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Challenge - Challenge


Answer:

Source: Math Workshop - 8th. - Santillana Bicentennial

NEM: First Middle.

Main Topic: I. Numbers and Proportionality.

CMO: Powers. Powers Properties.

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Powers - Exponential Decay


Answer:

Source: Math Workshop - 8th. - Santillana Bicentennial

NEM: Fourth Medium (pre-set curriculum)

Main Topic: I. Álgabra and Functions.

CMO: Exponential Decay.

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Challenge - Probability

Which of the following alternatives is false?

A) A random experiment is the main property that its outcome is not predictable, and there is a set of possible outcomes.

B) The value of the probability of an event ranges from zero to one.

C) The probability of an event, a percentage is the value 0% and 100% maximum.

D) The probability of an event is equal to the number of favorable outcomes of the event divided by the number of cases is not favorable.

E) None of the above.

Answer:

Source: Math Workshop - 8th. - Santillana Bicentennial.

NEM: Middle East.

Main Topic: III. Probability and Statistics

CMO: Probability. Probability Basics.

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Challenge - Pattern Formation


Answer:

Source: Math Workshop - 8th. Santillana - Bicentennial

NEM: First Half (Curriculum old PSU)

Main Topic: III. Geometry.

CMO: Isometric Transformations.

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Challenge - Challenge Role


Answer:

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO: Quadratic Function.

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Quadratic - Quadratic Function


Answer:

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO: Quadratic Function.

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Challenge - Challenge


Answer:

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO: Quadratic Function.

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Quadratic Function - Sample Space

A $ 10 coin, a $ 50, $ 100 and $ 500, are released into the air and watch the seals and faces that appear. How many possible outcomes is this experiment?

A) 4

B) 8

C) 16

D) 32

E) 64

Answer:

Prime reasoning: Each coin inserted 2 choices, and multiplicative principle, then we have: 2 x 2 x 2 x 2 = 2 raised to the fourth = 16. Alternative C)

Second argument: See the tree diagram, which is explicitly the possibilities of this space Sample are 16:

Alternative C)

Source: Santillana - 3rd. Medium.

NEM: Tercero Medio.

Main Topic: III. Probability and Statistics.

CMO: Sample Space. Tree diagram.

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Challenge - Techniques

A candidate for president wants to visit 8 cities. How many ways can order the first three visits?

A) 3! , B) 8, C) 56, D) 336, E) 8!

Answer:

First line of reasoning: the first visit I can choose 8 cities in the second only between 7 (and I visited it before) and at the third visit by 6. by the multiplicative principle I can organize the visit of 8 x 7 x 6 = 336 ways.

second way of thinking: This is clearly an exercise in permutations. Must permute 8 cities in 3, ie

P (8,3) = 8! / (8-3)! = 8! / 5! = (8 x 7 x 6 x 5!) / 5! = 8 x 7 x 6 = 336 ways.

Alternative D)

Source: Santillana - 3rd. Medium.

NEM: Tercero Medio.

Main Topic: III) Probability and Statistics.

CMO: Counting Techniques.

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Counting Challenge -

launched a die 3,000 times. The number of times it appears an even number greater than 3 can be estimated at:

A) 500

B) 1,000

C) 1,500

D) 2,000

E) None of the Above.

Answer:

the theoretical probability of rolling a die to see a number greater than 3, is 2 6 possibilities (appears on 4 or 6) ....

Replaying a experiment many times (3,000 times), the experimental probability will be closer to the theoretical .... then it is highly probable that 1,000 of the times displayed an even number greater than 3.

Alternative B)

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: III: Probability and Statistics.

CMO: Law of Large Numbers.

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Chance Challenge - Probability

What is the probability of getting a club or an ace when randomly choose a card from a card deck of English?

A) 9 / 52

B) 10/52

C)

12/52 D) 16/52

E) 17/52

Answer: As events: A: "Get a club" and B "to get an ace" are NOT mutually exclusive, we proceed as follows:

P (getting a club or an ace) =

= P (getting a shamrock) + P (getting Ace) - P (get a club and an ace)

P (getting a shamrock) = 13/52

P (getting an ace) = 4 / 52

P (get a club and an ace ) = 1 / 52

P (getting a club or an ace) = 13/52 + 4 / 52 - 1 / 52 = 16/52; Alternative D)

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: III: Probability and Statistics.

CMO: Probability of the Union of 2 events not mutually exclusive.

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Challenge - Power


Answer:

Source: Workshop Santillana - Bicentennial - 1st. Middle

NEM: First Middle.

Main Topic: I. Numbers and Proportionality.

CMO: Powers

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Challenge - Challenge


Answer:

Source: 2009

CEPECH NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO. Inequalities.

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inequality - Polygon

If the sum of the interior angles of a polygon is 900 °, how many diagonals can be drawn on the polygon?

A) 4, B) 5, C) 14, D) 18, E) 28

Answer:

Source: NEM

CEPECH 2009: First Half.

Main Topic: III. Geometry.

CMO: Polygons. Basic Geometry.

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Challenge - Likeness

Which (is) of these cases we can say that two triangles are similar?

I) When different sized triangles.

II) When isosceles triangles of different sizes.

III) When are equilateral triangles of different sizes.

A) Only I

B) Only II

C) Only III

D) I and II

E) I and III

Answer:

Source: European A. Sánchez.

NEM: Middle East.

Main Topic: II. Geometry.

CMO: Likeness.

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Challenge - Challenge

If a rectangular site has an area of \u200b\u200b448 square meters and the length is 4 meters more than twice its width, its perimeter is:

A) 14 m, B) 32 m , C) 46 m, D) 92 m; missing data.

Answer: We call "A" to the width, we will express the length in terms of width and then build a quadratic equation around the area .... from there we will achieve the value of the width and therefore the length .... see:

Alternative D), the perimeter is 92!

Source: Santillana 3rd. Medium.

NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO: Quadratic Equation.

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Perimeter - Volume

Answer: What is produced is a cone, we see a drawing:

Alternative B)

Source: PSU 4th. Middle - Mare Nostrum / P.Valdivia.

NEM: Fourth Medium.

Main Topic: II. geometry.

CMO: Voluemn in Rotation.

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rotating Challenge - Total area of \u200b\u200bParallelepiped

What is the total surface area of \u200b\u200bthe rectangular parallelepiped in the following figure?

A) 48, B) 52, C) 64, D) 88, E) 96

Answer: 2 faces (2 x 4) + 2 sides / 2 x 6) + 2 faces (6 x 4)

Total Area: 2 (2x4) + 2 (2x6) + 2 (6x4) = 2 (8) + 2 (12) + 2 (24) = 16 + 24 + 48 = 88

Alternative D)

Source: Mare Nostrum - Pedro Valdivia - PSU 4th. Middle

NEM: Fourth Medium.

Main Topic: II. Geometry.

CMO: Volume Paralelpípedo.

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Challenge - Logarithms

Answer:

Alternative B)

Source: Mare Nostrum - Pedro de Valdivia

NEM: Fourth Medium.

Main Topic: I. Algebra and Functions.

CMO: Logarithms

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Challenge - Algebraic Fractions

Which of the above fractions are equal to 1?

A) Only I

B) I and II

C) I and III

D) II and III

E) I, II, III

Answer: Orders (switch in I)) , develop (the sum of the difference in II)) , compress (the denominator in III)) as appropriate for each algebraic fractions:

I and III

true, Alternative C )

Source: DEMRE

NEM: Middle East.

Main Topic: Algebra and Functions.

CMO: Algebraic Expressions simple.

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Challenge - Challenge

How much is the previous function when x = -2.2?

A) -1.2

B)

-0.8 C) -0.2

D) 0.2

E) 0.8

Answer:

Alternative D)

Source: Text 2nd. Middle - Eduardo Cid Figueroa.

NEM: Middle East.

Main Topic: Functions.

CMO: Functions.

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Function - Fraction with roots

Answer: The answer is the alternative C) .... One way to do without using rationalization

And how do you do with rationalization?

Source: Santillana 2nd. Middle - Bicentennial

NEM: Tercero Medio.

Main Topic: I. Algebra and Functions.

CMO: Roots, Rationalization.

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Challenge - Logarithms

The value of the logarithm above is:

A) -6

B) -3

C) 3

D) 6

E) 16

Response: Alternative B) .... By definition of logarithms

Source: Santillana 2nd. Middle - Bicentennial.

NEM: Fourth Medium. (In the current PSU curriculum, unadjusted)

Main Topic: I. Algebra and Functions.

NEM: Logarithms.

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Challenge - Standard deviation

can get the standard deviation of a dataset, if known:

(1) the distance between each data and media.

(2) the range of data and the number of them.

A) (1) alone.

B) (2) alone.

C) Both Together (1) and (2).

D) Each one by itself (1) or (2).

E) additional information is required.

A: remember the definition of Standard Deviation:

http://diccio-mates.blogspot.com/search/label/Desviaci% C3% B3n% C3% A1ndar 20Est%

In this formula we need the distance of each data to the average, which is given in (1), but also the numbers of sample data, which is derived from the number of distances to be .... ie (1) alone is enough ....

Let

(2) .... does not give the number of data, but the distance between the maximum and minimum is NOT the same as the distance of each data average. (2) does not work by itself and does not provide relevant data to help (1), which has ALL the required information.

Alternative A)

Source: Santillana 2nd. Middle - Bicentennial.

NEM: Fourth Medium (in the current curriculum PSU unchanged)

Main Topic: III: Probability and Statistics.

AS: Standard deviation.

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Challenge - Density

Which one (s) of the following is FALSE?

I) All Naturals is dense.

II) The set of integers is dense.

III) The set of rational numbers is not dense.

A) Only I

B) Only II

C) Only III

D) Only I and II

E) I, II, III.

Answer:

A numerical set is dense, whether taking two elements of it, whatever, there are infinitely many elements of the partnership between the two elected. Thus, neither the natives nor the integers are dense, because if you take the numbers 2 and 3 (the same holds for the integers) there is none among them that is natural and full. I and II are false.

addition complex of the Rational is dense because between any pair of numbers

a / b and c / d there are infinitely many rational

one can be achieved by the formula:

{a / b + c / d} / 2, which gives the number of the medium, which is equidistant between a / b and c / d .... III) is false.

Three: I, II, III are false, alternative E)

Source: PSU - Santillana - Bicentennial

NEM: First Middle.

Main Topic: I. Numbers and Proportionality.

CMO: Numerical sets.

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HISTORY 1.

Here are "The Story of 1" to begin to understand how it emerged the number system and how important it is "1." The idea is to help you better understand some mathematics.



As the story progresses and reaches our days with a technological breakthrough, the "1" is importante.Observa videos, draw your conclusions and discuss them with your teacher or peers class.

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Teaching Sequence Activity 6 Unit 2 Activity 5




NATIONAL AUTONOMOUS UNIVERSITY OF MEXICO
COLLEGE OF SCIENCES AND HUMANITIES
PLATEL Azcapotzalco MATHEMATICS 2 UNIT 2
didactic sequence


ACTIVITY 6 "CIRCLE"
Description of Activity:
The student will understand that is a circle. Mentioned and chart their lines and significant segments using GeoGebra. Carry out examples to help understand this concept and relates to everyday life.
Development Activity:
1. Mentioned the concepts of circumference and circle. Are they different? Explain.
2. In the next figure mentioned the name of each segment or line and write its definition.

















3. Describe examples of everyday life that represent a circle and straight segments and notable figure involved in (at least 5 examples and preferably not tapas). You can take photos for your example and append them to work.
4. Draw a circle in GeoGebra using the circle tool given its center and radius of which is 17.5 cm diameter. Draw two chords that do not pass through the center. Trace the bisectors and checks that pass through the center of the circle. Do not delete your auxiliary lines marks only give them a different color.
5. Describe the method to draw a tangent line passing through a point that belongs to the circle and then take it out on the lines marking GeoGebra be addressed.
6. Now with the procedure seen in the face session in GeoGebra draw a circle with the circle tool given its center and radius, now select a point that is outside of the circle and then draw the tangent line. Describe your procedure by checking each line of a different color for the procedure performed.