Here is the list of free online exercises of mathematics 10th Grade, sophmore year, year 11. Each corrected exercise is accompanied by indications, reminders of course, methodological advice which allows you to practice independently.

37 exercises
• N°1418 (10th 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°1423 (10th 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°1430 (10th 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 (10th 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°1438 (10th 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 (10th 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°1501 (10th Grade) : This corrected exercise allows to practice solving linear equations with one unknown of the form ax+b=0.

Exercise example :

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

• N°1502 (10th Grade) : The purpose of this exercise on quadratic equations is to practice solving 2nd degree equations and null product equations.

Exercise example :

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

• N°1503 (10th Grade) : The purpose of this exercise is to solve a second degree equation by reducing it to solving a first degree equation.

Exercise example :

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

• N°1504 (10th Grade) : 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 :

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

• N°1505 (10th Grade) : 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 10th Grade is_odd_or_even_function
• N°1506 (10th Grade) : 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 10th Grade is_odd_or_even_function
• N°1507 (10th Grade) : 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 10th Grade
• N°1508 (10th Grade) : The purpose of this exercise is to solve graphically an equation.

Exercise example :

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.

• N°1509 (10th Grade) : 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 10th Grade
• N°1510 (10th Grade) : 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 10th Grade simplify_trig
• N°1511 (10th Grade) : 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 10th Grade abs
• N°1512 (10th Grade) : 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 10th Grade abs
• N°1513 (10th Grade) : 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.

• N°1514 (10th Grade) : 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.

• N°1515 (10th Grade) : The purpose of this corrected exercise is to complete the decomposition of a number into prime numbers.

Exercise example :

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*?*?

1515 order, absolute value, inequations 10th Grade prime_factorization
• N°1516 (10th Grade) : The purpose of this exercise is to find the ordered decomposition of a number into primes.

Exercise example :

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

1516 order, absolute value, inequations 10th Grade prime_factorization
• N°1517 (10th Grade) : The purpose of this corrected arithmetic exercise is to determine if a number is a prime number.

Exercise example :

51 is an integer, is it prime ?

1517 order, absolute value, inequations 10th Grade prime_factorization
• N°1518 (10th Grade) : The goal of this exercise is to find the ordered decomposition of a product of numbers into primes.

Exercise example :

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

1518 order, absolute value, inequations 10th Grade prime_factorization
• N°1520 (10th Grade) : The purpose of this exercise is to simplify a fraction using the decomposition of a number into a product of prime factors.

Exercise example :

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

• N°1524 (10th Grade) : The objective of this exercise is to determine the ordinate of a direction vector from a line equation.

Exercise example :

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

• N°1539 (10th Grade) : The purpose of this exercise is to use algebraic computation techniques to determine the irreducible form of a division of fractions.

Exercise example :

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

• N°1541 (10th Grade) : The purpose of this corrected calculus exercise is to use algebraic calculus techniques to simplify a product of fractions.

Exercise example :

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

• N°2413 (10th 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 (10th 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 (10th 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 (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 :

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 (10th 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 (10th 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 (10th 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°24121 (10th 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 (10th 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