AY Honors/Math Skills IV/Answer Key/en

Math Skills IV

Skill Level

3

Year

2012

Version

18.06.2025

Approval authority

South American Division

1

Have the Math Skills III honor.

For tips and instruction see Math Skills III.

2

Present a bibliographic report with at least five persons who contributed to the development of mathematics throughout the history of mankind.

3

Develop and present the calculations of the following equations:

3a

5x² - 3x - 2 = 0

3b

3x² + 55 = 0

3c

x² - 10x + 25 = 0

4

Present and develop the percentage calculations of the following problems:

4a

3% of 450

4b

25% of 1440

4c

30% of 2500

5

Present three practical situations, in written form, of situations in which we use percentages in our daily routine.

6

Present and develop three practical situations of everyday problems in which we use the quadratic equation.

7

Solve and present the development of the following functions, assuming that f(x) = x - 3 and g(x) = -3x + 4.

If f(x) = x - 3 and g(x) = -3x + 4, determine:

7a

f(f(0))

7b

f(f(1)) + g(f(3))

8

Represent the following functions in a Cartesian graph:

8a

y = 3x-1

8b

f(x) = 2x + 3

9

Demonstrate the ability to solve problems with circles; how to calculate the circumference and area using the formula for each. Present two examples of each.

10

Present the ability to calculate the area of ​​regular polygons, such as a hexagon inscribed in a circle, area of ​​a cylinder surface, volume of a prism, and the volume of a pyramid.

11

In our daily routine, we have to deal with all prices of tax rates. Demonstrate the ability to solve the two most common situations of interest.

11a

Luciana made an investment of $100 at 2% simple interest a month. How much will she have in total after 8 months of investing?

11b

David asked for a bank loan of $3000 and will pay in 6 months a composite interest rate of 1.5% a month. Calculate the total to be paid to the bank after 6 months.

References