The goal of this math exercise is to convert angles expressed in degrees into radians.

Exercise example :

Convert to degrees pi/3 radians.

• N°1510 (High School) : The aim of this math exercise is to calculate expressions that contain sines, cosines and remarkable angles.

Exercise example :

The angles are expressed in radians. Give the exact value of the following expression pi/3

• N°1511 (High School) : This corrected exercise consists simply in calculating the absolute value of a numerical expression.

Exercise example :

Calculate the absolute value of C=8+9.

• N°1512 (High School) : This corrected exercise consists simply in calculating the absolute value of an algebraic expression composed of fractions.

Exercise example :

Calculate the absolute value of F=2/3-3/7.

• N°1513 (High School) : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).

Exercise example :

Solve the following equation |x-4|=2.

• N°1514 (High School) : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).

Exercise example :

Solve the following equation |x+9/2|=9/4.

• N°1515 (High School) : The purpose of this corrected exercise is to complete the decomposition of a number into prime numbers.

Exercise example :

Indicate by which number the "question mark" must be replaced in the prime decomposition of 60 so that the following equality is verified.
60 = 3*5*?*?

• N°1516 (High School) : The purpose of this exercise is to find the ordered decomposition of a number into primes.

Exercise example :

Give the decomposition of 854 into a product of prime numbers by ordering the factors and using the power operator ^ if necessary.

• N°1517 (High School) : The purpose of this corrected arithmetic exercise is to determine if a number is a prime number.

Exercise example :

51 is an integer, is it prime ?

• N°1518 (High School) : The goal of this exercise is to find the ordered decomposition of a product of numbers into primes.

Exercise example :

Give the product decomposition of the following expression 30*16 by ordering the factors and using the power operator ^ if necessary.

• N°1520 (High School) : The purpose of this exercise is to simplify a fraction using the decomposition of a number into a product of prime factors.

Exercise example :

Write in the form of an irreducible fraction the following fraction (40*28)/(35*24) using the decomposition into prime factors.

• N°1524 (High School) : The objective of this exercise is to determine the ordinate of a direction vector from a line equation.

Exercise example :

Find the ordinate of the direction vector of the line whose equation is y=-7/10*x+6 which has abscissa 1

• N°1539 (High School) : The purpose of this exercise is to use algebraic computation techniques to determine the irreducible form of a division of fractions.

Exercise example :

Put into irreducible fraction form: ((-9)/(20))/((-36)/(-15)).

• N°1541 (High School) : The purpose of this corrected calculus exercise is to use algebraic calculus techniques to simplify a product of fractions.

Exercise example :

Put into irreducible fraction form: ((-9)/(20))/((-36)/(-15)).

• N°1601 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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
• N°1701 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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 (High School) : 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.

• N°1709 (High School) : 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) .

• N°1710 (High School) : 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)

• N°1711 (High School) : 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)

• N°1712 (High School) : 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)

• N°1713 (High School) : 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^+ .

• N°1714 (High School) : 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^+ .

• N°1715 (High School) : 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.

• N°1716 (High School) : 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).

• N°1717 (High School) : 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).

• N°1718 (High School) : 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).

• N°1719 (High School) : 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)).

• N°1731 (High School) : 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).

• N°1740 (High School) : 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.

• N°2413 (High School) : The purpose of this exercise is to find the equation of a line from two points.

Exercise example :

Determine the reduced equation of the line passing through the points A(3;5 )and B(2;4).

2413 equation_straight_line
• N°3441 (High School) : The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.

Exercise example :

Let(O,vec(i),vec(j)) be a reference frame of the plane. Let A and D be two points of coordinates (13,8) and (7,6) respectively in this frame, compute the coordinates of the vector vec(AD).

3441 vector_coordinates
• N°3442 (High School) : The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.

Exercise example :

The plane is given an orthonormal reference frame (O,vec(i),vec(j)). Let A and D be two points of coordinates (13,8) and (7,6) respectively in this frame, calculate the distance between A and D .

3442 vector_norm
• N°3443 (High School) : The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.

Exercise example :

Let(O,vec(i),vec(j)) be a reference frame of the plane. Let D and H be two points of coordinates (2,8) and (2,7) respectively in this frame, compute the coordinates of the middle of the segment [DH].

3443
• N°4401 (High School) : The purpose of this corrected statistics exercise is to practice calculating an arithmetic mean.

Exercise example :

In a library open from Tuesday to Saturday inclusive, we counted, day by day, the number of books lent during a week and we obtained the results in the following table:

Tuesday73
Wednesday16
Thursday4
Friday73
Saturday79
1. Calculate the total number of books loaned during the entire week.
2. Calculate the average number of books loaned, per day, during this five-day week.

4401 statistics average
• N°4402 (High School) : The purpose of this corrected statistics exercise is to practice calculating the frequency of a series.

Exercise example :

After a test, the marks of 26 students have been grouped in the table below :

grade n0<=n<44<=n<88<=n<1212<=n<1616<=n<=20
Number of students457?7

1. What is the number of students having obtained a mark between 12 and 16 (excluding 16).
2. How many students got less than 12?

4402 statistics
• N°4403 (High School) : The purpose of this corrected statistics exercise is to determine from a table the frequency of a series.

Exercise example :

Here are the ages of the employees of a company, give the frequency of employees who are between 25 and 29 years old.

Age20-2425-2930-3940-4949-60
Employees26213

4403 statistics
• N°24121 (High School) : The purpose of this exercise is to read on a graph the image of a number by a function.

Exercise example :

Let f be a function whose representation is given opposite. What is the image of -3 by f?

24121 linear functions and affine functions
• N°24122 (High School) : The purpose of this exercise is to read on a graph the antecedent by a function of a number.

Exercise example :

Let f be a function whose representation is given opposite. What is the antecedent by f of -2 ?

24122 linear functions and affine functions