The HOT List of TAKS Vocabulary “Words you should know…”
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Transcript of The HOT List of TAKS Vocabulary “Words you should know…”
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The HOT List of TAKS Vocabulary
“Words you should know…”
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Dilation:
• A change in the size of a figure that results in the image getting smaller (reduction) or bigger (enlargement)
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Scale factor:
• A factor is a number you use to multiply. In this case, a scale factor is a number that is used to DILATE a figure. It could make the figure smaller (reduction, less than 1) or bigger (enlargement, greater than 1).
> 1< 1
EnlargementReduction
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To find a scale factor:
• Write the new measurement over the original measurement. Simplify or consider other ways to express the value.
new
original
3
7
7
3
This also equals 2 1/3 OR 2.333…
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Similar Figures:
• Figures that have congruent angles and proportional sides (CAPS)
• A scale factor exists between similar figures (sometimes, it’s obvious, but other times you must write and solve a proportion)
2.1 cm
3.2 cm
4.3 cm x
2.1 4.3
3.2 x
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Reflection:
• A transformation that “flips” an image, usually over the x or y axis.
Y axis
X axis
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Rotation:
• A transformation that “turns” an image around a center point
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Translation• A transformation that “slides” an image
up/down, left/right, or a combination of both
I am the original image
I am the new, or prime, image
,
This transformation was “to the right and up”
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Coordinate Graph
• A graph that uses ordered pairs to name locations
x
y
(+,+)(-,+)
(-,-) (+,-)
I
IVIII
II
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Scientific Notation:
• A way of writing very large or very small numbers
___ x 10?
A number between 1 and 9.99999…
Must be times 10
Requires an exponent
+ for big #
- for small #
The exponent used tells how many times to move the decimal!
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Rational number:
• A number that can be written as the ratio of a to b, as long as b ≠ 0
• Examples: ½ = .5 = 50%
3 = 3/1 = 3.0 = 300%
16
For the most part, these are the numbers that we convert into other forms: fractions, decimals, and percents
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Square root
36 6
A number, that when multiplied by itself, equals a given product. Occasionally, a
square root is represented as being the side of a square.
5 25121 11
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Irrational number:
• Numbers that CANNOT be written as the ratio of a to b
• For example: and
The square root of 17 is larger than 4, but less than 5. It is closer to the 4.
4 5
17
16 25
x
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Pythagorean Theorem• This formula works with RIGHT triangles to
determine the length of a leg or hypotenuse. • a2 + b2 = c2
• a and b are legs and create the right angle• c is the hypotenuse, or longest side
a = 4
b =
3
c = 5
a2 = 16
b2 =
9
c 2 = 2524 feet
26 feet
x
z
POND
How long is a bridge from point x to point z?
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Proportional Relationship
• Passes thru the origin when graphed
• The ratio of y to x can be simplified to the same thing
• The equation has no constant y = mx
x y
3 6
7 14
3.1 6.2
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Non-Proportional Relationship
• Does NOT pass thru the origin
• The ratio of y to x varies
• The equation has a constant
Y = mx + b
x y
3 5
4 8
7 11
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Proportions
• Used to make comparisons• Used in similar figures• Used to make measurement conversions• Used to find unit rates• Used to work with percents
• Can be written 4 different ways, as long as the cross-products are the same!
a c
b d %
100
part
whole
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Percent words:
• Commission – the money someone makes selling goods or merchandise
• Discount – savings; the money you save when something is on sale
• Tax – the money you pay when you buy something
• Tip – the money you leave a waiter or waitress
• Sale price – a reduced price
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Scatter plot:
• A graph that shows the relationship between 2 things
• Allows trends or correlations to be determined
Positive (uphill) Negative (downhill)
No trend
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Venn diagram
• Allows similarities and differences to be made between data
Neither set
Set A
Set B
Both sets
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Box and Whisker Plot
• A way to organize data using the median and quartiles to show distribution
least value
greatest value
median
lower quartile
upper quartile
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Histogram
• Used to make comparisons and show distribution of data
• Very similar to a bar graph, but data is grouped into intervals
Notice that the bars are touching and represent a range of data:
0 to 10, 10 to 20, etc.
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Bar Graph
• Used to make comparisons
Notice that the bars do not touch and each one represents a single piece of data on the x-axis.
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Line Graph
• Shows change over time
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Line Plot
• Shows distribution of data
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Circle graph:
• shows the parts of a whole, often in percentages
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Measures of Central Tendency
• Mean – find the sum of the values and divide (makes all the data the same size)
• Median – least to greatest, find the middle (cuts the data into the top and bottom half)
• Mode – the most, or favorite (indicates frequency or distribution of data)
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Another measure of data…
• Range – the difference between the largest and smallest piece of data (used to show variation or consistency of data)
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Outlier:
• A piece of data that is significantly smaller or larger than the rest and stands out as being “out of place”
• An outlier doesn’t have much affect on the median or mode, but can really affect a range or a mean
• Example: 2, 4, 4, 7, 89
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Sampling Methods:
• Random – no specific rule is applied to determine who will be surveyed
• Systematic – a rule is followed, such as every 10th person OR only the students in the 8th grade
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Validity/Bias
• If careful thought is not given to a sample being taken, then the results may not be accurate to reflect a larger population
• Example: If you question the PE boys about if the girls should get their locker room remodeled before the boys do…OR if you ask the kids in math club their favorite class…
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Perimeter/Circumference
• The distance around the outside of a polygon or circle
• For perimeter, add• For circumference, use the formula• Measured in linear units: feet, inches, cm
• Can be “disguised” as fencing, a frame, a revolution on a ferris wheel, the distance a tire rolls
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Area
• The amount of space inside a 2-dimensional object
• Measured in square units: ft2, in2, yd2
• Use the appropriate formula for the shape
• Can be “disguised” as grass in a yard, paint on a wall, glass over a picture
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Surface area (also measured in square units)
• Total surface area
Covers the entire outer surface of a 3-dimensional figure! May also be for a net.
• Lateral surface area
Leaves off the base or bases of a 3-dimensional figure! May also be for a net.
Leave off the two circles!
Leave off the bottom of a pyramid.
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Volume
• The amount needed to fill (capacity) a 3-dimensional object
• Measured in cubic units: yd3, ft3, m3
• Use the correct formula for the shape
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Probability
• The likelihood of a single event occurring
• P(event) =
• Written as a fraction, it can be simplified or converted into other equivalent forms
event
totaloutcomes
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Compound Probability
• The likelihood of more than one event occurring
• P (event, another event)
• Write a fraction for each event and then multiply
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Independent Probability
• In compound probability, the first event has no effect on future events
• Examples: – a spinner and a number cube– flipping a coin 3 times– an experiment WITH replacement
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Dependent Probability
• In compound probability, the first event has an effect on the outcome of future events
• Example:– An experiment WITHOUT replacement
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