Math Exercises for High School Seniors

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°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.

Exercise example N°1701 :

Write in algebraic form the complex number Z = `(-4-5*i)/(2+3*i)`

complex numbers 12th Grade complex_number

The goal of this corrected exercise is to write a complex number in its algebraic form z=a+ib.

Exercise example N°1702 :

Compute the real part of the complex number Z = `(2-4*i)/(1+2*i)`

complex numbers 12th Grade real_part

To succeed in this exercise, you must know how to determine the real part of a complex expression.

Exercise example N°1703 :

Calculate the imaginary part of the complex number Z = `(1-3*i)/(5+i)`

complex numbers 12th Grade imaginary_part

The purpose of this exercise is to determine with the help of calculation, the imaginary part of a complex number.

Exercise example N°1704 :

Compute the conjugate of the complex number Z = `(5-2*i)/(1+i)`

complex numbers 12th Grade complex_conjugate

This exercise allows to implement the techniques of calculation of the conjugate of a complex number.

Exercise example N°1705 :

z = `-3+2i`
z' = `5-4i`
Compute `z*z'`.

complex numbers 12th Grade complex_number

The purpose of this exercise is to find the result of arithmetic operations (sum, difference, product) that involve complex numbers.

Exercise example N°1706 :

Compute the imaginary part of the complex number, Z = `-3+2*i`

complex numbers 12th Grade imaginary_part

The objective of this exercise is to find the imaginary part of a complex number from its algebraic form.

Exercise example N°1707 :

Compute the real part of the complex number, Z = `-5+7*i`

complex numbers 12th Grade real_part

The objective of this exercise is to find the real part of a complex number from its algebraic form.

Exercise example N°1708 :

Represent in the complex plane, the point of affix `4+5i`.

complex numbers 12th Grade

The purpose of this graphing exercise is to place in the plane the affix of a complex number.

Exercise example N°1709 :

Express ln(25) as a function of ln(5) .

neperian logarithm functions 12th Grade

The purpose of this corrected exercise is to simplify a neperian logarithm containing a power.

Exercise example N°1710 :

Express `ln(1/27)` as a function of ln(3)

neperian logarithm functions 12th Grade

The goal of this corrected exercise is to simplify a neperian logarithm containing a quotient.

Exercise example N°1711 :

Express `-3/8*ln(1/(27))` as a function of ln(3)

neperian logarithm functions 12th Grade

The goal of this corrected exercise is to simplify the product of a fraction and a neperian logarithm containing a quotient.

Exercise example N°1712 :

Express `-5/8*ln(sqrt(2))` as a function of ln(2)

neperian logarithm functions 12th Grade

The aim of this corrected exercise is to simplify the neperian logarithm of a square root.

Exercise example N°1713 :

Compute an antiderivative of the function `f(x)=7/(9+7*x)` on `RR^+` .

neperian logarithm antiderivatives functions 12th Grade antiderivative

The aim of this corrected exercise is to use the neperian logarithm to calculate one of the primitives of a rational fraction of the first degree.

Exercise example N°1714 :

Compute an antiderivative of the function `f(x)=(8*x)/(1+4*x^2)` on `RR^+` .

neperian logarithm antiderivatives functions 12th Grade antiderivative

The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation of a rational fraction of degree 2.

Exercise example N°1715 :

Calculate the derivative of the function `ln(x)^5`.

neperian logarithm derivatives of functions functions 12th Grade derivative

The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.

Exercise example N°1716 :

Calculate the derivative of the function `ln(9+9*x^2)`.

neperian logarithm derivatives of functions functions 12th Grade derivative

The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.

Exercise example N°1717 :

Simplify the following expression `e^ln(3)+e^ln(4)`.

exponential functions 12th Grade calculator

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 N°1718 :

Simplify the following expression `e^ln(8)/e^ln(4)`.

exponential functions 12th Grade calculator

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 N°1719 :

Simplify the following expression `e^(ln(8)*ln(4))`.

exponential functions 12th Grade

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 N°1731 :

Calculate the derivative of the function `e^(3+5*x^2)`.

exponential derivatives of functions functions 12th Grade derivative

The aim of this corrected exercise is to use the exponential for the calculation of derivatives.

Exercise example N°1740 :

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.

antiderivatives functions 12th Grade integral

The aim of this corrected exercise is to use integration methods to calculate one of the antiderivative of a polynomial function.