AY Honors/Math Skills III/Answer Key

Math Skills III

Skill Level

3

Year

2012

Version

22.12.2024

Approval authority

South American Division

1

Have the Math Skills II honor.

For tips and instruction see Math Skills II.

2

Solve the following operations using the traditional algorithm:

2a

641 + 135

2b

845 - 124

2c

34 x 125

2d

856 ÷ 24

3

Identify and classify the numerical sets.

4

Demonstrate the ability to solve the following equations:

4a

2x - 10 = -4x + 14

4b

18x - 43 = 65

4c

23x - 16 = 14 - 17x

4d

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

4e

x(x + 4) + x(x + 2) = 2x² + 12

4f

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

4g

4x(x + 6) - x² = 5x²

5

Demonstrate the ability to solve the following products:

5a

(x + 3y)²

5b

(a⁵ + 2bc)²

5c

(3x + y²)²

5d

(1 + 5m)(1 - 5m)

5e

(ab - c)²

5f

(m - 1)³

5g

(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:

10a

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?

10b

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?

10c

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:

11a

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?

11b

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

11c

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?

References