Math Skills III: Answer Key
1. Have the Math Skills II honor.
For tips and instruction see AY Honor 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 AY Honor 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 AY Honor 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
Adapted from AY Honors/Math Skills III/Answer Key on the Pathfinder Wiki, licensed under CC BY-SA 3.0. See the original page's history for its authors.
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