The document serves as a template for a presentation on calculus, detailing its significance and historical context while also providing technical elements like fonts and editable resources. It highlights various branches of mathematics, such as propositional and logical calculus, and includes examples of how calculus is applied in different fields like economics and engineering. Additionally, the template includes references to planets in our solar system as metaphors for teaching concepts related to calculus.

1. Calculus -
Mathematics
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12th grade

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3. Table of contents
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01
04
02
05
03
06
Introduction Features Infinitesimal
Systematization Formulas References

4. Whoa!
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you introduce yourself, write your email…

5. Introduction to calculus
Mercury takes a little more than 58 days to
complete its rotation, so try to imagine how
long days must be there! Since the
temperatures are so extreme, albeit not as
extreme as on Venus, Mercury has been
deemed to be non-habitable for humans
Mercury is the closest planet to the Sun and
the smallest one in the entire Solar System.
Contrary to popular belief, this planet's name
has nothing to do with the liquid metal.
Mercury was, instead, named after the
famous Roman messenger god Mercurius

6. Introduction
01
You can enter a subtitle here if you need it

7. What is calculus?
Do you know what helps you make your point
crystal clear? Lists like this one:
● They’re simple
● You can organize your ideas clearly
● You’ll never forget to buy milk!
And the most important thing: the audience won’t
miss the point of your presentation

8. Features
02
You can enter a subtitle here if you need it

9. Logical-mathematical
Two important meanings
Venus has a beautiful name
and is the second planet from
the Sun. It’s hot and has a
poisonous atmosphere
Mercury is the closest planet to
the Sun and the smallest one
in the Solar System—it’s only a
bit larger than the Moon
Reasoning

10. Three conditions
Mercury is the closest
planet to the Sun and the
smallest of them all
Venus has a beautiful
name and is the second
planet from the Sun
Despite being red, Mars
is actually a cold place.
It’s full of iron oxide dust
Consistent Decidable Complete

11. Natural language as logical calculus
Mars is actually a very
cold place
Venus has extremely
high temperatures
Jupiter is the biggest
planet of them all
Saturn is a gas giant and
has several rings
Propositional
calculus
Calculation of
predicates
Calculus as a
class logic
Calculus as a
logic of relations

12. Venus has extremely
high temperatures
Neptune is the farthest
planet from the Sun
History of calculus
Mars is actually a very
cold place
Mercury is the closest
planet to the Sun
Saturn is a gas giant
and has several rings
Jupiter is the biggest
planet of them all
Early ages Renaissance 17th & 18th cent.
19th century 20th century Today

13. Awesome
words

14. “This is a quote, words full of wisdom that
someone important said and can make the
reader get inspired”
—Someone Famous

15. Infinitesimal
03
You can enter a subtitle here if you need it

16. A picture is worth a
thousand words

17. A picture always
reinforces
the concept
Images reveal large amounts of data, so
remember: use an image instead of a long
text. Your audience will appreciate it

18. 1622
The first calculation rules were created, based
on the logarithmic scales previously used

19. Jupiter’s rotation period
9h 55m 23s
333,000
The Sun’s mass compared to Earth’s
386,000 km
Distance between Earth and the Moon

20. Mercury is the closest
planet to the Sun and the
smallest of them all
Physics
Venus has a beautiful
name and is the second
planet from the Sun
Engineering
Despite being red, Mars
is actually a cold place.
It’s full of iron oxide dust
Economics
Where is calculus currently applied?
50% 75%
25%

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24. Systematization
04
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25. Woolsthorpe
Where did calculus come from?
Venus is the second
planet from the Sun

26. A correct mental calculation: steps
Mental picture
Venus is the second planet
from the Sun
Focus
Mercury is the closest
planet to the Sun
Simplify
Despite being red, Mars
is a very cold place
01 02 03

27. Actuarial
science
Applications of calculus
Applications
Economics &
finance
Computer
science
Engineering &
statistics
Mars is a red planet
Mercury is very small
Venus is a hot planet
Jupiter is a gas giant

28. Use tables to represent data
Result 01 Result 02 Result 03 Result 04
Exercise 01 0.06 0.53 0.38 0.38
Exercise 02 0.11 9.4 0.53 0.78
Exercise 03 95.2 1.16 9.4 1.16

29. Show data with a graph
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Data B
Mercury is quite a
small planet
Data A
Venus has very
high temperatures
Data C
Saturn is a gas
giant with rings

30. Exercise 1: answer this question
At how many points do the following
parabolas intersect the abscissa axis?
y=x²-5x+3
y=2x²-4x+4
y=x²-x+3
y=2x²-5x+4

31. Exercise 1: solutions
At how many points do the following
parabolas intersect the abscissa axis?
2
1
y=x²-5x+3
y=x²-4x+4
2
0
y=-x²-x+3
y=2x²-5x+4

32. Exercise 2: complete the table
Problem 01
Statement
Three kilograms of anchovies are worth €18. Write and represent
the function that defines the cost of the anchovies based on the
kilograms purchased
Solution
Problem 02
Statement
In the 10 first weeks of cultivation of a plant, which measured 2 cm,
it has been observed that its growth is directly proportional to time,
seeing that in the first week it has grown to measure 2.5 cm. Set up
a function so that gives the height per time of the plant
Solution

33. Exercise 2: solutions
Problem 01
Statement
Three kilograms of anchovies are worth €18. Write and represent
the function that defines the cost of the anchovies based on the
kilograms purchased
Solution
The ordinate to the origin is 0 because it equals 0 kg
The slope is 18/3=6
The line equation is y=6x
Problem 02
Statement
In the 10 first weeks of cultivation of a plant, which measured 2 cm,
it has been observed that its growth is directly proportional to time,
seeing that in the first week it has grown to measure 2.5 cm. Set up
a function so that gives the height per time of the plant
Solution
Initial height = 2 cm (ordinate at origin)
Weekly growth = 2,5-2 = 0,5 (slope)
The line equation is y=0,5x+2

34. Exercise 3: find the values
y=ax²+bx+c
(1,1), (0,0), (-1,1)
Function 01
g(x)=x²+2
h(x)=2x²-2
Function 02
y=x²+ax+a
(1,9)
Function 03
Calculate a, b and c
Calculate their
intersection points
Calculate a

35. Exercise 3: solutions
y=ax²+bx+c
(1,1), (0,0), (-1,1)
Function 01
g(x)=x²+2
h(x)=2x²-2
Function 02
y=x²+ax+a
(1,9)
Function 03
a=1; b=0; c=0 (-2,6) and (2,6) a=4
Calculate a, b and c
Calculate their
intersection points
Calculate a

36. Exercise 4: represent the functions
It has slope -3 and ordinate at the origin -1
It has for slope 4 and passes through the point (-3,2)
It passes through the points A(-1,5) and B(3,7)
It passes through the point P(2,-3) and is parallel to
the line of equation y=-x+7
Data Function

37. Exercise 4: solutions
Data Function
It has slope -3 and ordinate at the origin -1
It has for slope 4 and passes through the point (-3,2)
It passes through the points A(-1,5) and B(3,7)
It passes through the point P(2,-3) and is parallel to
the line of equation y=-x+7
y=-3x-1
y=4x+14
y=1/2x+11/2
y=-x-1

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“Despite being red,
Mars is actually a
very cold place”
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smallest planet in
the Solar System”
“Neptune is the
farthest planet from
the Sun”
“Saturn is a gas
giant and has
several rings”
“Venus is the
second planet from
the Sun and is
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