Here is the list of corrected exercises for the preparation of mathematics exams. Each corrected exercise is accompanied by indications, reminders of the course, and methodological advice, which allows you to practice independently.

6 exercises
• N°1436 (mathematics exams and competitions) : 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 (mathematics exams and competitions) : 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 (mathematics exams and competitions) : 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 (mathematics exams and competitions) : 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 (mathematics exams and competitions) : 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 (mathematics exams and competitions) : 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?