Download Example - AllSaintsMath7-8

least common multiple
(LCM)
The smallest number, other than zero, that is a multiple of
two or more given numbers
Example:
6
9
The LCM of 6 and 9 is 18.
x1
6
9
x2
12
18
x3
18
27
x4
24
36
factor
A number that is multiplied by another number to get a product
Example:
2X3=6
2 and 3 are factors of 6.
greatest common factor
(GCF)
The largest common factor of two or more given numbers
Example:
18: 1, 2, 3, 6, 9, 18
30: 1, 2, 3, 5, 6, 10, 15, 30
6 is the GCF of 18 and 30.
power
The value of a number represented by a base and an exponent
Example:
43 = 4 X 4 X 4
= 64
base
A number used as a repeated factor
Example:
83 = 8 X 8 X 8
The base is 8. It is used as a factor three times.
The exponent is 3.
exponent
The number that indicates how many times the base is used
as a factor
Example:
43 = 4 X 4 X 4
4 is the base; 3 is the exponent
perfect square
A number that has an integer as its square root
Example:
16 is a perfect square.
square number
A number that can be represented with a square array
Examples:
square root
One of the two equal factors of a number
Example:
6 is the square root of 36
since 62 = 6 X 6 = 36
So, 36 = 6 because we are looking for the one value or
factor (which is 6 for this example) that gives us the
number below the square root sign.
order of operations
The order in which the operations are done within an
expression
1. Operate inside parentheses.
2. Multiply as indicated by exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
Example:
10 ÷ (2 + 8) X 23 - 4
10 ÷ 10 X 23 - 4
10 ÷ 10 X 8 – 4
1X8–4
8–4
4
Add inside parentheses
Solve the exponent
Divide
Multiply (remember left to right)
Subtract
Final answer!
divisibility rules
a way to determine if one number is a factor of another
number without actually dividing
Characteristic of number
Number
divisible by:
Last digit is EVEN
The sum of the digits is divisible by 3
The last two digits form a number divisible by 4
The last digit is 0 or 5
The number is divisible by both 2 and 3
Take the last digit, double it, and subtract it from the
rest of the number.
If you get an answer divisible by 7 (including zero),
then the original number is divisible by seven. If
you don’t know the new original number is
divisible by seven.
If you don’t know the new number’s divisibility,
you can apply the rule again.
2
3
4
5
6
7
Example: Check to see if 203 is divisible by 7.
• double the last digit:
3x2=6
• subtract that from the rest of the number:
20 - 6 = 14.
• check to see if the difference is divisible by 7:
14 is divisible by 7, therefore 203 is also
divisible by 7.
The last three digits form a number divisible by 8
The sum of the digits is divisible by 9
The numeral ends in 0
8
9
10
Bar Graph
A graph that uses separate bars
(rectangles) of different heights
(lengths) to show and compare
data
Biased Sample
A sample that does not fairly represent the
population
Box-and-Whisker Graph
A graph that shows how far apart and how evenly
data are distributed
Example:
Central Tendency
Any of three measures (mean, median, mode) that
represent averages of a set of data
Circle Graph
A graph used to compare
the relationship of the parts
to the whole
Data
Information collected about people or things
Double-Bar Graph
A bar graph showing two or
more sets of data at once
Frequency Distribution Table
A table used to organize a collection of data
Example:
** Cumulative means to continuously add
the new frequency to all those above it.
Histogram
A bar graph that shows the frequency of data within
equal intervals
Example:
Distance (in cm)
Line Graph
A graph in which line segments
are used to show changes
over time
Line Plot
A number line with dots or other marks to show
frequency
Mean (or Equal Sharing)
The sum of a set of numbers divided by the number
of addends (or the number of entries in our list)
2, 3, 4, 5, 5, 8
(2 + 3 + 4 + 5 + 5 + 8) ÷ 6 = 4.5
number of entries in our list
The mean is 4.5
** Addends are the numbers that we add together. **
Temperature (in oC)
Add to the multi-line graph example
Census
The counting of an entire population
Example:
The Canadian Census involves collecting
information about every single person living
in Canada – whether they are Canadian
born or have immigrated to the country.
Primary Data
Information that is YOU collect and use
Secondary Data
Information that SOMEONE ELSE collects and passes
on to another person to use
Database
An organized set of information, often stored on a
computer
Name
Talia
Matteo
HB
7-4
8-2
Math
68
72
English
78
65
Phys. Ed.
75
78
Record
All the data about one item in the database; for
example, one student
Name
Talia
HB
7-4
Math
68
English
78
Phys. Ed.
75
Field
A category used as part of a database; for example,
Math (yellow cell)
Name
Talia
HB
7-4
Math
68
English
78
Phys. Ed.
75
Entry
A single piece of data in a database; for example,
English mark for one student (yellow cell)
Name
Talia
HB
7-4
Math
68
English
78
Phys. Ed.
75
Sort
Order information from greatest (or first) to least (or
last); a database can be sorted by fields
Name
Matteo
Talia
HB
8-2
7-4
Math
72
68
English
65
78
Phys. Ed.
78
75
This database is sorted greatest to least by Phys. Ed. marks.
(yellow cells)
Spreadsheet
An orderly arrangement of numerical data using rows
and columns. A computer spreadsheet can also use
formulas to make calculations for you!
Interval
The space between two values; for example, 0-9
represents the interval 0 to 9, including 0 and 9.
Cell
The intersection of a column and a row, where
individual data entries are stored; for example cell B2
shows the entry in Column B and in Row 2.
1
2
3
A
Name
Talia
Matteo
B
HB
7-4
8-2
C
Math
68
72
D
English
78
65
E
Phys. Ed
75
78
In this example, cell B2 has entry 7-4.
Formula
Calculations made within a cell using data from other
cells. Formulas may vary depending on the
spreadsheet program you use (Excel, Quattro Pro,
TinkerPlots, etc.).
Measure of Central Tendency
A measure used to describe data; the mean,
median, and mode are measures of central
tendency
Median
The middle number or the average of the two middle
numbers in an ordered set of data
1, 3, 4, 6, 7
The median is 4.
1, 2, 4, 5, 8, 9
The median is 4.5
(4.5 is the middle value between 4 and 5)
Survey
A method of gathering information about a
population
Mode
The number or numbers that occur most frequently in
a set of data; there can be one mode, more than
one mode or no mode.
2, 3, 4, 5, 5, 6, 7, 8, 8, 8, 9, 11
The mode is 8.
2, 3, 4, 5, 5, 5, 7, 8, 8, 8, 9, 11
The modes are 5 and 8.
2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17
There is no mode. Each entry appears an equal
number of times in the data set.
Multiple-Line Graph
A line graph showing two or more sets of data at
once
40
35
30
25
20
15
10
5
0
Population
The total or entire group to be studied
Random Sample
A population sample for which every individual in the
population had an equal chance of being chosen
Random Selection
A selection made so that each person or item has an
equal chance of being chosen
Sample
A smaller group of people or objects chosen from a
larger group, or population
Range
The difference between the greatest and the least
numbers in a set of data
Month
Temperature
Jun
25oC
Jul
32oC
Aug
30oC
Sept
24oC
Oct
20oC
Nov
12oC
The greatest temperature is 32oC.
The least temperature is 12oC.
Since 32 - 12 = 20, the range is 20oC.
Scatterplot
A graph made by plotting points on a coordinate
plane to show the relationship between two variables
in a data set
Example:
Stem-and-Leaf Plot
A method of organizing intervals or groups of data
Number of Sit-Ups
Stem
Each tens
digit is
called the
stem.
3
4
5
Leaves
4
0
0
Key: 3
6
3
0
8
6
1
8
7
2
7
The ones
digits are
called the
leaves.
6 = 36
Tally Table
A table with categories for recording each piece of
data as it is collected
Favourite Snack Foods
Snack
Tally
Fruit
Cereal
Chips
Cookies
Venn Diagram
A diagram that is used to show relationships between
sets
Example:
CENSUS
In this example, we are looking at whole numbers. All prime
numbers and all composite numbers are also ALL
COUNTING NUMBERS!
That is why they are both inside the purple circle.
What are the common factors of 18 and 42?
18
42
9
18
1
2
3
6
7
14
21
42
The common factors are 1, 2, 3, and 6.
SEQUENCE
An ordered list of numbers
Example:
1, 3, 5, 7, 9, …
• shows the odd numbers in order
Example: 1, 4, 16, 64, 256, . . .
12, 22, 42, 82, 162, …
• shows numbers doubling and squared
TERM
A real number, a variable, or a product
of real numbers and variables
Example:
In the expression 5x + 4,
the terms are 5x and 4.
TERM
A number in a sequence
Example:
3, 6, 12, 24, . . .
6 is a term in the sequence
TERM
One of the numbers in a ratio
Example:
REAL NUMBERS
The set of numbers that includes all
rational and all irrational numbers
VARIABLE
A letter used to represent one or
more numbers in an expression,
equation, or inequality
Examples: 5a
2x = 8
3y + 4 10
a, x, and y are variables.
PRODUCT
The answer in a multiplication problem
Example:
The product is 12.
EXPRESSION
A mathematical phrase that combines operations,
numerals, and/or variables to name a number
Examples:
35 – 15.5
32 x a
** Notice that there is NO EQUAL sign.
COORDINATES
An ordered pair, used to describe a location on a
grid labeled with an x-axis and a y-axis;
Example
y-axis
4
3
vertical 3 units
2
1
0
1
2
3
4
x-axis
horizontal 2 units
The coordinates (2, 3) describe this location
VOLUME
The number of cubic units needed to
occupy a given space
Example:
The volume of the cube is 8 cubic units.
VERTEX
A point where two or more rays meet,
where sides of a polygon meet, or where
edges of a polyhedron meet; the top
point of a cone or pyramid; in a network,
a point that represents an object
Examples:
TRIGONOMETRIC RATIOS
Ratios which compare the lengths of the
sides of a right triangle; the common
ratios are tangent, sine, and cosine.
Example:
TRIANGLE
A three-sided polygon
Examples:
TRAPEZOID
A quadrilateral with only one pair of
parallel sides
Example:
TRANSVERSAL
A line that intersects two or more lines
Example:
Line AB is a transversal.
THREE-DIMENSIONAL
Having length, width, and height
Example:
The rectangular prism is 3-dimensional.
SIMILAR FIGURES
Figures that have the same shape but
may not have the same size
Examples:
SURFACE AREA
The sum of the areas of all the faces, or
surfaces, of a solid figure
Example:
Area of face A =
Area of face B =
Area of face C =
Area of face D =
Area of face E =
Area of face F =
11 X 5 =
21 X 11 =
21 X 5 =
21 X 11 =
21 X 5 =
11 X 5 =
55
231
105
231
105
55
55 + 231 + 105 + 231 + 105 + 55 = 782
So, the surface area is 782 m2.
SUPPLEMENTARY ANGLES
Two angles whose measures have
a sum of 180°
Example:
ABD + DBC = 124° + 56° = 180°
SPHERE
A solid figure with all points the
same distance from the center
Example:
SQUARE
A rectangle with 4 congruent sides
Example:
The product of a number and itself
Example:
25 is the square of 5
because 5 X 5 = 25.
5 X 5 = 52 Read as 5-squared.
STRAIGHT ANGLE
An angle whose measure is 180°
Example:
ABC is a straight angle.
SOLID FIGURE
A three-dimensional figure
Examples:
SIDE-ANGLE-SIDE (SAS)
A triangle congruence rule stating that
two sides and the included angle of one
triangle match two sides and the
included angle of another triangle
Example:
SIDE-SIDE-SIDE (SSS)
A triangle congruence rule stating
that three sides of one triangle
match three sides of another
Example:
SEMIREGULAR POLYHEDRON
A solid formed from patterns of more
than one kind of regular polygon
Example:
SCALENE TRIANGLE
A triangle with no congruent sides
Example:
RIGHT TRIANGLE
A triangle with exactly one right angle
Examples:
RIGHT ANGLE
An angle whose measure is 90°
Example:
RHOMBUS
A parallelogram whose four sides are
congruent and whose opposite
angles are congruent
Example:
REGULAR POLYGON
A polygon in which all sides and
all angles are congruent
Example:
RECTANGULAR PRISM
A polyhedron whose bases are
rectangles and whose other
faces are parallelograms
Example:
RECTANGLE
A parallelogram with 4 right angles
Example:
RAY
A part of a line that has one endpoint
and goes on forever in only one direction
Example:
RADIUS
A line segment with one endpoint at
the center of a circle and the other
endpoint on the circle
Example:
PRISM
A polyhedron whose two bases are
congruent, parallel polygons in parallel
planes and whose lateral faces are
parallelograms
Example:
rectangular prism
PYTHAGOREAN THEOREM
In any right triangle, if a and b are the
lengths of the legs and c is the length of
the hypotenuse, then a2 + b2 = c2
Example:
a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25
Replace the variables
with the known lengths.
QUADRILATERAL
A four-sided polygon
Examples:
PYRAMID
A polyhedron with a base that is a
polygon and with lateral faces that are
triangles which share a common vertex
Example:
square pyramid
POLYHEDRON
A solid figure with flat faces
that are polygons
Examples:
POLYGON
A closed plane figure formed by
three or more line segments
Examples:
POINT OF INTERSECTION
The point where two or
more lines intersect
Example:
POINT
An exact location
PLANE FIGURE
A figure which lies in a plane
Examples:
PLANE
A set of points forming a flat surface that
extends without end in all directions
Example:
PI ()
The ratio of the circumference of a circle
to the length of its diameter
PERSPECTIVE
A technique used to make 3-dimensional
objects appear to have depth and
distance on a flat surface
Example:
PERPENDICULAR LINES
Lines that intersect to form 90° angles,
or right angles
Example:
Read: Line RS is perpendicular to line MN.
PERPENDICULAR BISECTOR
A line or line segment that intersects
a given line segment at its midpoint
and forms right angles
Example:
PERIMETER
The distance around a polygon
Example:
3 cm + 3 cm + 2 cm = 8 cm
The perimeter of this figure is 8 centimeters.
PENTAGON
A five-sided polygon
Examples:
PARALLELOGRAM
A quadrilateral whose opposite sides
are parallel and congruent
Example:
PARALLEL LINES
Lines in a plane that do not intersect
Example:
Read: Line AB is parallel to line CD.
OCTAGON
An eight-sided polygon
Examples:
OBTUSE ANGLE
An angle whose measure is
greater than 90° and less than 180°
Example:
NET
A connected arrangement of
polygons in a plane that can be
folded up to form a polyhedron
Example:
MIDPOINT
The point that divides a line segment
into two congruent line segments
Example:
M is the midpoint of
.
LINE SEGMENT
A part of a line or ray, consisting
of two endpoints and all points
between those endpoints
Examples:
LINE
A set of points that extends without
end in opposite directions
Example:
LEG
In a right triangle, either of the two sides
that intersect to form the right angle; in
an isosceles triangle, one of the two
congruent sides
Examples:
LATERAL SURFACE
The curved surface of a cylinder or a
cone
Example:
LATERAL FACE
In a prism or a pyramid,
a face that is not a base
Example:
Rectangular Prism
ISOSCELES TRIANGLE
A triangle with two congruent sides
Example:
INTERSECTING PLANES
Flat surfaces that intersect in a line,
such as the sides of a box
Example:
INTERSECTING LINES
Two lines that cross at exactly one point
Example:
INTERIOR ANGLES
Angles on the inner sides of
two lines cut by a transversal
Example:
Angles 3, 4, 5, and 6 are interior angles
HYPOTENUSE
In a right triangle, the side opposite
the right angle; the longest side
in a right triangle
Example:
HORIZON LINE
A horizontal line that represents
the viewer's eye level
Example:
HEXAGON
A six-sided polygon
Examples:
HELIX
A spiral-shaped curve in space
that goes around an axis
Examples:
FORMULA
A rule that is expressed using symbols
Examples:
The area and the circumference
of a circle can be computed by
using the following formulas:
A = r2
C= d
FACE
A flat surface of a polyhedron
Example:
The cube has 6 faces.
EXTERIOR ANGLES
The angles on the outer sides of
two lines cut by a transversal
Example:
Angles 1, 2, 7, and 8 are exterior angles.
EQUILATERAL TRIANGLES
A triangle with three congruent sides
and three congruent angles
Example:
EDGE
The line segment along which
two faces of a polyhedron intersect
Example:
EDGE
A connection between vertices in a
network
Example:
DIAMETER
A chord that passes through the
center of a circle
Example:
DIAGONAL
A line segment that connects two
non-adjacent vertices of a polygon
Example:
CYLINDER
A solid figure with two parallel,
congruent circular bases connected
by a curved surface
Example:
CUBE
A square prism with six
congruent square faces
Example:
CROSS SECTION
The figure formed by the intersection
of a plane and a solid figure
Example:
CORRESONDING ANGLES
Angles that are in the same position and
are formed by a transversal cutting two or
more lines
Example:
2 and 6 are corresponding angles.
CONGRUENT
Having the same size and shape
Example:
CONE
A solid figure with a circular base
and one vertex
Example:
COMPLEMENTARY ANGLES
Two angles whose measures
have a sum of 90°
Example:
DBE and EBC are complementary.
CIRCUMFERENCE
The distance around a circle
C= d
CIRCLE
A closed curve with all points on the
curve an equal distance from a given
point called the center of the circle
Example:
CHORD
A line segment with endpoints on a circle
Example:
CENTRAL ANGLE
An angle formed by two rays with a
common vertex at the center of a circle
Example:
BISECT
To divide into two congruent parts
Example:
AREA
The number of square units needed
to cover a given surface
Example:
The area is 9 square units.
BASE
A side of a polygon or a face of
a solid figure by which the figure
is measured or named
Examples:
A number used as a repeated factor
Example:
83 = 8 X 8 X 8
The base is 8. It is used as a
factor three times.
ANGLE
A geometric figure formed by two rays
that have a common endpoint
Examples:
ALTERNATE INTERIOR
ANGLES
A pair of angles on the inner sides of two
lines cut by a transversal, but on opposite
sides of the transversal
Example:
3 and 6 and 4 and 5 are alternate
interior angles.
ALTERNATE EXTERIOR
ANGLES
A pair of angles on the outer sides of two
lines cut by a transversal, but on opposite
sides of the transversal
Example:
1 and 8 and 2 and 7 are alternate
exterior angles.
ACUTE ANGLE
An angle whose measure is
greater than 0° and less than 90°
Example:
ACUTE TRIANGLE
A triangle in which all
three angles are acute
Example:
ADJACENT ANGLES
Angles that share a common side, have
the same vertex, and do not overlap
Example:
ABD is adjacent to DBC.
ANGLE-SIDE-ANGLE (ASA)
A triangle congruence rule stating that
when two angles and the included side
of one triangle are congruent to two
angles and the included side of another
triangle, the two triangles are congruent.
Example:
ADDITION PROPERTY
OF OPPOSITES
The property which states that the
sum of a number and its opposite is
zero
Examples:
5 + -5 = 0
-15 + 15 = 0
INTEGERS
The set of whole numbers and their
opposites. All positive and negative
numbers including zero.
Example:
IDENTITY PROPERTY
OF ZERO
The property which states that
adding zero to a number does not
change the number's value
Examples:
3+0=3
0+y=y
NEGATIVE INTEGER
An integer less than zero.
Example: -1, -2, -3, -4, . . .
OPPOSITE INTEGERS
Two numbers that are represented
by points on the number line that are
the same distance from zero but are
on opposite sides of zero.
Example:
4 and -4 are opposites
POSITIVE INTEGER
An integer greater than zero.
Example:
1, 2, 3, 4, . . .
ZERO PRINCIPLE
The sum of two opposite integers
equal zero.
Examples:
(-1) + (+1) = 0
(+20) + (-20) = 0
REGROUP
When you group the integers in an
equation by their positive and
negative values.
Example:
(+5) + (-7) + (+11) + (+3) + (-8) = (+4)
= (-2) + (+11) + (+3) + (-8)
+ (+3) + (-8)
=
(+9)
=
(+12)
+ (-8)
=
(+4)
(+5) + (+11) + (+3) + (-7) + (-8) = (+4)
= (+16) + (+3) + (-7) + (-8)
+ (-7) + (-8)
=
(+19)
+ (-8)
=
(+12)
=
(+4)
NUMBER LINE
A series of numeric values (numbers)
listed on a line from least (smallest)
to greatest (biggest).
-10
-8
-6
-4
-2
0
+2
+4
+6
+8
+10
This number line demonstrates
integer values from -10 to +10.
NEGATIVE means to go in the
OPPOSITE DIRECTION.
Example
Walk Forward (+)
Ascend (+)
or Go Up
(-) Walk Backward
(-) Descend
or Go Down
Coordinate plane
A plane formed by two perpendicular number
lines called axes; every point on the plane can
be named by an ordered pair of numbers.
Axes
Two perpendicular lines that intersect to form
the coordinate plane.
Dilation
A transformation that
enlarges or reduces
a figure.
Inequality
A mathematical sentence that shows the
relationship between quantities that are not
equal, using <, >, <, , or .
Examples:
6<9
3x > 12
Image
The figure in a new position or location
as the result of a transformation.
Example:
A'B'C'D' is the image
of ABCD.
Tessellation
A repeating pattern of congruent plane
figures that completely cover a plane with no
gaps or overlapping.
Ordered pair
A pair of numbers used to locate a
point on a coordinate plane.
Example:
(3,2) represents 3
spaces
to the right of zero
and 2 spaces up.
Rotation
A type of transformation, or movement,
that results when a geometric figure
is turned about a fixed point.
Example:
Origin
The point on the coordinate plane where
the x-axis and the y-axis intersect, (0,0)
Example:
Quadrant
One of the four regions of the
coordinate plane.
Translation (slide)
A movement of a geometric figure to a new
position without turning or flipping it.
Example:
Rotational symmetry
A figure has rotational symmetry when it
can be rotated less than 360° around a
central point, or point of rotation and
still match the original figure.
Example:
Transformation
A change in size, shape,
or position of a
geometric figure;
translations, reflections,
rotations,
and dilations are
transformations.
Example:
x-axis
The horizontal axis on the coordinate plane.
Example:
x-coordinate
The first number in an ordered pair; tells
whether to move right or left along the
x-axis of the coordinate plane.
Example:
(3, 2)
3 is the x-coordinate.
y-axis
The vertical axis on the coordinate plane.
Example:
y-coordinate
The second number in an ordered pair; tells
whether to move up or down along the
y-axis of the coordinate plane.
Example:
(3, 2)
2 is the y-coordinate.
y-intercept
The y-coordinate of the point where
the graph of a line crosses the y-axis.
Example:
The y-intercept of 2x + 3y = 6 is 2.
TRINOMIAL
The sum of three monomials
Example:
3x + 5y + 7
INTERCEPT
The place (or point) where a
graph crosses the axis
Example:
The x-intercept is 1 and
the y-intercept is -2.
SYSTEM OF EQUATIONS
Two or more linear equations graphed
in the same coordinate plane
MONOMIAL
An expression that is a number,
a variable, or the product of a
number and one or more variables
Examples:
3x
7
5xy
SUBSTITUTE
To replace a variable with a value
Example:
Which of the values 12, 20,
and 21 are solutions of x - 4 = 16?
Substitute each of the values
for x in the equation.
Use x = 12.
x - 4 = 16
12 - 4 = 16
8 16
not a solution
Use x = 20.
x - 4 = 16
20 - 4 = 16
16 = 16
solution
Use x = 21.
x - 4 = 16
21 - 4 = 16
17 16
not a solution
POLYNOMIAL
A monomial or the sum of two or more
monomials
Examples:
3a2 + 8
a2 - 4a + 3
SOLUTION
The value or values that make an
equation an inequality, or
system of equations true
Examples:
x – 4 = 16
x – 4 + 4 = 16 + 4
x = 20
20 is the solution.
x+3>9
x+3–3>9–3
x>6
Any number greater
than 6 is a solution.
NONLINEAR FUNCTION
A function whose graph is not
a straight line
Example:
SLOPE
The measure of the steepness of a line;
the ratio of vertical change to
horizontal change
Example:
NUMERICAL EXPRESSION
An expression that includes numbers
and at least one operation (addition,
subtraction, multiplication, or division)
Examples:
6 + 8.1
57 – 48
21.6 – 18.6
LINEAR EQUATION
An equation whose graph is a straight line
Example:
The linear equation for the graph
below is y = 2x + 1.
TERM
A real number, a variable, or a product
of real numbers and variables
Example:
In the expression 5x + 4, the
terms are 5x and 4.
LINE OF BEST FIT
A straight line drawn through as much
data as possible on a scatterplot
Example:
LIKE TERMS
Expressions that have the same variables
and the same powers of the variables.
Example:
8y, -4y, and 9.1y are like terms.
BINOMIAL
The sum of two monomials
Example:
3x + 5y
INTERPOLATION
An estimated value between
two known values
Example:
Suppose you work for 2.5 hr and are
paid $4.50 per hour. Use the graph
to predict your earnings.
On the horizontal axis of
the graph, locate 2.5
Draw a vertical line
segment from this point
to the line of the graph.
From there, draw a horizontal line segment
to the vertical axis. It intersects the axis
halfway between $9.00 and $13.50.
So, if you work 2.5 hr, you will earn $11.25.
IDENTITY PROPERTY OF ONE
The property which states that
multiplying a number by 1 does
not change the number's value
Examples:
6X1=6
1Xa=a
DISTRIBUTIVE PROPERTY OF
MULTIPLICATION OVER
ADDITION
The property which states that multiplying
a sum by a number gives the same result
as multiplying each addend by the
number and then adding the products
a(b + c) = a X b + a X c
Examples:
3(4 + 5) = 3 X 4 + 3 X 5
3(a + b) = 3a + 3b
EXTRAPOLATION
An estimate or a prediction of an unknown
value, based upon known values
Example:
The trend is an increase
with no declines.
From 1970 to 1990, the
population increased
about 25 million every 10
years.
Since the population increased about 25
million every 10 years from 1970 to 1990, a
good prediction for the year 2000 would be
about 250 million + 25 million, or 275 million.
COEFFICIENT
The number that is multiplied by the variable
in an algebraic expression such as 5b
ASSOCIATIVE PROPERTY OF
MULTICATION
The property which states that for all real
numbers a, b, and c, their product is always
the same, regardless of their grouping:
(a X b) X c = a X (b X c)
Example:
(5 X 6) X 7 = 5 X (6 X 7)
ASSOCIATIVE PROPERTY
OF ADDITION
The property which states that for all real
numbers a, b, and c, their sum is always
the same, regardless of their grouping:
(a + b) + c = a + (b + c)
Example:
(2 + 3) + 4 = 2 + (3 + 4)
COMMUNICATIVE PROPERTY
OF MULTIPLICATION
The property of multiplication that allows
two or more factors to be multiplied in any
order without changing the product
aXb=bXa
Examples:
3Xc=cX3
4 X 5 X y7 = 5 X 4 X y7
COMMUNICATIVE PROPERTY
OF ADDITION
The property of addition that allows
two or more addends to be added in
any order without changing the sum;
a+b=b+a
Examples:
c+4=4+c
(2 + 5) + 4r = 4r + (2 + 5)
ALGEBRAIC EXPRESSION
An expression that is written using
one or more variables
Examples:
3x
x–4
2a + 5
RISE
The vertical change of a line
Example:
The rise of line PQ is 2.
a+b
RUN
The horizontal change of a line
Example:
The run of line PQ is 1.
SOLVE
To find the correct value of
the variable in an equation
Example:
x + 5 = 17
x + 5 – 5 = 17 – 5
x = 12
SOLUTION
The value that makes two sides
of an equation equal
Example:
x+7=9
2+7=9
2 is the solution.
SOLUTION OF THE SYSTEM
The values for the variables that make
each of the equations in a system of
equations true; the coordinates of the
point where the graphs of the
equations in the system intersect
Example:
The equations of these lines are
y = 2x – 1 and y = x + 1
The solution of the system is (2,3).
EQUIVALENT FRACTIONS
Fractions that name the same number
3 = 6 = 75
4
8
100
EQUIVALENT RATIOS
Ratios that make the same comparisons
Examples:
FACTOR
A number that is multiplied by
another number to get a product
Example:
2X3=6
2 and 3 are factors of 6.
SCALE FACTOR
The common ratio for pairs of
corresponding sides of similar figures
Example:
SIMILAR FIGURES
Figures that have the same shape
but may not have the same size
Example:
SCALE MODEL
A proportional model of a solid, or threedimensional object
Example:
SIMPLEST FORM
A fraction is in simplest form when the
numerator and denominator have no
common factors other than 1.
Example:
The form of an expression when
all like terms are combined
Example:
4x + 3x + 2
= 7x + 2 (in its simplest form)
INDIRECT MEASUREMENT
A method of measuring distances
by solving a proportion
Example:
RECIPROCAL
One of two numbers whose product is 1
Example:
COMPLEMENTARY ANGLES
Two angles whose measures have a
sum of 90°
Example:
DBE and EBC are complementary.
EQUIANGULAR TRIANGLE
A triangle with three congruent angles
and three congruent sides
Example:
BISECT
To divide into two congruent parts
Example:
PERPENDICULAR BISECTOR
A line or line segment that intersects a
given line segment at its midpoint and
forms right angles
Example:
ALTERNATE EXTERIOR
ANGLES
A pair of angles on the outer sides of
two lines cut by a transversal, but on
opposite sides of the transversal
Example:
1 and 8 and 2 and 7 are
alternate exterior angles.
RIGHT TRIANGLE
A triangle with exactly one right angle
Examples:
ALTERNATE INTERIOR ANGLES
A pair of angles on the inner sides of
two lines cut by a transversal, but on
opposite sides of the transversal
Example:
3 and 6 and 4 and 5 are
alternate interior angles.
SUPPLEMENTARY ANGLES
Two angles whose sum equals 180°
Example:
mABD + mDBC = 124° + 56° = 180°
CORRESPONDING ANGLES
Angles that are in the same position
and are formed by a transversal cutting
two or more lines
Example:
2 and 6 are corresponding angles.
CONGRUENT
Having the same size and shape
Example:
PERPENDICULAR LINES
Lines that intersect to form 90° angles, or
right angles
Example:
Read: Line RS is perpendicular
to line MN.
POINT OF INTERSECTION
The point where two or more lines
intersect
Example:
EQUILATERAL TRIANGLE
A triangle with three congruent sides
and three congruent angles
Example:
INTERSECTING LINES
Two lines that cross at exactly one point
Example:
INTERIOR ANGLES
Angles on the inner sides of two lines cut
by a transversal
Example:
Angles 3, 4, 5, and 6 are interior angles.
ISOSCELES TRIANGLE
A triangle with two congruent sides
Example:
LINE
A set of points that extends without end
in opposite directions
Example:
LINE SEGMENT
A part of a line or ray, consisting of two
endpoints and all points between those
endpoints
Examples:
MIDPOINT
The point that divides a line segment
into two congruent line segments
Example:
M is the midpoint of
.
PARALLEL LINES
Lines in a plane that do not intersect
Example:
Read: Line AB is parallel to line CD.
RAY
A part of a line that has one endpoint
and goes on forever in only one
direction
Example:
RIGHT ANGLE
An angle whose measure is 90°
Example:
SCALENE TRIANGLE
A triangle with no congruent sides
Example:
SIMILAR FIGURES
Figures that have the same shape but
may not have the same size
Example:
NET
A connected arrangement of polygons
in a plane that can be folded up to
form a polyhedron
Example:
PRISM
A polyhedron whose two bases are
congruent, parallel polygons in parallel
planes and whose lateral faces are
parallelograms
Example:
rectangular prism
VERTEX
A point where two or more rays meet,
where sides of a polygon meet, or
where edges of a polyhedron meet; the
top point of a cone or pyramid; in a
network, a point that represents an
object
Examples:
SURFACE AREA
The sum of the areas of all the faces, or
surfaces, of a solid figure
Example:
Area of face A = 11 X 5 = 55
Area of face B = 21 X 11 = 231
Area of face C = 21 X 5 = 105
Area of face D = 21 X 11 = 231
Area of face E = 21 X 5 = 105
Area of face F = 11 X 5 = 55
55 + 231 + 105 + 231 + 105 + 55 = 782
So, the surface area is 782 cm2.
BIASED SAMPLE
A sample that does not fairly represent
the population
COMBINATION
An arrangement of items or events in
which order does not matter
Example:
Two-letter combinations of A, B,
C, and D:
AB
AC
AD
BC
BD
CD
There are 6 combinations.
POPULATION
The total or entire group to be studied.
THEORETICAL PROBABILITY
The ratio of the number of favorable
outcomes to the number of all possible
outcomes
EXPERIMENTAL PROBABILITY
The ratio of the number of times the
event occurs to the total number of
trials or times the activity is performed
SIMULATION
A model of an experiment that would
be too difficult or too time-consuming
to actually perform.
COMPLEMENT
In probability, the complement of an
event is all outcomes different from the
favorable outcome. The sum of the
probability of an event and its
complement is 1.
Example:
The number cube is labeled 1-6.
PROBABILITY
The number used to describe the
chance of an event occurring
ESTIMATE
An answer that is close to the
exact answer and is found by
rounding, by using front-end
digits, by clustering, or by using
compatible numbers to compute
COMPATIBLE NUMBERS
Numbers that are close to a
dividend and divisor and divide
evenly, with no remainder
Example:
EVALUATE
To find the value
INVERSE OPERATIONS
Operations that undo each other
Examples:
20 – 5 = 15 and 15 + 5 = 20
20 ÷ 5 = 4 and 4 x 5 = 20
PRECISION
A property of measurement that is
related to the unit of measure
used; the smaller the unit of
measure used, the more precise
the measurement is.
Example:
27 mm is more precise than 3 cm.