This site offers many math exercises to review the main high school concepts. It uses the calculator to display a detailed correction.
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Solve the following equation: `x/2-3=0`.
1501 solving equations | equations 10th Grade equation_solverExercise example :
Solve the following equation: `z^2+1-2*z=0`.
1502 solving equations | equations 10th Grade equation_solverExercise example :
Solve the following equation: `y^2-16=0`.
1503 solving equations | equations 10th Grade equation_solverExercise example :
Solve the following equation: `z^2+1-2*z=0`.
1504 solving equations | equations 10th Grade equation_solverExercise 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_functionExercise 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_functionExercise example :
To which type of curve corresponds the following plot ?
1507 square and inverse functions 10th GradeExercise 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.
1508 solving equations | square and inverse functions | equations 10th Grade equation_solverExercise 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_trigExercise example :
Calculate the absolute value of `C=8+9`.
1511 order, absolute value, inequations 10th Grade absExercise example :
Calculate the absolute value of `F=2/3-3/7`.
1512 order, absolute value, inequations 10th Grade absExercise example :
Solve the following equation `|x-4|=2`.
1513 order, absolute value, inequations | equations 10th Grade equation_solverExercise example :
Solve the following equation `|x+9/2|=9/4`.
1514 order, absolute value, inequations | equations 10th Grade equation_solverExercise 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*?*?
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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_factorizationExercise example :
51 is an integer, is it prime ?
1517 order, absolute value, inequations 10th Grade prime_factorizationExercise 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_factorizationExercise example :
Write in the form of an irreducible fraction the following fraction `(40*28)/(35*24)` using the decomposition into prime factors.
1520 fractions | integers and rational numbers 10th Grade fractionExercise example :
Find the ordinate of the direction vector of the line whose equation is `y=-7/10*x+6` which has abscissa 1
1524 vectors | equations | equations of lines and linear systems 10th Grade fractionExercise example :
Put into irreducible fraction form: `((-9)/(20))/((-36)/(-15))`.
1539 fractions 10th Grade fractionExercise example :
Put into irreducible fraction form: `((-9)/(20))/((-36)/(-15))`.
1541 fractions 10th Grade fractionExercise example :
Compute the discriminant of the following polynomial: `2*x^2+4*x`.
1601 second degree polynomials | solving equations 11th Grade discriminantExercise example :
How many solutions does the following equation have: `2*x^2-x` ?
1602 equations | second degree polynomials | solving equations 11th Grade discriminantExercise example :
Give the roots of the following equation `4*x^2+x-2`
1603 equations | second degree polynomials | solving equations 11th Grade equation_solverExercise example :
Calculate the derivative number of the function f(x) = `2+2*x^2` at point a = -2
1604 derivatives of functions 11th Grade derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise 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 derivativeExercise example :
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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)`.
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Let the sequence (`u_(n)`) defined by `u_(n)` = `-3-3*n`.
Express as a function of n the terms of `u_(n+1)`.
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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?
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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?
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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.
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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.
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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)`
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Compute the roots of P(x) =`-4+8*x+3*x^2-x^3`.
1634 polynomial functions 11th Grade | 12th Grade equation_solverExercise example :
Write in algebraic form the complex number Z = `(-4-5*i)/(2+3*i)`
1701 complex numbers 12th Grade complex_numberExercise example :
Compute the real part of the complex number Z = `(2-4*i)/(1+2*i)`
1702 complex numbers 12th Grade real_partExercise example :
Calculate the imaginary part of the complex number Z = `(1-3*i)/(5+i)`
1703 complex numbers 12th Grade imaginary_partExercise example :
Compute the conjugate of the complex number Z = `(5-2*i)/(1+i)`
1704 complex numbers 12th Grade complex_conjugateExercise example :
z = `-3+2i`
z' = `5-4i`
Compute `z*z'`.
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Compute the imaginary part of the complex number, Z = `-3+2*i`
1706 complex numbers 12th Grade imaginary_partExercise example :
Compute the real part of the complex number, Z = `-5+7*i`
1707 complex numbers 12th Grade real_partExercise example :
Represent in the complex plane, the point of affix `4+5i`.
1708 complex numbers 12th GradeExercise example :
Express `-3/8*ln(1/(27))` as a function of ln(3)
1711 neperian logarithm 12th GradeExercise example :
Express `-5/8*ln(sqrt(2))` as a function of ln(2)
1712 neperian logarithm 12th GradeExercise example :
Compute an antiderivative of the function `f(x)=7/(9+7*x)` on `RR^+` .
1713 neperian logarithm | antiderivatives 12th Grade antiderivativeExercise example :
Compute an antiderivative of the function `f(x)=(8*x)/(1+4*x^2)` on `RR^+` .
1714 neperian logarithm | antiderivatives 12th Grade antiderivativeExercise example :
Calculate the derivative of the function `ln(x)^5`.
1715 neperian logarithm | derivatives of functions 12th Grade derivativeExercise example :
Calculate the derivative of the function `ln(9+9*x^2)`.
1716 neperian logarithm | derivatives of functions 12th Grade derivativeExercise example :
Simplify the following expression `e^ln(3)+e^ln(4)`.
1717 exponential 12th Grade calculatorExercise example :
Simplify the following expression `e^ln(8)/e^ln(4)`.
1718 exponential 12th Grade calculatorExercise example :
Calculate the derivative of the function `e^(3+5*x^2)`.
1731 exponential | derivatives of functions 12th Grade derivativeExercise 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 integralExercise example :
Determine the reduced equation of the line passing through the points A(3;5 )and B(2;4).
2413 linear functions and affine functions | equations of lines and linear systems | equations 9th Grade | 10th Grade equation_straight_lineExercise 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 9th Grade | 10th Grade vector_coordinatesExercise 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 9th Grade | 10th Grade vector_normExercise 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 9th Grade | 10th GradeExercise 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:
Tuesday | 73 |
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Wednesday | 16 |
Thursday | 4 |
Friday | 73 |
Saturday | 79 |
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After a test, the marks of 26 students have been grouped in the table below :
grade n | `0<=n<4` | `4<=n<8` | `8<=n<12` | `12<=n<16` | `16<=n<=20` |
---|---|---|---|---|---|
Number of students | 4 | 5 | 7 | ? | 7 |
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Here are the ages of the employees of a company, give the frequency of employees who are between 25 and 29 years old.
Age | 20-24 | 25-29 | 30-39 | 40-49 | 49-60 |
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Employees | 2 | 6 | 2 | 1 | 3 |
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Let f be a function whose representation is given opposite. What is the image of -3 by f?
24121 linear functions and affine functions 9th Grade | 10th GradeExercise 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 9th Grade | 10th GradeList of exercises by class : all levels, 6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade.