Here is the list of free online math exercises for 9th Grade, freshman year, year 10 Each corrected exercise is accompanied by indications, reminders of course, methodological advice which allows you to practice independently.

37 exercisesExercise example N°1110 :

Use yellow numbers and blue arithmetic operators to calculate the target number.

Target

mental math games Numbers 6th Grade 7th Grade 8th Grade 9th Grade arithmetic_solver

Countdown is an arithmetic exercise that allows you to practice quick mental calculation in an efficient way. The goal is to reconstruct an integer using other integers and basic arithmetic operations (+,-,*,/).

Exercise example N°1412 :

Using the appropriate special expansion develop the following expression `(8*a+5*b)*(8*a-5*b)`.

algebraic calculation and remarkable identities algebraic calculus 9th Grade expand

The purpose of this exercise is to develop an algebraic expression using the most suitable remarkable identity.

Exercise example N°1413 :

Using the appropriate remarkable identity calculate the following expression `999^2`.

algebraic calculation and remarkable identities algebraic calculus 9th Grade expand

The purpose of this exercise is to calculate the square of a number using a remarkable identity.

Exercise example N°1414 :

Calculate the following expression `sqrt(939)^2`.

functions square roots 9th Grade simplify_surd

The purpose of this corrected math exercise is to simplify the square root of an integer.

Exercise example N°1415 :

Find x such that `x^2`=9.

square roots solving equations equations functions 9th Grade equation_solver

The purpose of this corrected math exercise is to solve an equation of the form `x^2=a`.

Exercise example N°1416 :

Put under the same radical the following expression `sqrt(35)*sqrt(31)`.

square roots functions 9th Grade simplify_surd

The purpose of this corrected math exercise is to simplify a product of square roots.

Exercise example N°1417 :

Put under the same radical the following expression `sqrt(16)/sqrt(25)`.

square roots functions 9th Grade simplify_surd

The purpose of this corrected math exercise is to simplify a quotient of square roots.

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°1419 :

Write in the form `a*sqrt(b)`, the following expression `sqrt(140)/sqrt(20)`, where a and b represent two integers.

square roots functions 9th Grade simplify_surd

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

Exercise example N°1422 :

For what value of x, is the following expression `7*x+6">-"6` true?

solving equations and inequations of the first degree 9th Grade inequality_solver

The objective of this corrected math exercise is to solve a first order inequation.

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°1427 :

Calculate the gcd of 225 and 84.

integers and rational numbers Numbers 9th Grade gcd

The objective of this corrected arithmetic exercise is to calculate the gcd of two integers.

Exercise example N°1428 :

Are the following numbers 205 and 318 prime to each other ?

integers and rational numbers Numbers 9th Grade gcd

The objective of this exercise is to use the GCD to check if two integers are prime to each other.

Exercise example N°1429 :

Put the following fraction in its irreducible form: `144/210`.

fractions Numbers integers and rational numbers 9th Grade fraction

The purpose of this exercise is to put a fraction into its irreducible form.

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°1434 :

Write D as an irreducible fraction: D = `((9/6+5/7)*2)/8`

fractions Numbers 9th Grade fraction

The objective of this corrected calculus exercise is to simplify an expression containing fractions.

Exercise example N°1435 :

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).

integers and rational numbers Numbers functions 9th Grade array_values

The purpose of this corrected math exercise is to calculate the value of a function for a given number.

Exercise example N°1436 :

- Let `A=3/8+10/6-8/4` , `B=-8*sqrt(24)-4*sqrt(216)-5*sqrt(54)-1*sqrt(54)` and `C=(18*10^5*3*10^6)/(6*10^11)`
- Compute A and give the result as an irreducible fraction.
- Write B in the form `a*(sqrt(6))` where a is a relative integer.
- Write C as an integer.

mathematics exams and competitions fractions Numbers square roots 9th Grade fraction

The objective of this exercise is to reduce a fraction, simplify a square root, and calculate a fraction that contains powers.

Exercise example N°1437 :

- Compute the GCD of the numbers 5104 and 968.
- Write the fraction `5104/968` in irreducible form.

mathematics exams and competitions fractions Numbers integers and rational numbers 9th Grade fraction

The objective of this exercise is to calculate the gcd of two numbers and simplify a fraction.

Exercise example N°1438 :

- Consider the expression `E=(8*x+4)^2-(8*x+4)*(7*x-5)`.
- Expand and reduce E.
- Factor E.
- 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)`.
- Expand and reduce E.
- Factor E.
- 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°1440 :

Today Tom is 15 years old and Steve is 37 years old. In how many years the age of Steve will be double that of Tom?

mathematics exams and competitions solving equations and inequations of the first degree equations 9th Grade equation_solver

The objective of this exercise is to equate a problem in order to solve it.

Exercise example N°1441 :

- Solve the system

`2*x+2*y=30`

`3*x+10*y=101` To organize photos a store offers two types of storage albums or boxes : Tom buys 2 boxes and 2 albums and pays 30. Victoria buys 3 boxes and 10 albums and pays 101. - What is the price of a box?
- What is the price of an album?

mathematics exams and competitions equations of lines and linear systems equations 9th Grade solve_equations

The purpose of this exercise is to use a system of two equations with two unknowns to solve a problem.

Exercise example N°2411 :

Determine the equation of the linear function whose graphical representation passes through the point D of coordinates (`3/5`,`2`).

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

The purpose of this exercise is to find the equation of a line representing a linear function that passes through a given point.

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:

Tuesday | 73 |
---|---|

Wednesday | 16 |

Thursday | 4 |

Friday | 73 |

Saturday | 79 |

2. Calculate the average number of books loaned, per day, during this five-day week.

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 :

grade n | `0<=n<4` | `4<=n<8` | `8<=n<12` | `12<=n<16` | `16<=n<=20` |
---|---|---|---|---|---|

Number of students | 4 | 5 | 7 | ? | 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?

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.

Age | 20-24 | 25-29 | 30-39 | 40-49 | 49-60 |
---|---|---|---|---|---|

Employees | 2 | 6 | 2 | 1 | 3 |

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°14110 :

Write in the form `sqrt(a)/b`, the following expression `1/sqrt(360)`, where a and b represent two integers.

square roots fractions Numbers 9th Grade simplify_surd

The purpose of this corrected math exercise is to simplify a square root.

Exercise example N°14111 :

Put `8+sqrt(20)` in the form `a+b*sqrt(5)`, where a and b are two natural numbers.

square roots functions 9th Grade simplify_surd

The objective of this exercise is to write an expression composed of the sum of an integer and a square root.

Exercise example N°14112 :

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)`

square roots functions 9th Grade simplify_surd

The objective of this exercise is to simplify an expression composed of several square roots.

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.