Corrected online exercises of mathematics: 10th Grade, sophmore year, year 11

Exercise example N°1418 :

Write in the form `a*sqrt(b)`, the following expression `sqrt(480)`, where a and b represent two integers.

square roots order, absolute value, inequations numbers and equations functions 9th Grade 10th Grade simplify_surd

The purpose of this corrected math exercise is to write a square root in a simplified form.

Exercise example N°1423 :

Solve the following system:

`-x-2*y = 3`

`3*x = -2`

solving equations and inequations of the first degree equations of lines and linear systems equations 9th Grade 10th Grade solve_equations

The objective of this corrected math exercise is to solve a system of two equations with two unknowns.

Exercise example N°1430 :

Factor the following expression `x^2-20*x`.

algebraic calculation and remarkable identities numbers and equations factoring algebraic calculus 9th Grade 10th Grade factor

The purpose of this corrected algebraic calculus exercise is to factor an algebraic expression that involves squares.

Exercise example N°1431 :

Factor the following expression `9*x^2-49`.

algebraic calculation and remarkable identities numbers and equations factoring algebraic calculus 9th Grade 10th Grade factor

The purpose of this exercise is to factor an algebraic expression using a remarkable identity of the form a² - b².

Exercise example N°1438 :

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`.

mathematics exams and competitions expansion of algebraic expressions solving equations and inequations of the first degree factoring equations 9th Grade 10th Grade expand_and_simplify

The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example N°1439 :

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`.

mathematics exams and competitions expansion of algebraic expressions solving equations and inequations of the first degree factoring equations 9th Grade 10th Grade expand_and_simplify

The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example N°1501 :

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

solving equations equations 10th Grade equation_solver

This corrected exercise allows to practice solving linear equations with one unknown of the form ax+b=0.

Exercise example N°1502 :

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

solving equations equations 10th Grade equation_solver

The purpose of this exercise on quadratic equations is to practice solving 2nd degree equations and null product equations.

Exercise example N°1503 :

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

solving equations equations 10th Grade equation_solver

The purpose of this exercise is to solve a second degree equation by reducing it to solving a first degree equation.

Exercise example N°1504 :

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

solving equations equations 10th Grade equation_solver

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 N°1505 :

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

square and inverse functions functions 10th Grade is_odd_or_even_function

The purpose of this corrected exercise is to determine the parity of a function (specify whether the function is even or odd).

Exercise example N°1506 :

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.

square and inverse functions functions 10th Grade is_odd_or_even_function

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 N°1507 :

To which type of curve corresponds the following plot ?

square and inverse functions functions 10th Grade

The aim of this corrected exercise is to recognize from their graphical representations the square and inverse functions.

Exercise example N°1508 :

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.

solving equations square and inverse functions equations 10th Grade equation_solver

The purpose of this exercise is to solve graphically an equation.

Exercise example N°1509 :

Convert to degrees `pi/3` radians.

sine and cosine functions functions 10th Grade

The goal of this math exercise is to convert angles expressed in degrees into radians.

Exercise example N°1510 :

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

sine and cosine functions functions 10th Grade simplify_trig

The aim of this math exercise is to calculate expressions that contain sines, cosines and remarkable angles.

Exercise example N°1511 :

Calculate the absolute value of `C=8+9`.

order, absolute value, inequations functions Numbers 10th Grade abs

This corrected exercise consists simply in calculating the absolute value of a numerical expression.

Exercise example N°1512 :

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

order, absolute value, inequations functions Numbers 10th Grade abs

This corrected exercise consists simply in calculating the absolute value of an algebraic expression composed of fractions.

Exercise example N°1513 :

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

order, absolute value, inequations equations functions 10th Grade equation_solver

The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).

Exercise example N°1514 :

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

order, absolute value, inequations equations functions 10th Grade equation_solver

The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).

Exercise example N°1515 :

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*?*?

order, absolute value, inequations Numbers 10th Grade prime_factorization

The purpose of this corrected exercise is to complete the decomposition of a number into prime numbers.

Exercise example N°1516 :

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

order, absolute value, inequations Numbers 10th Grade prime_factorization

The purpose of this exercise is to find the ordered decomposition of a number into primes.

Exercise example N°1517 :

51 is an integer, is it prime ?

order, absolute value, inequations Numbers 10th Grade prime_factorization

The purpose of this corrected arithmetic exercise is to determine if a number is a prime number.

Exercise example N°1518 :

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

order, absolute value, inequations Numbers 10th Grade prime_factorization

The goal of this exercise is to find the ordered decomposition of a product of numbers into primes.

Exercise example N°1520 :

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

fractions Numbers integers and rational numbers 10th Grade fraction

The purpose of this exercise is to simplify a fraction using the decomposition of a number into a product of prime factors.

Exercise example N°1524 :

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

vectors equations equations of lines and linear systems 10th Grade fraction

The objective of this exercise is to determine the ordinate of a direction vector from a line equation.

Exercise example N°1539 :

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

fractions Numbers 10th Grade fraction

The purpose of this exercise is to use algebraic computation techniques to determine the irreducible form of a division of fractions.

Exercise example N°1541 :

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

fractions Numbers 10th Grade fraction

The purpose of this corrected calculus exercise is to use algebraic calculus techniques to simplify a product of fractions.

Exercise example N°2413 :

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

linear functions and affine functions equations of lines and linear systems equations 9th Grade 10th Grade equation_straight_line

The purpose of this exercise is to find the equation of a line from two points.

Exercise example N°3441 :

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)`.

vectors geometry 9th Grade 10th Grade vector_coordinates

The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.

Exercise example N°3442 :

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 .

vectors geometry 9th Grade 10th Grade vector_norm

The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.

Exercise example N°3443 :

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].

vectors geometry 9th Grade 10th Grade

The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.

Exercise example N°4401 :

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:

statistics 9th Grade 10th Grade average

The purpose of this corrected statistics exercise is to practice calculating an arithmetic mean.

Exercise example N°4402 :

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

statistics 9th Grade 10th Grade

The purpose of this corrected statistics exercise is to practice calculating the frequency of a series.

Exercise example N°4403 :

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

statistics 9th Grade 10th Grade

The purpose of this corrected statistics exercise is to determine from a table the frequency of a series.

Exercise example N°24121 :

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

linear functions and affine functions 9th Grade 10th Grade

The purpose of this exercise is to read on a graph the image of a number by a function.

Exercise example N°24122 :

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

linear functions and affine functions 9th Grade 10th Grade

The purpose of this exercise is to read on a graph the antecedent by a function of a number.