Preparation for Middle School Math Exams

The solved exercises for preparing for middle school math exams in the United States play a crucial role in training students. These exercises are designed to cover various aspects of the curriculum, allowing students to strengthen their skills and effectively prepare for exams.

A typical exercise addresses the simplification of fractions, the simplification of square roots, and the calculation of fractions involving exponents, essential skills for middle school exams. Another type of exercise focuses on the calculation of the greatest common divisor (GCD) and the simplification of fractions, thereby enhancing the understanding of whole and rational numbers. Other exercises emphasize the expansion, simplification, and factoring of algebraic expressions, as well as solving equations, essential algebra skills. Some exercises enable students to practice setting up and solving equations, while others focus on solving linear systems of equations, applying the concepts of linear equations and systems of equations.

These exercises, directly linked to the middle school math curriculum in the United States, offer a comprehensive methodological approach and allow students to practice independently. They are accompanied by course reviews, methodological advice, and valuable guidance, helping students consolidate their knowledge and develop essential skills to succeed in their math exams.

6 exercises

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)`
  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.

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 :

  1. Compute the GCD of the numbers 5104 and 968.
  2. 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)`.
  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°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 :

  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.
  2. What is the price of a box?
  3. 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.

The mathematics exams and competitions topic is available for : 9th Grade