Unit 11 June 1. CARTESIAN COORDINATES. Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is: The point (12,5) is 12 units along, and 5 units up. The left-right (horizontal) direction is commonly called X. Is also called The X- Coordinate Axis or Abscissa Axis. The up-down (vertical) direction is commonly called Y. Is also called the Y- Coordinate Axis or Ordinate Axis. Put them together on a graph: Axel Cotón Gutiérrez Mathematics 1º ESO 11.1
Transcript
Unit 11 June
1. CARTESIAN COORDINATES.
Using Cartesian Coordinates we mark a point on a graph by how far along and
how far up it is:
The point (12,5) is 12 units along, and 5 units up.
The left-right (horizontal) direction is commonly called X. Is also called The X-
Coordinate Axis or Abscissa Axis.
The up-down (vertical) direction is commonly called Y. Is also called the Y-
Coordinate Axis or Ordinate Axis.
Put them together on a graph:
Axel Cotón Gutiérrez Mathematics 1º ESO 11.1
Unit 11 June
Where they cross over is the "(𝟎𝟎,𝟎𝟎)" point, called Origin of Coordinates; you
measure everything from there.
It is like we put two Number Lines together, one going left-right, and the other
going down-up.
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As 𝒙𝒙 increases, the point moves further right. When 𝒙𝒙 decreases, the point
moves further to the left. As 𝒚𝒚 increases, the point moves further up. When 𝒚𝒚
decreases, the point moves further down. The coordinates are always written in a
certain order:
• the Horizontal distance first,
• then the Vertical distance.
This is called an "Ordered Pair" (a pair of numbers in a special order)
And usually the numbers are separated by a comma, and parentheses are put
around the whole thing like this:
(𝟒𝟒,𝟓𝟓)
Just like with the Number Line, you can also have Negative Values. Negative:
start at zero and head in the opposite direction:
• Negative 𝒙𝒙 goes to the left.
• Negative 𝒚𝒚 goes down.
MATH VOCABULARY: Cartesian Coordinates, Graph, Axis, Origin of Coordinates,
Abscissa, Ordinate, Ordered Pair.
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2. GRAPHS.
In everyday life, many quantities depend on one or more changing Variables.
For example:
• Plant growth depends on sunlight and rainfall.
• Distance travelled depends on speed and time taken.
• Test marks depend on attitude, listening in lectures and doing tutorials (among
many other variables!!).
Graphs can be used to quickly get an idea of how one quantity varies as
another quantity changes.
This graph shows Dan’s journey on his bike. We can see we use points to see where
the graphs changes.
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A Function is a relation between two variables such that for every value of the
first, there is only one corresponding value of the second. We say that the second
variable is a function of the first variable.
The first variable is the Independent Variable (usually 𝒙𝒙), and the second
variable is the Dependent Variable (usually 𝒚𝒚). A good way of presenting a Function is
by Graphical Representation. Graphs give us a visual picture of the function.
Normally, the values of the Independent Variable (generally the 𝒙𝒙 − 𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗)
are placed on the Horizontal Axis, while the values of the Dependent Variable
(generally the 𝒚𝒚 − 𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗) are placed on the Vertical Axis.
The following graph shows the present people (in thousands) in a shopping centre
during a day.
The function increases in the intervals (9, 12) and (14, 18).
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The function decreases in the intervals (12, 14) and (18, 24).
The point (12, 3) is a local maximum and the point (14, 2) is a local minimum.
At 09:00 the function has the global minimum and at 18:00 the function has the global
maximum (5000 people).
MATH VOCABULARY: Function, Independent Variable, Dependent Variable, Graphical
Representation, Interval, Maximum, Minimum.
3. STATISTICS.
Statistics is the science of making effective use of data relating to groups of
individuals or experiments. It deals with all aspects of this, including not only the
collection, organization, presentation, analysis and interpretation of data, but also the
planning of the collection of them, in terms of the design of surveys and experiments.
Imagine you have to make a study of the leisure activities in a city. The
Population of this study will be the group of inhabitants of that city. A part of this
group is called Sample. Therefore, the Population is the whole group of units that you
are going to study and a Sample is a subset of the population. Each unit of the
population is called Individual.
The owner of a screw factory wants to make a quality control. He picks up 1 out of
every 100 produced screws and then he analyses them.
The population is the total number of the screws of the factory.
The sample is 1% of the population.
The individuals are each one of the screws.
Statistical Variables are things that we measure, control or manipulate in
research. They can be numbers, words, measurements, observations ... Statistical
Variables can be Qualitative or Quantitative.
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• Qualitative Variable is descriptive information (describes something).
Examples: eyes color, car brands, leisure activities …
• Quantitative Variable is numerical information (numbers). Examples: height,
age, number of televisions in each house …
You can collect data using a Data-Collection Sheet. This one is a tally chart.
Data can also be shown in a Frequency Table:
The number of televisions in each house of my street is shown in the frequency table.
The number of houses in my street are:
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1 + 5 + 12 + 9 + 1 = 28 houses
The number of TVs are:
0 + 5 + 24 + 27 + 4 = 60 TVs
The Relative Frequency is a percentage of the Frequency:
