Math Gloss Act

8/9/2019 Math Gloss Act

1/14

ABSOLUTE VALUEthe magnitude of a number, irrespec-

tive of its sign. Written as a number inside vertical lines:

3=3 and 3 = 3.

ACUTE ANGLEan angle measuring less than 90.

A triangle with three acute angles is called an acute

triangle.

ADJACENT ANGLEStwo angles having a common side

and a common vertex.

In the figure above, angles x and y are adjacent. (They

are also supplementary.)

ALGEBRAIC EXPRESSIONone or more algebraic terms

connected with plus and minus signs. An algebraic

expression is not an equation because it has no equal

sign.

ALTITUDEa perpendicular segment whose length can be

used in calculating the area of a triangle or other polygon.

In the figure above, BDis an altitude ofABC, andGJis

an altitude of parallelogram EFGH.

ANGLEtwo line segments coming together at a point

called the vertex.

The angle above could be called ABC, B, or x.

ARCa portion of the circumference of a circle.

Because the central angle is of a full circles 360, the

length of minor arc AB is the circumference.

AREAa measure, in square units, of the size of a region

in a plane. Finding the area of a figure invariably involvesmultiplying two dimensions, such as length and width, or

base and height.

1

9

1

9

A

CB

Math Glossary

ACT Resources 433

24_ACT-Appendix B.qxd 9/26/05 12:24 PM Page 433


2/14

AVERAGEthe sum of a group of numbers divided by the

number of numbers in the group. To find the average of

2, 7, and 15, divide the sum (2 + 7 + 15 = 24) by the

number of numbers (3): 24 3 = 8.

AVERAGE RATEAverageA per B = . Average

speed = . To get the average speed, dont

just average the speeds.

AXESthe perpendicular number lines in the coordinate

plane.

BASEa side of a polygon that will be used with an

altitude in calculating the area; a face of a solid, the area

of which will be used with an altitude in calculating the

volume.

In the figure above,ACis the base of the triangle, and

circle O is the base of the cone.

BINOMIALan algebraic expression with two terms.

The FOIL method of multiplying works only for a pair of

binomials.

BISECTORa line or line segment that divides an angle in

half. The bisector of a 90 angle divides it into two 45

angles.

CENTRAL ANGLEan angle formed by two radii of a circle.

In the figure above, AOB is a central angle.

CHORDa line segment connecting two points on a circle.

In the figure above, AB and AC are chords of circle O.

Because it passes through the center, ACis also a

diameter.

CIRCLEthe set of points in a plane at a particular

distance from a central point. A circle is not a polygon

because it is not made up of straight sides.

CIRCUMFERENCEthe distance around a circle. The

circumference of a circle is analogous to the perimeter

of a polygon.

CIRCUMSCRIBEDdrawn outside another figure with as

many points touching as possible.

central angle

A

BO

y-axis

x-axis

Total distance

Total time

TotalA

Total B

ACT ResourcesMath Glossary

434



3/14

In the figure above, the circle is circumscribed about

the square; d is both a diagonal of the square and a

diameter of the circle.

COEFFICIENTthe numerical or constant part of an

algebraic term. In the monomial 4x2y, the coefficient is4. In the expression ax2 +bx+ c, a,b, and c are the

coefficients.

COMMON DENOMINATORa number that can be used

as the denominator for two or more fractions so that they

can be added or subtracted. Before you can add the

fractions and , you first re-express them with a

common denominator, such as 24: = and =

.

COMMON FACTORa factor shared by two integers. Anytwo integers will have at least 1 for a common factor.

COMMON MULTIPLEa multiple shared by two integers.

You can always get a common multiple for two integers

by multiplying them, though that will not necessarily be

the least common multiple.

COMPLEMENTARY ANGLEStwo angles whose

measures add up to 90.A 30 angle and a 60 angle

are complementary.

CONEa solid with a circle at one end and a single point

at the other.

CONGRUENTidentical; of the same size and shape.

Congruent polygons have the same angles and sidelengths.

CONSECUTIVEone after another, in order, without skip-

ping any. The numbers 6, 9, 12, 15, 18, and 21 are

consecutive multiples of 3.

COORDINATESthe pair of numbers, written inside paren-

theses, that specifies the location of a point in the coordi-

nate plane. The first number is the x-coordinate and the

second number is the y-coordinate.

COSECANTthe ratio of the hypotenuse to the opposite

leg. The cosecant ofA in the figure below is

= .

COSINEthe ratio of the adjacent leg to the

hypotenuse. The cosine ofA in the figure above is

= .1213adjacent

hypotenuse

13 inches

12 inches

5 inches

13

5hypotenuseopposite

15

24

5

820

245

6

5

85

6


435



4/14

COTANGENTthe ratio of the adjacent leg to the opposite

leg. The cotangent ofA in the figure above is= .

CUBEa rectangular solid whose faces are all squares.

CUBE (of a number)the third power. The cube of a

negative number is negative.

CYLINDERa solid with two circular ends connected by

straight sides.

DECIMALa noninteger written with digits and a decimal

point. A decimal is equivalent to a common fraction

whose denominator is 10, 100, or 1,000, etcetera .

DEGREEone 360th of a full rotation. A right angle

measures 90 degreesoften written 90.

DEGREE OF AN EQUATIONthe greatest exponent in a

single-variable equation. The equationx3 9x= 0is a

third-degree equation because the biggest exponent is 3.

DENOMINATORthe number below the fraction bar.

When you increase the denominator of a positive fraction,

you decrease the value of the fraction: is less than

.

DIAGONALa line segment connecting two nonadjacent

vertices of a polygon. A diagonal divides a rectangle into

two right triangles.

DIAMETER(the length of) a line segment connecting

two points on a circle and passing through the center.A

diameter is a chord of maximum length .

DIFFERENCEthe result of subtraction. The positive

difference between 3 and 7 is 4.

DIGITone of the numbers from 0 through 9. In the

3-digit number 355, the hundreds digit is 3, the tens

digit is 5, and the ones digit is 5.

DISTINCTdifferent, distinguishable. The number 355 has

2 distinct digits: 3 and 5.

EDGEa line segment formed by the intersection of two

faces.

A rectangular solid has 12 edges.

ELLIPSEa set of points in a plane for which the sum of

the distances from two points (called foci) is constant.

edge

7

10

7

11

12

5

adjacent

opposite


436



5/14


6/14

GRAPH OF AN EQUATIONa line or curve in the coordi-

nate plane that represents all the ordered pair solutions of

an equation.

The figure above shows the graph of the equation x2 + y2

= 25.

GREATEST COMMON FACTORthe greatest integer that

is a factor of both numbers under consideration. The

greatest common factor (GCF) of relative primes is 1 .

HEXAGONa six-sided polygon.

The six angles of a regular hexagon each measure 120 .

HYPOTENUSEthe side of a right triangle opposite the

right angle.

The hypotenuse is always the longest side.

IMAGINARYnot real, usually because of the square

root of a negative number. The square root of 4 is an

imaginary number.

IMPROPER FRACTIONa fraction with a numerator thats

greater than the denominator. is an improper fraction

and is therefore greater than 1.

INEQUALITYa statement that compares the size of two

quantities. There are four inequality symbols: < (lessthan), (less than or equal to), > (greater than), and (greater than or equal to).

INSCRIBEDdrawn inside another figure with as many

points touching as possible.

When a circle is inscribed within a square, the diameter d

of the circle is the same as a length of a side s of the

square.

INTEGERa whole number; 325, 0, and 29 are integers.

INTERCEPTthe point where a given line crosses

thex-axis ory-axis.

d

s

35

8

hypotenuse

120

120

120

120

120

120


438



7/14

The y-intercept is the b in the slope-intercept formy = mx + b.

INTERIOR ANGLEan angle inside a polygon formed by

two adjacent sides. Every polygon has the same number

of interior angles as sides.

The interior angles of a regular pentagon each measure

108.

IRRATIONALreal, but not capable of being expressed as

a ratio of integers. 2, 3, and are irrational numbers.

ISOSCELES TRIANGLEa triangle with two sides of equal

length.

The angles opposite the equal sides of an isosceles

triangle are also equal.

LEAST COMMON MULTIPLEthe smallest number that

is a multiple of both given numbers. The least common

multiple of relative primes is their product.

LEGS (of a right triangle)the sides that make up the

right angle.

You can use the legs as the base and altitude to find the

area of a right triangle.

LIKE TERMSalgebraic terms in which the elements other

than the coefficients are alike. 2ab and 3ab are like

terms, and so they can be added: 2ab + 3ab = 5ab.

LINEa straight row of points extending infinitely in both

directions. A line has only one dimension.

LINE SEGMENTa straight row of points connecting two

endpoints. Each side of a polygon is a line segment.

LINEAR EQUATIONa single-variable equation with noexponent greater than 1.A linear equation is also called a

first-degree equation.

interior angle108

108

108 108

108

y = x+ 1

x-intercept

y-intercept

y

Ox


439



8/14

MIDPOINTthe point that divides a line segment in half.

In the figure above, B is the midpoint of AC, so AB = BC.

MIXED NUMBERa noninteger greater than 1 written with

a whole number part and a fractional part. The mixed

number4 can also be expressed as the improper

fraction .

MONOMIALan algebraic expression consisting of exactly

one term.

MULTIPLE (ofn)a number thatn will divide into with no

remainder. Some of the multiples of 18 are: 0, 18, and

90.

NEGATIVEless than zero. The greatest negative integer

is 1.

NUMERATORthe number above the fraction bar. When

you increase the numerator of a positive fraction, you

increase the value of the fraction: is greater than

.

OBTUSE ANGLEan angle measuring more than 90 and

less than 180. An obtuse triangle is one that has one

obtuse angle.

OCTAGONan eight-sided polygon.

Each of the interior angles of a regular octagon measures

135.

ODD NUMBERan integer that is not a multiple of 2.

Any integer thats not even is odd.

ORIGINthe point where thex- andy-axes intersect.

The origin represents the point (0,0) .

PARABOLAthe set of points in a plane that are the same

distance from a point called the focus and a line called the

directrix.

PARALLEL LINEScoplanar lines that never intersect.

Parallel lines are the same distance apart at all points.

PARALLELOGRAMa quadrilateral with two pairs of

parallel sides.

Opposite sides of a parallelogram are equal; opposite

angles of a parallelogram are also equal.

parabola

directrix

focus

1217

13

17

14

3

2

3


440



9/14

PENTAGONa five-sided polygon.

The interior angles of any pentagon add up to 540.

Each of the interior angles of a regular pentagonmeasures 108.

PERCENTone hundredth. 20% means 20 hundredths, or

= .

PERCENT INCREASE/DECREASEamount of increase or

decrease expressed as a percent of the original amount.A

decrease from 100 to 83 is a 17% decrease.

PERIMETERthe sum of the lengths of the sides of a

polygon. Two polygons with the same area do not

necessarily have the same perimeter.

PERPENDICULARintersecting at a right angle. Thealtitude and base of a triangle are perpendicular.

PIan irrational number, approximately 3.14, which is

equal to the ratio of the circumference of any circle to its

diameter. The symbol for pi is . Pi appears in the formu-

las for the circumference and area of a circle, as well for

the volumes of a sphere, a cylinder, and a cone.

POINTa precise position in space.A point has no length,

breadth, or thickness.

POLYGONa closed figure composed of any number of

straight sides.

Triangles, squares, trapezoids, and pentagons are all

polygons, but circles and ellipses are not.

POLYNOMIALan algebraic expression that is the sum of

two or more terms. Binomials and trinomials are just two

types of polynomials.

POSITIVEgreater than zero.Zero is not a positive

number.

POWERa product obtained by multiplying a quantity by

itself one or more times. The fifth power of 2 is 32.

PRIME FACTORIZATIONan integer expressed as the

product of prime numbers. The prime factorization of 60

is 2 2 3 5.

PRIME NUMBERan integer greater than 1 that has no

factors other than 1 and itself. The first 10 prime numbers

are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Notice that 2 is

the only even prime number.

PROBABILITYthe likelihood of a particular event,

expressed as the ratio of the number of favorable

occurrences to the total number of possible occurrences.

Probability is a part-to-whole ratio and can therefore never

be greater than 1.

PRODUCTthe result of multiplication. The product of 3

and 4 is 12.

1

520

100


441



10/14

PROPORTIONan expression of the equality of ratios.

Corresponding sides of similar figures are proportional.

PYTHAGOREAN THEOREMthe rule that states, for any

right triangle, the sum of the squares of the legs is equal

to the square of the hypotenuse.

If you call the lengths of the legs a and b and the length

of the hypotenuse c, you can write a2 + b2= c2.

QUADRANTone of the four regions into which the axes

divide the coordinate plane.

When you know the signs of the coordinates, you know

which quadrant contains that point. For any point in

Quadrant IV, for example, the x-coordinate is positive and

the y-coordinate is negative.

QUADRATIC EQUATIONa second-degree equation.

Quadratic equations with one unknown often have two

solutions.

QUADRILATERALa four-sided polygon.Squares,

rectangles, parallelograms, and trapezoids are all

quadrilaterals.

QUOTIENTthe result of division. When 12 is divided by

3, the quotient is 4.

RADIANa unit for expressing the measure of an angle.

The angle shown in the figure above measures

radians, which is the same as 135. Its no coincidencethat is also the length of the arc shown.

RADICALthe symbol, which by itself represents the

positive square root, and with a little number written in

as in 3

32represents a higher root. By convention,

represents the positive square root only.

RADIUS(the length of) a line segment connecting the

center and a point on a circle. The radius is half the

diameter.

RATEa ratio of quantities measured in different units. Themost familiar rates have units of time after the word per,

such as: meters per second, pages per hour, inches per

year.

3

4

3

4

Quadrants


442



11/14

RATIOa fraction that expresses the relative sizes of two

quantities.A ratio is generally expressed with the words

of and to: as in the ratio of girls to boys.

RATIONALcapable of being expressed as a ratio of

integers. The repeating decimal .074074074074 . . . is a

rational number because it can be written as .

REALhaving a place on the number line. is a real

number because it has a locationsomewhere just to the

right of 3.14on the number line.

RECIPROCALSa pair of numbers whose product is 1. To

get the reciprocal of a fraction, switch the numerator and

denominator: the reciprocal of is .

RECTANGLEa quadrilateral with four right angles. All

rectangles are parallelograms, but not all parallelograms

are rectangles.

RECTANGULAR SOLIDa solid whose faces are all

rectangles.

REDUCING A FRACTIONexpressing a fraction in lowest

terms by factoring out and canceling common factors.

reduces to .

REGULAR POLYGONa polygon with all equal sides

and all equal angles. Equilateral triangles and squares are

regular polygons.

RELATIVE PRIMESpositive integers that have no

factors in common. Thirty-five and 54 are relative primes

because their prime factorizations (35 = 5 7, and 54 =2 3 3 3) have nothing in common.

REPEATING DECIMALa decimal with a digit or cluster of

digits that repeats indefinitely. The fraction is equivalent

to the repeating decimal .142857142857142857. . . ,

which can be written as .142857.

RHOMBUSa quadrilateral with four equal sides.

The diagonals of a rhombus are perpendicular.

RIGHT ANGLEan angle measuring 90. A rectangle is a

polygon with four right angles.

RIGHT TRIANGLEa triangle with a right angle. Every right

triangle has exactly two acute angles.

ROOTa number that multiplied by itself a certain

number of times will yield the given quantity. The third

root of 8 is 2.

SCALENE TRIANGLEa triangle with sides of different

lengths.A 3-4-5 triangle is a scalene triangle.

1

7

3

4

6

8

rectangular solids

7

22

7

2

27


443



12/14

SECANTthe ratio of the hypotenuse to the adjacent leg.

The secant is the reciprocal of the cosine.

In the figure above, the secant ofA is .

SECTORa region bounded by two radii and an arc.

Because the central angle of 40 is 19 of the full circles

360, the area of the shaded sector is 19 of the area of

the whole circle.

SIMILARproportional; of the same shape. Similar

polygons have the same angles.

SINEthe ratio of the opposite leg to the hypotenuse.

In the figure above, the sine ofA is .

SLOPEa description of the steepness of a line in the

coordinate plane, defined as . Lines that gouphill (left to right) have positive slopes, and lines that

go downhill have negative slopes. A horizontal line

that is, a line parallel to the x-axisis flat and has a

slope of 0.

SLOPE-INTERCEPT FORMan equation in the form

y = mx + b. In this form, m is the slope and b is the y-

intercept. Line 1 in the figure above has a slope of 1 and

a y-intercept of 4, so its equation is y = x + 4. Line 2s

equation is y = 4. Line 3s equation is y = x 3.

line 1

line 2

line 3

slope = 1

slope = 0

slope = 1

Change iny

Change inx

5

13

5 inches

12 inches

13 inches

13

12

13 inches

12 inches

5 inches


444



13/14

SOLIDa three-dimensional figure.

Cubes, cylinders, cones, and spheres are all solids.

SOLVINGisolating the given variable.

SPHEREthe set of all points in space a particular distance

from a central point. Visualize a sphere as a ball.

SQUAREa quadrilateral with four equal sides and fourright angles.A square can be thought of as a rectangular

rhombus.

SQUARE ROOTa number that when squared yields the

given quantity. Positive numbers each have two square

roots, but negative numbers have no real square roots.

SUMthe result of addition. The sum of 3 and 4 is 7 .

SUPPLEMENTARY ANGLEStwo angles whose measures

add up to 180.

SURFACE AREAthe sum of the areas of the surfaces of a

solid.Surface area is measured in square units.

SYSTEM OF EQUATIONStwo or more equations in

which each variable represents the same quantity in one

equation as in another.

TANGENTthe ratio of the opposite leg of a right triangle

to the adjacent leg.

TANGENT (of a circle)a line that intersects a circle at

exactly one point. Visualize a tangent as a line that just

barely touches the circle.

TERMa part of an algebraic expression that either stands

by itself or is connected to other terms with plus and

minus signs.A term has three parts: the coefficient, thevariable(s), and the exponent(s).

TRANSVERSALa line that intersects two parallel lines.

A transversal across parallel lines creates two sets of four

equal angles.

TRAPEZOIDa quadrilateral with one pair of parallel sides.

TRIANGLEa three-sided polygon. The three angles of a

triangle add up to 180.

tangent


445



14/14

UNDEFINEDnot covered by the rules. Division by 0 is

undefined.

VARIABLEa letter representing an unknown or

unspecified quantity. The letter most commonly used

for a variable is x.

VERTEXa point of intersection, such as a corner of a

rectangular solid or a polygon.

VERTICAL ANGLESangles across the vertex of

intersecting lines. Vertical angles are equal.

In the figure above,q ands are vertical angles, as arep andr.

VOLUMEa measure of the amount of space contained

within a solid. Computing volume invariably involves

multiplying three dimensions, such as length, width, and

height.

vertices


446


Documents

Math Gloss Act