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 exercises
• N°1110 (9th Grade) : 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 :

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

## Countdown

1110 mental math games arithmetic_solver
• N°1412 (9th Grade) : The purpose of this exercise is to develop an algebraic expression using the most suitable remarkable identity.

Exercise example :

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

1412 algebraic calculation and remarkable identities 9th Grade expand
• N°1413 (9th Grade) : The purpose of this exercise is to calculate the square of a number using a remarkable identity.

Exercise example :

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

1413 algebraic calculation and remarkable identities 9th Grade expand
• N°1414 (9th Grade) : 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 square roots 9th Grade simplify_surd
• N°1415 (9th Grade) : 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.

• N°1416 (9th Grade) : 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 9th Grade simplify_surd
• N°1417 (9th Grade) : 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 9th Grade simplify_surd
• N°1418 (9th Grade) : 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 simplify_surd
• N°1419 (9th Grade) : 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 9th Grade simplify_surd
• N°1422 (9th Grade) : The objective of this corrected math exercise is to solve a first order inequation.

Exercise example :

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

1422 solving equations and inequations of the first degree 9th Grade inequality_solver
• N°1423 (9th Grade) : The objective of this corrected math exercise is to solve a system of two equations with two unknowns.

Exercise example :

Solve the following system:

-x-2*y = 3

3*x = -2

1423 solve_equations
• N°1427 (9th Grade) : The objective of this corrected arithmetic exercise is to calculate the gcd of two integers.

Exercise example :

Calculate the gcd of 225 and 84.

1427 integers and rational numbers 9th Grade gcd
• N°1428 (9th Grade) : The objective of this exercise is to use the GCD to check if two integers are prime to each other.

Exercise example :

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

1428 integers and rational numbers 9th Grade gcd
• N°1429 (9th Grade) : The purpose of this exercise is to put a fraction into its irreducible form.

Exercise example :

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

• N°1430 (9th Grade) : The purpose of this corrected algebraic calculus exercise is to factor an algebraic expression that involves squares.

Exercise example :

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

1430 factor
• N°1431 (9th Grade) : The purpose of this exercise is to factor an algebraic expression using a remarkable identity of the form a² - b².

Exercise example :

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

1431 factor
• N°1434 (9th Grade) : The objective of this corrected calculus exercise is to simplify an expression containing fractions.

Exercise example :

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

• N°1435 (9th Grade) : 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 9th Grade array_values
• N°1436 (9th Grade) : The objective of this exercise is to reduce a fraction, simplify a square root, and calculate a fraction that contains powers.

Exercise example :

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)
1. Compute A and give the result as an irreducible fraction.
2. Write B in the form a*(sqrt(6)) where a is a relative integer.
3. Write C as an integer.

• N°1437 (9th Grade) : The objective of this exercise is to calculate the gcd of two numbers and simplify a fraction.

Exercise example :

1. Compute the GCD of the numbers 5104 and 968.
2. Write the fraction 5104/968 in irreducible form.

• N°1438 (9th Grade) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

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.

1438 expand_and_simplify
• N°1439 (9th Grade) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

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.

1439 expand_and_simplify
• N°1440 (9th Grade) : The objective of this exercise is to equate a problem in order to solve it.

Exercise example :

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?

• N°1441 (9th Grade) : The purpose of this exercise is to use a system of two equations with two unknowns to solve a problem.

Exercise example :

1. Solve the system
2*x+2*y=30
3*x+10*y=101
2. 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.
3. What is the price of a box?
4. What is the price of an album?

• N°2411 (9th Grade) : 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 :

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

• N°2413 (9th Grade) : The purpose of this exercise is to find the equation of a line from two points.

Exercise example :

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

2413 equation_straight_line
• N°3441 (9th Grade) : The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.

Exercise 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 vector_coordinates
• N°3442 (9th Grade) : The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.

Exercise 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 vector_norm
• N°3443 (9th Grade) : The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.

Exercise 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
• N°4401 (9th Grade) : The purpose of this corrected statistics exercise is to practice calculating an arithmetic mean.

Exercise 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:

Tuesday73
Wednesday16
Thursday4
Friday73
Saturday79
1. Calculate the total number of books loaned during the entire week.
2. Calculate the average number of books loaned, per day, during this five-day week.

4401 statistics average
• N°4402 (9th Grade) : The purpose of this corrected statistics exercise is to practice calculating the frequency of a series.

Exercise example :

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

grade n0<=n<44<=n<88<=n<1212<=n<1616<=n<=20
Number of students457?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?

4402 statistics
• N°4403 (9th Grade) : The purpose of this corrected statistics exercise is to determine from a table the frequency of a series.

Exercise example :

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

Age20-2425-2930-3940-4949-60
Employees26213

4403 statistics
• N°14110 (9th Grade) : The purpose of this corrected math exercise is to simplify a square root.

Exercise example :

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

14110 square roots 9th Grade simplify_surd
• N°14111 (9th Grade) : 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 9th Grade simplify_surd
• N°14112 (9th Grade) : 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 9th Grade simplify_surd
• N°24121 (9th Grade) : The purpose of this exercise is to read on a graph the image of a number by a function.

Exercise example :

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

24121 linear functions and affine functions
• N°24122 (9th Grade) : The purpose of this exercise is to read on a graph the antecedent by a function of a number.

Exercise 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