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.

1505 square and inverse functions 10th Grade is_odd_or_even_function
• 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.

1506 square and inverse functions 10th Grade is_odd_or_even_function
• 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 ?

1507 square and inverse functions 10th Grade
• 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.

1509 sine and cosine functions 10th Grade
• 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

1510 sine and cosine functions 10th Grade simplify_trig
• 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.

1511 order, absolute value, inequations 10th Grade abs
• 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.

1512 order, absolute value, inequations 10th Grade abs
• 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*?*?

1515 order, absolute value, inequations 10th Grade prime_factorization
• 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.

1516 order, absolute value, inequations 10th Grade prime_factorization
• 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 ?

1517 order, absolute value, inequations 10th Grade prime_factorization
• 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.

1518 order, absolute value, inequations 10th Grade prime_factorization
• 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

1604 derivatives of functions 11th Grade derivative
• 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).

1605 derivatives of functions 11th Grade derivative
• 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).

1606 derivatives of functions 11th Grade derivative
• 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).

1607 derivatives of functions 11th Grade derivative
• 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).

1608 derivatives of functions 11th Grade derivative
• 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).

1609 derivatives of functions 11th Grade derivative
• 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).

1610 derivatives of functions 11th Grade derivative
• 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).

1611 derivatives of functions 11th Grade derivative
• 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).

1612 derivatives of functions 11th Grade derivative
• 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 ?

1631 polynomial functions 11th Grade 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 ?

1632 polynomial functions 11th Grade 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 polynomial functions 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 vectors 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 vectors 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 vectors
• 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