algebraic expression angle - big ideas math algebraic expression in which the exponent of the...

Vocabulary Flash Cards

Copyright © Big Ideas Learning, LLC Big Ideas Math Red Accelerated All rights reserved.

algebraic expression

angle

center of a sphere

coordinate plane

degree

enlargement

equation

expression

Review Review

Review Review

Review Review

Review Review



A figure formed by two rays with the same endpoint

An expression that contains numbers, operations, and one or more symbols

8 , 6x a b+ × −

A coordinate plane is formed by the intersection of a horizontal number line and a vertical number line.

The point inside a sphere that is the same distance from all points on the sphere

See sphere.

A dilation with a scale factor greater than 1

A B C′ ′ ′ is an enlargement of .ABC

A unit used to measure angles

90 , 45 , 32° ° °

A mathematical phrase containing numbers, operations, and/or variables

12 6, 18 3 4,+ + ×

8 , 6+ × −x a b

A mathematical sentence that uses an equal sign to show that two expressions are equal

4 16, 7 21= + =x a

vertex

x

y

3

4

5

2

1

−3

−2

−4

−5

4 5321O−2−3−4−5

Quadrant II Quadrant I

Quadrant IVQuadrant III

The origin isat (0, 0).

x-axis y-axis

x

y

3

4

5

6

7

8

9

2

1

4 5 6321

AB

C

A′ B′

C′

O



factor

negative number

ordered pair

origin

parallel lines

percent

perpendicular lines

polygon

Review Review

Review Review

Review Review

Review Review



A number less than 0.

0.25, 10, 500− − −

When whole numbers other than zero are multiplied together, each number is a factor of the product.

2 3 4 24,× × = so 2, 3, and 4 are factors of 24.

The point, represented by the ordered pair (0, 0), where the horizontal the vertical number lines intersect in a coordinate plane

See coordinate plane.

A pair of numbers (x, y) used to locate a point in a coordinate plane; The first number is the x-coordinate, and the second number is the y-coordinate.

The x-coordinate of the point ( )2, 1− is 2,− and

the y-coordinate is 1.

The number of parts per one hundred.

37

37% 37 out of 100100

= =

Lines in the same plane that do not intersect;

Nonvertical parallel lines have the same slope. All vertical lines are parallel.

A closed figure in a plane that is made up of three or more line segments that intersect only at their endpoints

Lines in the same plane that intersect at right angles; Two nonvertical lines are perpendicular when the product of their slopes is 1.− Vertical lines are perpendicular to horizontal lines.

1

−2 21

(−2, 1)

O x

y

p q

Indicates linesand are parallel.q

p

vertex



polyhedron

positive number

prism

pyramid

quadrilateral

radius of a sphere

reduction

right angle

Review Review

Review Review

Review Review

Review Review



A number greater than 0.

0.5, 2, 100

A solid whose faces are all polygons

A polyhedron that has one base; The lateral faces are triangles.

A polyhedron that has two parallel, congruent bases; The lateral faces are parallelograms.

The distance from the center of a sphere to any point on the sphere

See sphere.

A polygon with four sides

An angle whose measure is 90°

A dilation with a scale factor greater than 0 and less than 1

W X Y Z′ ′ ′ ′ is a reduction of WXYZ.

lateral face

base

baselateral face

base

x

y

6

10

2

−8

6−6

X

W

Y

Z

Y′X′

Z′W ′

O



right triangle

solid

solution (of an equation)

terms (of an algebraic expression)

three-dimensional figure

two-dimensional figure

variable

vertex (of an angle)

Review Review

Review Review

Review Review

Review Review



A three-dimensional figure that encloses a space

A triangle that has one right angle

The parts of an expression that are added together.

The terms of 4 7+x are 4x and 7.

A value that makes an equation true

6 is the solution of the equation 4 2.− =x

A figure that has only length and width

A figure that has length, width, and depth; also known as a solid

The point at which the two sides of an angle meet

A symbol that represents one or more numbers

x is a variable in 2 1.x +

vertex



vertex (of a polygon)

whole numbers

x-axis

x-coordinate

y-axis

y-coordinate

Review Review

Review Review

Review Review



The numbers 0, 1, 2, 3, 4,…

A point at which two sides of a polygon meet; The plural of vertex is vertices.

See polygon.

The first coordinate in an ordered pair, which indicates how many units to move to the left or right from the origin

In the ordered pair ( )3, 5 , the x-coordinate is 3.

The horizontal number line in a coordinate plane


The second coordinate in an ordered pair, which indicates how many units to move up or down from the origin

In the ordered pair ( )3, 5 , the y-coordinate is 5.

The vertical number line in a coordinate plane




absolute value

additive inverse

Additive Inverse Property

integers

opposites

Chapter 1 Chapter 1

Chapter 1 Chapter 1

Chapter 1



The opposite of a number

The additive inverse of 8 is 8.−

The distance between a number and 0 on a number line; The absolute value of a number a is written as .a

5 5− =

5 5=

The set of whole numbers and their opposites

3, 2, 1, 0, 1, 2, 3,− − −… …

The sum of an integer and its additive inverse is 0.

( )8 8 0+ − =

Two numbers that are the same distance from 0, but on opposite sides of 0

3− and 3 are opposites.



rational number

repeating decimal

terminating decimal

Chapter 2 Chapter 2

Chapter 2



A decimal that has a pattern that repeats

0.555... 0.5

1.727272... 1.72

=

=

A number that can be written as a

b where

a and b are integers and 0b ≠

3

3 ,1

= 2 2

5 5

−− =

1

0.25 ,4

= 1 4

13 3

=

A decimal that ends

1.5, 2.58, 5.605−



Addition Property of Equality

Division Property of Equality

equivalent equations

factoring an expression

like terms

linear expression

Multiplication Property of Equality

simplest form (of an algebraic expression)

Chapter 3 Chapter 3

Chapter 3 Chapter 3

Chapter 3 Chapter 3

Chapter 3 Chapter 3



Dividing each side of an equation by the same number produces an equivalent equation.

3 18

3 18

3 3

6

− =− =− −

= −

y

y

y

Adding the same number to each side of an equation produces an equivalent equation.

5 1

5 5

4

− = −+ +

=

x

x

Writing an expression as a product of factors

( )5 15 5 3x x− = −

Equations that have the same solutions

2 8 0x − = and 2 8x =

An algebraic expression in which the exponent of the variable is 1

1

4 , 3 5, 56

x x x− + −

Terms of an algebraic expression that have the same variables raised to the same exponents

4 and 8, 2x and 7x

An algebraic expression is in simplest form when it has no like terms and no parentheses.

26 9 , 3 5a a t+ +

Multiplying each side of an equation by the same number produces an equivalent equation.

( )

63

3 3 63

18

= −

• = • −

= −

x

x

x



Subtraction Property of Equality

Chapter 3



Subtracting the same number from each side of an equation produces an equivalent equation.

5 25

5 5

20

w

w

+ =− −

=



Addition Property of Inequality

Division Property of Inequality

graph of an inequality

inequality

Multiplication Property of Inequality

solution of an inequality

solution set

Subtraction Property of Inequality

Chapter 4 Chapter 4

Chapter 4 Chapter 4

Chapter 4 Chapter 4

Chapter 4 Chapter 4



When you divide each side of an inequality by the same positive number, the inequality remains true. When you divide each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true.

4 12

4 12

4 43

x

x

x

> −−>

> −

5 30

5 30

5 56

x

x

x

− >− <− −

< −

When you add the same number to each side of an inequality, the inequality remains true.

3 10

3 3

7

x

x

− > −+ +

> −

A mathematical sentence that compares expressions; It contains the symbols , , , or .< > ≤ ≥

4 14, 5 12x x− < + ≥ −

A graph that shows all the solutions of an inequality on a number line

2> −x

A value that makes an inequality true

A solution of the inequality 3 9+ > −x is 2.=x

When you multiply each side of an inequality by the same positive number, the inequality remains true.

When you multiply each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true.

( )

92

2 2 92

18

< −

• < • −

< −

x

x

x

36

6 6 36

18

<−

− • > − •−

> −

x

x

x

When you subtract the same number from each side of an inequality, the inequality remains true.

7 20

7 7

27

+ > −− −

> −

x

x

The set of all solutions of an inequality

−1−3 −2 0 1 2 3



complex fraction

constant of proportionality

cross products

Cross Products Property

direct variation

proportion

proportional

rate

Chapter 5 Chapter 5

Chapter 5 Chapter 5

Chapter 5 Chapter 5

Chapter 5 Chapter 5



The number k in the direct variation equation y kx=

The constant of proportionality in the equation 2 is 2.y x=

A fraction that has at least one fraction in the numerator, denominator, or both

1412

The cross products of a proportion are equal.

=2 43 6

2 6 3 4• = •

In the proportion ,a c

b d= the products a d•

and b c• are called cross products.

=2 43 6

2 6 and 3 4• •

An equation stating that two ratios are equivalent

3 12

4 16=

Two quantities x and y show direct variation when ,=y kx where k is a number and 0.≠k

The graph of y kx= is

a line with a slope of k that passes through the origin.

A ratio of two quantities with different units

You read 3 books every 2 weeks.

Two quantities that form a proportion are proportional.

Because 3

4 and

12

16 form a proportion,

3

4 and

12

16 are proportional.

x

y3

2

1

−3

321−2−3 −1

y = 2x



ratio

slope

unit rate

Chapter 5 Chapter 5

Chapter 5



A ratio of the change in y (vertical change) to the change in x (horizontal change) between any two points on a line; It is a measure of the steepness of a line.

change in slope

change in

y

x=

A comparison of two quantities using division; The ratio of a to b ( )where 0≠b can be written

as a to b, a : b, or .a

b

4 to 1, 4 : 1, or 4

1

A rate with a denominator of 1

The speed limit is 65 miles per hour.

x

y

1 2 3 4 5 6 7

1

2

3

4

5

6

7

Slope =

3

2 32



discount

interest

markup

percent of change

percent of decrease

percent error

percent of increase

principal

Chapter 6 Chapter 6

Chapter 6 Chapter 6

Chapter 6 Chapter 6

Chapter 6 Chapter 6



Money paid or earned for the use of money

See simple interest.

A decrease in the original price of an item

The original price of a pair of shoes is $95. The sale price is $65. The discount is $30.

The percent that a quantity changes from the original amount

amount of changepercent of change

original amount=

The percent of change from 20 to 25 is:

25 20 5

25%20 20

− = =

The increase from what a store pays to the selling price

A store buys a hat for $12 and sells it for $20. The markup is $8.

The percent that an estimated quantity differs from the actual amount

amount of errorpercent error

actual amount=

Estimated length: 16 feet Actual length: 21

Percent error: 21 16

, or 23.8%21

−

The percent of change when the original amount decreases

percent of decrease

original amount new amount

original amount

−=

The price of a shirt decreases from $20 to $10.

The percent of decrease is 20 10

, or 50%.20

−

An amount of money borrowed or deposited

You deposit $200 in an account that earns 4% simple interest per year. The principal is $200.

The percent of change when the original amount increases

percent of increase

new amount original amount

original amount

−=

The price of a shirt increases from $20 to $30.

The percent of increase is 30 20

, or 50%.20

−



simple interest

Chapter 6



Money paid or earned only on the principal

=I Prt

You put $200 into an account. The account earns 5% simple interest per year. The interest earned after 3 years is $200 0.05 3,× × or $30. The account balance is $200 $30 $230+ = after 3 years.

Simple Interest Annual interest rate (in decimal form)

Principal Time (in years)



adjacent angles

complementary angles

congruent angles

congruent sides

kite

scale

scale drawing

scale factor (of a scale drawing)

Chapter 7 Chapter 7

Chapter 7 Chapter 7

Chapter 7 Chapter 7

Chapter 7 Chapter 7



Two angles whose measures have a sum of 90°

Two angles that share a common side and have the same vertex

1 and 2∠ ∠ are adjacent.

2 and 4∠ ∠ are not adjacent.

Sides that have the same length

Side AB and side FG are congruent sides.

Angles that have the same measure

A ratio that compares the measurements of a drawing or model with the actual measurements

12 cm : 1 cm

2 in.

15 ft

A quadrilateral with two pairs of congruent adjacent sides and opposite sides that are not congruent

A scale without units

See ratio.

A proportional, two-dimensional drawing of an object

A blueprint or a map

1 234

30°60°

12

60°60°

120°120°

A

B

F

G



scale model

supplementary angles

vertical angles

Chapter 7 Chapter 7

Chapter 7



Two angles whose measures have a sum of 180°

A proportional, three-dimensional model of an object

The angles opposite each other when two lines intersect; Vertical angles are congruent angles.

1 and 3 are vertical angles.

2 and 4 are vertical angles.

∠ ∠∠ ∠

135° 45° 3 4

24

3

1



center (of a circle)

circle

circumference

composite figure

diameter (of a circle)

pi

radius (of a circle)

semicircle

Chapter 8 Chapter 8

Chapter 8 Chapter 8

Chapter 8 Chapter 8

Chapter 8 Chapter 8



The set of all points in a plane that are the same distance from a point called the center

The point inside a circle that is the same distance from all points on the circle

See circle.

A figure made up of triangles, squares, rectangles, semicircles, and other two-dimensional figures

The distance around a circle

The ratio of the circumference of a circle to its diameter

The value of π can be approximated as 3.14 or22

.7

The distance across a circle through the center

See circumference.

One-half of a circle

The distance from the center of a circle to any point on the circle

See circumference.

centercircle

C

d

rsquare

triangle



cross section

lateral surface area (of a prism)

regular pyramid

slant height (of a pyramid)

Chapter 9 Chapter 9

Chapter 9 Chapter 9



The sum of the areas of the lateral faces of a prism

( )( ) ( )( )2

Lateral surface area 2 4 3 2 5 3

24 30 54 cm

= +

= + =

A two-dimensional shape formed by the intersection of a plane and a solid

The intersection of the plane and the cone is a circle.

The height of each triangular face of a pyramid

A pyramid whose base is a regular polygon

5 cm4 cm

3 cm

slant height



biased sample

compound event

dependent events

event

experiment

experimental probability

favorable outcomes

Fundamental Counting Principle

Chapter 10 Chapter 10






An event that consists of two or more events

Spinning a spinner and flipping a coin

A sample that is not representative of a population; One or more parts of the population are favored over others.

You want to estimate the number of students in your school who like to play basketball. You survey 100 students at a basketball game.

A collection of one or more outcomes of an experiment

Flipping heads on a coin

Two events such that the occurrence of one event affects the likelihood that the other event(s) will occur

A bag contains 3 red marbles and 4 blue marbles. You randomly draw a marble, do not replace it, then randomly draw another marble. The events “first marble is blue” and “second marble is red” are dependent events.

Probability that is based on repeated trials of an experiment

( ) number of times the event occursevent

total number of trialsP =

A basketball player makes 19 baskets in 28 attempts. The experimental probability that the player makes a

basket is 19

, or about 68%.28

An investigation or procedure that has varying results

Rolling a number cube

An event M has m possible outcomes and event N has n possible outcomes. The total number of outcomes of event M followed by event N is

.m n×

You have 7 shirts, 5 pairs of pants, and 2 pairs of shoes. You can make 7 5 2 70× × = different outfits.

The outcomes of a specific event

When rolling a number cube, the favorable outcomes for the event “rolling an even number” are 2, 4, and 6.



independent events

outcomes

population

probability

relative frequency

sample

sample space

simulation







The possible results of an experiment

The outcomes of flipping a coin are heads and tails.

Two events such that the occurrence of one event does not affect the likelihood that the other event(s) will occur

You flip a coin and roll a number cube. The events “flipping tails” and “rolling a 4” are independent events.

A number from 0 to 1 that measures the likelihood that an event will occur

See experimental probability and theoretical probability.

An entire group of people or objects

Population: All of the 14-year-old females in the United States

Sample: All of the 14-year-old females in your town

A part of a population

See population.

The fraction or percent of the time that an event occurs in an experiment

You flip a coin 20 times. If you flip heads 11 times, the relative frequency of flipping heads

is 11

, or 55%.20

An experiment that is designed to reproduce the conditions of a situation or process

The set of all possible outcomes of one or more events

You flip a coin twice. The outcomes in the sample space are HH, HT, TH, and TT.



theoretical probability

unbiased sample




A sample that is representative of a population; It is selected at random and is large enough to provide accurate data.

You want to estimate the number of students in your school who like to play basketball. You survey 100 students at random during lunch.

The ratio of the number of favorable outcomes to the number of possible outcomes when all possible outcomes are equally likely

( ) number of favorable outcomesevent

number of possible outcomes=P

When rolling a number cube, the theoretical

probability of rolling a 4 is 1

.6



angle of rotation

center of dilation

center of rotation

congruent figures

corresponding angles

corresponding sides

dilation

image







A point with respect to which a figure is dilated

See dilation.

The number of degrees a figure rotates

has been rotated 180 to .′ ′ ′°RST R S T△ △

Figures that have the same size and the same shape

A point about which a figure is rotated

See rotation.

Matching sides of two congruent figures

ABC DEF≅△ △

Corresponding sides: side AB and side DE

side BC and side EF

side AC and side DF

Matching angles of two congruent figures

ABC DEF≅△ △

Corresponding angles: and ∠ ∠A D

and ∠ ∠B E

and ∠ ∠C F

The new figure formed by a transformation

See translation, reflection, rotation, and dilation.

A transformation in which a figure is made larger or smaller with respect to a fixed point called the center of dilation

A B C′ ′ ′ is a dilation of ABC with respect to the origin. The scale factor is 2.

x

y3

1

32O

SR

T

T′

S′ R′

180°

C

B

A

E

DFC

B

A

E

DF

x

y3

1

2

32O

CB

A

B′C′

A′ center of dilation



line of reflection

reflection

rotation

scale factor (of a dilation)

similar figures

transformation

translation




Chapter 11



A transformation in which a figure is reflected in a line called the line of reflection; A reflection creates a mirror image of the original figure.

′ ′ ′ ′K L M N is a reflection of KLMN over the y-axis.

A line that a figure is reflected in to create a mirror image of the original figure

See reflection.

The ratio of the side lengths of the image of a dilation to the corresponding side lengths of the original figure

See dilation.

A transformation in which a figure is rotated about a point called the center of rotation; The number of degrees a figure rotates is the angle of rotation.

RST△ has been

rotated about the origin O to .′ ′ ′R S T△

A transformation changes a figure into another figure.

See translation, reflection, rotation, and dilation.

Figures that have the same shape but not necessarily the same size; Two figures are similar when corresponding side lengths are proportional and corresponding angles are congruent.

A transformation in which a figure slides but does not turn; Every point of the figure moves the same distance and in the same direction.

ABC has been translated 3 units left and 2 units up to .A B C′ ′ ′

x

y

O

N

M

L

N′

K′ K

M′

L′

line of reflection

x

y3

1

2

32O

SR

T

T′

S′ R′

center of rotation

x

y

1

−2

2

3

3−1−2−3 O

C B

AB′C′

A′



concave polygon

convex polygon

exterior angles

exterior angles of a polygon

indirect measurement

interior angles

interior angles of a polygon

regular polygon







B

A

C

E

D

60 ft

50 ft

40 ft

x

A polygon in which every line segment connecting any two vertices lies entirely inside the polygon

A polygon in which at least one line segment connecting any two vertices lies outside the polygon

The angles outside a polygon that are adjacent to the interior angles

When two parallel lines are cut by a transversal, four exterior angles are formed on the outside of the parallel lines.

3, 4, 5, and 6∠ ∠ ∠ ∠ are interior angles.

1, 2, 7, and 8∠ ∠ ∠ ∠ are exterior angles.

When two parallel lines are cut by a transversal, four interior angles are formed on the inside of the parallel lines.

See exterior angles.

Indirect measurement uses similar figures to find a missing measure when it is difficult to find directly.

40

60 5040

60 6060 50

48

=

• = •

=

x

x

x

The distance across the river is 48 feet.

A polygon in which all the sides are congruent, and all the interior angles are congruent

The angles inside a polygon

q

t

p

1 2

7 8

3 4

5 6

exterior angles

interior angles



transversal

Chapter 12



A line that intersects two or more lines

transversal



linear equation

point-slope form

rise

run

slope

slope-intercept form

solution of a linear equation

standard form







A linear equation written in the form

( )1 1y y m x x− = − is in point-slope form.

The line passes through the point ( )1 1, ,x y and

the slope of the line is m.

( )21 6

3y x− = +

An equation whose graph is a line

1y x= −

The change in x between any two points on a line

See slope.

The change in y between any two points on a line

See slope.

A linear equation written in the form y mx b= +is in slope-intercept form. The slope of the line is m, and the y-intercept of the line is b.

The slope is 1 and the y-intercept is 2.

The slope m of a line is a ratio of the change in y (the rise) to the change in x (the run) between any two points ( ) ( )1 1 2 2, and , x y x y on a line. It is a

measure of the steepness of a line.

2 1

2 1

rise change in

run change in

ym

x

y y

x x

= =

−=−

The standard form of a linear equation is ,ax by c+ = where a and b are not both zero.

2 3 6− + = −x y

All of the points on a line

x

y

3

4

2

1

−3

−4

4321O−2−3−4

y = x − 1

x

y

1 2 3 4 5 6 7

1

2

3

4

5

6

7

slope =

3

2 32

x

y

3

4

5

1

321−3−4 −1

y = x + 2(1, 3)

(2, 4)

(3, 5)

(0, 2)



x-intercept

y-intercept




The y-coordinate of the point where a line crosses the y-axis

See x-intercept.

The x-coordinate of the point where a line crosses the x-axis

y

x(a, 0)

(0, b)

O

y-intercept = b

x-intercept = a



cube root

distance formula

hypotenuse

irrational number

legs

perfect cube

perfect square

Pythagorean Theorem







The distance d between any two points ( )1 1, x y and

( )2 2, x y is given by

the formula

( ) ( )2 22 1 2 1 .d x x y y= − + −

A number that, when multiplied by itself, and then multiplied by itself again, equals a given number

3

3

8 2

27 3

=

− = −

A number that cannot be written as the ratio of two integers

, 14π

The side of a right triangle that is opposite the right angle

A number that can be written as the cube of an integer

27, 8, 125−

The two sides of a right triangle that form the right angle

See hypotenuse.

In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

2 2 2a b c+ =

2 2 25 12 13+ =

A number with integers as its square roots

16, 25, 81

x

y

x2 − x1

d

(x2, y1)

(x1, y1)

(x2, y2)

y2 − y1

leg

leg

hypotenuse

12 cm

13 cm5 cm



radical sign

radicand

real numbers

square root

theorem


Chapter 14 Chapter 14 Chapter 14

Chapter 14



The number under a radical sign

The radicand of 25 is 25.

The symbol which is used to represent a square root

25 5=

49 7− = −

100 10± = ±

A number that, when multiplied by itself, equals a given number

The two square roots of 100 are 10 and −10.

100 10± = ±

The set of all rational and irrational numbers

4, 6.5, , 14π−

A rule in mathematics

The Pythagorean Theorem



hemisphere

similar solids

sphere


Chapter 15



Solids that have the same shape and proportional corresponding dimensions

One-half of a sphere

The set of all points in space that are the same distance from a point called the center

9 in.

3 in.6 in.

3 in.

1 in.2 in.

radius, r

center



base (of a power)

exponent

power

Power of a Power Property

Power of a Product Property

Product of Powers Property

Quotient of Powers Property

scientific notation







The exponent of a power indicates the number of times a base is used as a factor.

See power.

The base of a power is the common factor.

See power.

To find a power of a power, multiply the exponents.

( )( )

24 4 2 83 3 3

nm mna a

•= =

=

A product of repeated factors

�

51 1 1 1 1 1

2 2 2 2 2 21

power is used as a factor 5 times.2

= • • • • ��

To multiply powers with the same base, add their exponents.

7 10 7 10 173 3 3 3m n m na a a

+

+

• = =

• =

To find a power of a product, find the power of each factor and multiply.

( )( )

4 4 45 7 5 7

m m mab a b

• = •

=

A number is written in scientific notation when it is represented as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10.

48.3 10×

34 10−×

To divide powers with the same base, subtract their exponents.

7

7 3 43

99 9

9

, where 0m

m nn

aa a

a

−

−

= =

= ≠

exponent base



literal equation

Topic 3



An equation that has two or more variables

2 6 12y x+ =

algebraic expression angle - big ideas math algebraic expression in which the exponent of the...

Documents