Corrected exercises on numerical functions

Here is the list of mathematics exercises on the main numerical functions. Each corrected exercise is accompanied by indications, reminders of the course, and methodological advice, which allows you to practice independently.

41 exercises

N°1414 (functions) : The purpose of this corrected math exercise is to simplify the square root of an integer.

Exercise example :

Calculate the following expression `sqrt(939)^2`.
1414 functions | square roots 9th Grade simplify_surd
N°1415 (functions) : The purpose of this corrected math exercise is to solve an equation of the form `x^2=a`.

Exercise example :

Find x such that `x^2`=9.
1415 square roots | solving equations | equations | functions 9th Grade equation_solver
N°1416 (functions) : The purpose of this corrected math exercise is to simplify a product of square roots.

Exercise example :

Put under the same radical the following expression `sqrt(35)*sqrt(31)`.
1416 square roots | functions 9th Grade simplify_surd
N°1417 (functions) : The purpose of this corrected math exercise is to simplify a quotient of square roots.

Exercise example :

Put under the same radical the following expression `sqrt(16)/sqrt(25)`.
1417 square roots | functions 9th Grade simplify_surd
N°1418 (functions) : The purpose of this corrected math exercise is to write a square root in a simplified form.

Exercise example :

Write in the form `a*sqrt(b)`, the following expression `sqrt(480)`, where a and b represent two integers.
1418 square roots | order, absolute value, inequations | numbers and equations | functions 9th Grade | 10th Grade simplify_surd
N°1419 (functions) : The purpose of this corrected math exercise is to write a quotient of square roots in a simplified form.

Exercise example :

Write in the form `a*sqrt(b)`, the following expression `sqrt(140)/sqrt(20)`, where a and b represent two integers.
1419 square roots | functions 9th Grade simplify_surd
N°1435 (functions) : The purpose of this corrected math exercise is to calculate the value of a function for a given number.

Exercise example :

Let f be the application of R in R defined by f(x)=`2*(3*x+1)^2-6*(2*x+3)^2` :
Compute f(2).
1435 integers and rational numbers | Numbers | functions 9th Grade array_values
N°1505 (functions) : 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 | functions 10th Grade is_odd_or_even_function
N°1506 (functions) : 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 | functions 10th Grade is_odd_or_even_function
N°1507 (functions) : 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 | functions 10th Grade
N°1509 (functions) : 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 | functions 10th Grade
N°1510 (functions) : 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 | functions 10th Grade simplify_trig
N°1511 (functions) : 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 | functions | Numbers 10th Grade abs
N°1512 (functions) : 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 | functions | Numbers 10th Grade abs
N°1513 (functions) : 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`.
1513 order, absolute value, inequations | equations | functions 10th Grade equation_solver
N°1514 (functions) : 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`.
1514 order, absolute value, inequations | equations | functions 10th Grade equation_solver
N°1604 (functions) : 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 | functions 11th Grade derivative
N°1605 (functions) : 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 | functions 11th Grade derivative
N°1606 (functions) : 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 | functions 11th Grade derivative
N°1607 (functions) : 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 | functions 11th Grade derivative
N°1608 (functions) : 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 | functions 11th Grade derivative
N°1609 (functions) : 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 | functions 11th Grade derivative
N°1610 (functions) : 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 | functions 11th Grade derivative
N°1611 (functions) : 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 | functions 11th Grade derivative
N°1612 (functions) : 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 | functions 11th Grade derivative
N°1613 (functions) : 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 :
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°1709 (functions) : 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) .
1709 neperian logarithm | functions 12th Grade
N°1710 (functions) : 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)
1710 neperian logarithm | functions 12th Grade
N°1711 (functions) : 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)
1711 neperian logarithm | functions 12th Grade
N°1712 (functions) : 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)
1712 neperian logarithm | functions 12th Grade
N°1713 (functions) : 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^+` .
1713 neperian logarithm | antiderivatives | functions 12th Grade antiderivative
N°1714 (functions) : 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^+` .
1714 neperian logarithm | antiderivatives | functions 12th Grade antiderivative
N°1715 (functions) : 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`.
1715 neperian logarithm | derivatives of functions | functions 12th Grade derivative
N°1716 (functions) : 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)`.
1716 neperian logarithm | derivatives of functions | functions 12th Grade derivative
N°1717 (functions) : 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)`.
1717 exponential | functions 12th Grade calculator
N°1718 (functions) : 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)`.
1718 exponential | functions 12th Grade calculator
N°1719 (functions) : 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))`.
1719 exponential | functions 12th Grade
N°1731 (functions) : 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)`.
1731 exponential | derivatives of functions | functions 12th Grade derivative
N°1740 (functions) : 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.
1740 antiderivatives | functions 12th Grade integral
N°14111 (functions) : The objective of this exercise is to write an expression composed of the sum of an integer and a square root.

Exercise example :

Put `8+sqrt(20)` in the form `a+b*sqrt(5)`, where a and b are two natural numbers.
14111 square roots | functions 9th Grade simplify_surd
N°14112 (functions) : The objective of this exercise is to simplify an expression composed of several square roots.

Exercise example :

Write C in the form `a*sqrt(b)` where a is a relative integer and b a natural number: C=`1*sqrt(8)-2*sqrt(18)-1*sqrt(32)-2*sqrt(2)`
14112 square roots | functions 9th Grade simplify_surd

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