The HOT List of TAKS Vocabulary

“Words you should know…”

Dilation:

• A change in the size of a figure that results in the image getting smaller (reduction) or bigger (enlargement)

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

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…

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

Reflection:

• A transformation that “flips” an image, usually over the x or y axis.

Y axis

X axis

Rotation:

• A transformation that “turns” an image around a center point

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”

Coordinate Graph

• A graph that uses ordered pairs to name locations

x

y

(+,+)(-,+)

(-,-) (+,-)

I

IVIII

II

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!

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

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

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

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?

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

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

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

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

Scatter plot:

• A graph that shows the relationship between 2 things

• Allows trends or correlations to be determined

Positive (uphill) Negative (downhill)

No trend

Venn diagram

• Allows similarities and differences to be made between data

Neither set

Set A

Set B

Both sets

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

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.

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.

Line Graph

• Shows change over time

Line Plot

• Shows distribution of data

Circle graph:

• shows the parts of a whole, often in percentages

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)

Another measure of data…

• Range – the difference between the largest and smallest piece of data (used to show variation or consistency of data)

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

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

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…

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

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

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.

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

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

Compound Probability

• The likelihood of more than one event occurring

• P (event, another event)

• Write a fraction for each event and then multiply

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

Dependent Probability

• In compound probability, the first event has an effect on the outcome of future events

• Example:– An experiment WITHOUT replacement