AY Honors/Math Skills III/Requirements

Math Skills III

Skill Level

3

Year

2012

Version

23.12.2024

Approval authority

South American Division

1. Have the Math Skills II honor.

2. Solve the following operations using the traditional algorithm:

a. 641 + 135

b. 845 - 124

c. 34 x 125

d. 856 ÷ 24

3. Identify and classify the numerical sets.

4. Demonstrate the ability to solve the following equations:

a. 2x - 10 = -4x + 14

b. 18x - 43 = 65

c. 23x - 16 = 14 - 17x

d. 10y - 5(1 + y) = 3(2y - 2) - 20

e. x(x + 4) + x(x + 2) = 2x² + 12

f. (x - 5) / 10 + (1 - 2x) / 5 = (3-x) / 4

g. 4x(x + 6) - x² = 5x²

5. Demonstrate the ability to solve the following products:

a. (x + 3y)²

b. (a⁵ + 2bc)²

c. (3x + y²)²

d. (1 + 5m)(1 - 5m)

e. (ab - c)²

f. (m - 1)³

g. (a³ - b³) (a³ + b³)

6. Calculate the area of ​​the following figures:

7. In the Orienteering honor, the Pathfinder must have knowledge of angles to know how to use cartographic charts and to use a compass. Demonstrate the ability to convert angles to minutes, minutes to seconds, showing three practical examples.

8. In the Pioneering honor, we learned to build camp furniture, which has a whole mathematical relationship. Design and present some camp furniture where geometric shapes appear and classify each one. Cite three examples.

9. Present a poster showing ten practical examples of geometric figures used in a daily routine. It can be as cutouts, photos or design.

10. Demonstrate the ability to solve the following proportion problems:

a. At 60 km/h I travel between two cities in two hours. Traveling at 80 km/h, what is the estimated time to travel this route?

b. At an average of 90 km/h, I can make a journey in three hours. To make this journey in just two hours, what should my average speed be?

c. If 20 men working for 20 days build 500 meters of a wall, how many men will it take to build 1000 meters more of this wall in 30 days?

11. Demonstrate the ability to solve problem situations involving equations:

a. I have the following choice: I buy 20 units of a product with all the money I have, or buy only 14 units of a project with all the money I have, or buy only 14 units and I still have $15.00 in change. What is the unit value of this product?

b. What is the root of the equation 7x - 2 = -4x + 5?

c. If I add 8 to the amount of toy cars I own, I will have the same amount of cars as my brother if, of the 28 that he owns, the amount that I own is subtracted. How many toy cars do I have?