Математика (Teaching Math in English)

Добрый день, дорогие ребята!

Надеюсь, что моя лекция по теме "Математическая индукция" вам понравилась. Теперь надо закрепить ваши знания, умения и навыки, а для этого предлагаю вам порешать самостоятельно математические задачи. Я буду прикреплять задания для самостоятельной работы после каждой видео-лекции.

Problems for solution

Prove that:

1. for all n ≥ 3, the sum of the interior angles of a polygon with n vertices is 180(n−2)◦.

2. for every positve integer n ≥ 2, n^3 − n is a multiple of 6.

Problems for solution

Prove that:

1. For all n ≥ 3, n^2 ≥ 2n + 1

2. For all n ≥ 4, 2^n ≥ n^2

(Hint: Use the previous exercise to help you in the inductive step.)

3. For all n ≥ 3, the sum of the interior angles of a polygon with n vertices is 180(n−2)◦.

4. The number of non-empty subsets of a set of n elements is 2^n − 1.

Lesson 3

Deriving Hypothesis

Home task

Solve the problem:

Each of n famous scientists who meet at a conference (where n ≥ 2) wants to shake hands with all the others.

Work out how many handshakes there will be and prove your result by mathematical induction.

Lesson 4

Math Statistics ( measures of central tendency)

Home task

Consider the numbers 2 3 4 5 5

(a) Compute the mode, median, and mean.

(b) If the numbers represented codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense?

(c) If the numbers represented one-way mileages for trails to different lakes, which average(s) would make sense?

(d) Suppose the numbers represent survey responses from 1 to 5, with 1 disagree strongly, 2 disagree, 3 agree, 4 agree strongly, and 5 agree very strongly. Which averages make sense?

Lesson 5

Math Statistics ( measures of variation)

Home Task

Solve the following problem, using computation formulas

•Consumer: Radon Gas “Radon: The Problem No One Wants to Face” is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable.” Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L):

•1.9 2.8 5.7 4.2 1.9 8.6 3.9 7.2

•(a) Find the mean, median, and mode.

•(b) Find the sample standard deviation, coefficient of variation, and range.

Lesson 6

Chebyshev's Theorem

Homework

Solve problems:

• 1.The mean age of a flight attendant of PAL is 40 years old, with a standard deviation of 8. What percent of the data set lies between 20 and 60?

• 2.The mean age of salesladies in an ABC department store is 30, with a standard deviation of 6 . Between which two age limits must 75% of the data set lie?

Lesson 7

Introduction to Set Theory

Homework

Test yourself https://www.mathgoodies.com/lessons/sets/practice_unit15

Lesson 8

Operations on Sets

Homework

Challenge Exercises on Sets https://www.mathgoodies.com/lessons/sets/challenge_unit15

Do Worksheet on Set Theory https://www.math-only-math.com/worksheet-on-set-theory.html

Lesson 9

Common Number Patterns and Golden Ratio

Homework

Look online to answer the given questions.

1) What is the value of the Golden Ratio?

2) What is the Golden Ratio defined as?

3) What are some other names for the Golden Ratio (give at least four more)?

4) What mathematician discovered the Golden ratio?

5) When did this mathematician live and where is he from?

6) Name at least three more mathematicians that have researched and used the Golden Ratio. State when they lived and where they are from.

7) What structures have been built using the Golden Ratio (name at least three) and where are they located?

8) Name at least three pieces of art that use the golden ratio and state their artist.

9) Where else can the Golden Ratio be found in the real world? (Give at least three examples.)

Lesson 10

Types of Triangles

Homework: Triangle Worksheets for your needs

https://www.math-aids.com/Geometry/Triangle/

You can select different variables to customize these Triangle Worksheets for your needs. The Triangle Worksheets are randomly created and will never repeat so you have an endless supply of quality Triangle Worksheets ( a triangle fact sheet, identifying triangles, area and perimeters, the triangle inequality theorem, triangle inequalities of angles and angles, triangle angle sum, the exterior angle theorem, angle bisectors, median of triangles, finding a centroid from a graph and a set of vertices) to use at home.

! Triangle Worksheets are free to download, easy to use, and very flexible.