The 9th grade math exercises cover a wide range of essential topics from the U.S. math curriculum for this grade level. They offer students the opportunity to familiarize themselves with different mathematical concepts while practicing independently, thanks to the available corrected exercises online. These exercises cover key areas such as arithmetic (e.g., finding the GCD, checking for coprime numbers, and simplifying fractions) as well as algebraic operations (including expansion, factoring, and using special product identities).
These skills are crucial for success in ninth grade, as they form the foundation for the more advanced math taught in high school.
Exercises addressing square roots and their simplification are particularly relevant in courses on functions and equations. Through these exercises, students develop their skills in solving first-degree equations and inequalities, enhancing their understanding of manipulating and simplifying mathematical expressions involving radicals and fractions. Additionally, the expansion, simplification, and factoring of algebraic expressions are directly aligned with the chapters on special product identities and polynomials. For example, some exercises require calculating the value of a function for a given number and simplifying mathematical expressions.
Problems requiring formulating an equation to solve a real-world problem help students apply practical mathematics. Additionally, vector calculation exercises, such as solving systems of equations to determine coordinates or calculating the distance between two points, allow students to practice analytic geometry.
Finally, exercises in statistics, like calculating the average number of books borrowed per day over a week or analyzing student test scores, align perfectly with the chapters on averages and data analysis. This variety allows students to practice essential domains, in alignment with the U.S. ninth-grade curriculum.
This set of interactive exercises and corrected exercises prepares students thoroughly for their assessments, familiarizing them with the full range of mathematical skills required per the U.S. school program. The exercises cover topics from rational numbers to polynomials, including functions, systems of equations, and vectors, ensuring comprehensive and well-supported practice.
37 exercisesExercise example N°1110 :
Use yellow numbers and blue arithmetic operators to calculate the target number.
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 :
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 :
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 :
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 :
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 :
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 |
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 |
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.