Mathematics Skills III Honor

Science & Health

Requirements

  1. Have the Mathematics Skills II Honor.
  2. 2. Solve the following operations using the traditional algorithm:
    • 641 + 135
    • 845 - 124
    • 34 x 125
    • 856 : 24
  3. Identify and classify the number sets.

    Answer: • Natural numbers (N): 0, 1, 2, 3... (counting numbers). • Integers (Z): include the natural numbers and the negatives (...-2, -1, 0, 1, 2...). • Rational numbers (Q): numbers that can be written as a fraction a/b — includes integers, exact decimals, and repeating decimals. • Irrational numbers (I): cannot be written as a fraction — infinite, non-repeating decimals (e.g.: pi, the square root of 2). • Real numbers (R): the union of all the previous ones (rationals + irrationals). — The number sets keep expanding: from the naturals to the reals, each one contains the previous.

  4. Demonstrate the ability to solve the following equations:
    • 2x - 10 = - 4x + 14
    • 18x - 43 = 65
    • 23x - 16 = 14 - 17x
    • 10y - 5 (1 + y) = 3 (2y - 2) - 20
    • x(x + 4) + x(x + 2) = 2x² + 12
    • (x - 5)/10 + (1 - 2x)/5 = (3-x)/4
    • 4x (x + 6) - x² = 5x²
  5. Demonstrate the ability to solve the following special products:
    • (x + 3y)
    • (a5 + 2bc)2
    • (3x + y2)2
    • (1 + 5m) (1 - 5m)
    • (ab - c)2
    • (m - 1)3
    • (a3 - b3) (a3 + b3)
  6. Calculate the area of the following plane figures:
  7. In the Orienteering Honor, the Pathfinder needs to have knowledge of angles in order to know how to use a map and a compass: Demonstrate the ability to convert degrees to minutes, and minutes to seconds, showing three practical examples.
  8. In the Pioneering Honor we learn to build camp furniture, which in turn has an entire mathematical relationship. Draw and present some camp furniture in which geometric shapes appear and classify each one. Cite three examples.
  9. Present a poster showing ten practical examples of geometric figures used in everyday life. It can be in the form of cut-out figures, photos, or drawings.
  10. Demonstrate the ability to solve the following proportion problems:
    • At 60 km/h I travel the route between two cities in two hours. Driving at 80 km/h, what is the estimated time to cover this route?
    • At an average of 90 km/h I travel a route in three hours. For me to cover this route in only two hours, what should my average speed be?
    • If 20 men working for 15 days build 500 meters of a wall, how many men will be needed to build an additional 1000 meters of this wall in 30 days?
  11. Demonstrate the ability to solve word problems involving equations:
    • I have the following choice: Either I buy 20 units of a product with all the money I have, or I buy only 14 units and still have R$ 30.00 change left over. What is the unit price of this product?
    • What is the root of the equation 7x - 2 = -4x + 5?
    • If I add 8 to the number of toy cars I have, I will have the same number of toy cars as my brother, if the number I have is subtracted from the 28 he has. How many toy cars do I have?