URRBRAE AGRICULTURALHIGH SCHOOL

YEAR 10MathematicsGLOSSARY

x-3 -2 -1 1 2 3

y

-3-2-1

123

0

5

10

15

a b c d e f

50° 54°

76°

42°

elevation

depressionHORIZONTAL

x

minor majorarc arc

Triangle Rectangle SemiCircle

base base base

altitude altitudealtitude

A

a

B

C

c

b

Aabsolute value The positive value for a real number, disregarding the sign. Written |x|

e.g. |3| = 3, |-3| = 3.

acute angle : An angle whose measure is between 0o and 90o

acute triangle : A triangle with three acute angles.

adjacent angles or sides: Two angles or sides that are next to each other

algebraic fractions Normal fraction rules apply . To add or subtract the denominators must be the same. To multiply and divide (invert and multiply to divide). Cancel and multiply the numerators and denominators (top × top, bottom × bottom).

alternate angles Two angles that are on opposite sides of the transversal when parallel line are cut by a transversal. They are between the parallel lines and alternate left and right.

altitude The perpendicular ( ) length from a vertex of a triangle to the opposite side.

angle The figure formed by two line segments or rays that extend from a given point.angle of elevation The amount of turn up from the horizontal

angle of depression The amount of turn down from the horizontal

arc A part of the circumference of a circle.

area The measure, in square units, of the inside of a plane (flat) figure.Triangle Triangle Square Rectangle

Circle Sector Parallelogram Trapezium

area (composite) The shape must be divided into a combination of the shapes with known formula.The total area is the sum of the three known shapes.

A=Triangle + Rectangle + Semicircle. A= sh/2 + l× w + πr2/2

average The arithmetic mean. The sum of the values divided by the number of values

axis (axes) The horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is called the X-axis. The vertical axis is called the Y-axis. The point of intersection is called the Origin.

B bar graph A type of chart used to compare data in which the length of a bar represents the size of

the data. The columns are apart. Used for discrete data or categorical data. (the data is not connected )

x

A11%

B18%

C27%

D23%

E14%

F7%

N

E

S

W 147

147 TN

E

S

W 318

318 T

f(x)

x 2 4 6 8 10 12 14 16 18 20

angle at centre angle at centreand angle at circumference

y

x

2x x2x

N

E

S

W70

base of a triangle Any side of a triangle. A triangle has three bases and three altitudes.

bearing Uses NORTH and the amount of clockwise turn in DEGREES. It uses the letter T for True. Three digits are used for a bearing 070 0 T Means face NORTH and turn 70 degrees in a clockwise direction

147 0 T Means face NORTH and turn 147 degrees in a clockwise direction.

318 0 T Means face NORTH and turn 318 degrees in a clockwise directionBEDMAS Order of Operations-

1. Brackets 2. Exponents 3. Division 4. Multiplication 5. Addition and Subtraction. (Work from left to right, not necessarily addition

before subtraction.)

binomial A polynomial consisting of two terms. e.g. 3x2 - 8 bisector A line, segment or ray that divides an angle or a line into 2 equal parts.

box-and-whisker plot A type of graph used in data management showing the spread of the distribution of the data. Key points are minimum, lower quartile, median, upper quartile, maximum.

min LQ M UQ max

Ccapacity The amount a container holds. 1 centimetre3 = 1 millilitre

1000 millilitres = 1 Litre There is a link between the 1000 Litres = 1 Kilolitre volume, the capacity and the1000 Kilolitres = 1 Megalitre mass of water.

categorical data Data classified according to a property or characteristic. (shoe type, hair colour etc)

centi-- Prefix meaning a hundredth part

central angle of circle An angle subtended by an arc or a chord at the centre of a circle.

The angle at the centre is twice the angle at the circumference

chord A line joining two points on the circumference of a circle.

circle graph / pie chart / sector graph A graph of statistical data where a circle is subdivided into regions that represent the percentage of the total (relative frequency) converted to angles. The angles are calculated using percentage (as a decimal) of 360 or relative frequency multiplied by 360.

circum-centre The point of intersection of the perpendicular bisectors of each side of a triangle.It is the centre of the circle that passes through each vertex of the triangle.

circumference The distance around the boundary of a circle. (perimeter).

chord

180

N

N

E

S

W

NE

SESW

NW NNE

ENE

ESE

SSESSW

WSW

WNW

NNW

A B C

Angle at Circumference

Equal angles Angle at centreand circumference

xxx

2x

Or D is the Diameter r is the Radius

circumference angle of a circle The angle subtended by an arc or chord at the circumference of a circle. Angles in the same segment or arc are equal. The angle at the circumference is half the angle at the centre.

coefficient The numerical factor of a term. e.g. The coefficient of -3x2y is -3. The coefficient of a3b4c2 is 1. The coefficient of 7p4 is 7.

co-interior angles On parallel lines co-interior (together-inside) angles are supplementary.(add up to 1800)

collinear points Points that are on the same line. A, B, C are collinear.

commission Earnings based on sales. It is usually a percentage of sales.common denominator A multiple shared by the denominators of two or more fractions. Common

denominators must be used when adding or subtracting fractions.Both denominators are the same using equivalent fractions. (12 is part of both the 3 and 4 times tables). An easy way to get a common denominator is to multiply the denominators together.

compass points. North N, East E, South S, West W, Northeast NE, Southeast SE, Southwest SW, Northwest NW.Sometimes a further division is made creatingNNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW.

complementary angles Two angles whose sum is 90o.

completing the square Used to solve quadratic equations and finding the turning point of a parabola.Does not factorise using FOIL backwards. (There are no factors of 5 which add to 8) Force x2 + 8x to become a perfect square by adding and taking (½ of 8)2 .Write the perfect square and move the numbers to the right hand side of the equation.Find the square root of both sides (remember )Solve for x by removing the +4

NOTE:- If left in the format y = (x + 4)2 − 11 the Turning Point is (-4,-11)

composite number A whole number (integer) that has more than 2 different factors. e.g. 18 has factors 1, 18, 2, 9, 3, 6 so it is composite.

compound interest Compound interest is calculated by adding the interest to the Principal (P) each time the interest is calculated (the principal grows). The best ways to calculate the amount is to use the formula, a spreadsheet or a graphics calculator.A is the final value, P is the starting amount (Principal.) i is the rate as a decimal. (6% per year = .06 per year). If calculated monthly then .06 divided by 12 = .005 per calculation period (monthly)n is the total number of calculation periods.It is best to calculate (1+i ) first then raise it to the power of n, then multiply it by P.

concave A shape that goes in on itself. A line joining two points inside the shape can go outside the shape.

cone A cone has a circle as its base and the vertex is directly above or below the centre of the circle.

(Formulae for finding i or P)

x-4 -2 2 4 6

y

-6-4-2

24

x

hypotenuse opposite

adjacent

ab

c

da + c = 180b + d = 180

a

A

B

C

bc

y

x3 6 9-3-6-9

369

-3-6-9

congruent Figures that have exactly the same size and same shape. congruent triangles The rules for congruent triangles are.

SSS. If three sides of the triangles are equal. SAS. Two sides are equal and the included angle is equal. AAS. Two angles and a corresponding side (same position relative to the angles) are equal. RHS. Right triangles with equal hypotenuses and one other equal side.

continuous data Numerical data with an uninterrupted range of values.

convex A shape that ‘bulges’ outwards. Any line joining two points inside the shape remains inside the shape.

coordinate plane A plane (flat surface) that is divided into four quadrants by drawing a vertical and a horizontal line that intersect at a point called the origin. Used for graphing ordered pairs. The quadrants are numbered 1—4.

coordinates The ordered pair that names the location of a point in the coordinate plane. The first number in the ordered pair is the x coordinate (horizontal) the second number is the y coordinate (vertical) the point (3,-6) is shown

corresponding angles Angles that have the same relative positions on parallel lines. Above the parallel line and to the left of the transversal is shown. Corresponding angles are congruent (equal).

cosine A trigonometry ratio equal to the adjacent side over hypotenuse. ( CAH)Used when there is information about the angle, Adjacent side and the Hypotenuse.

cosine rule The side a is opposite the angle A and the same pattern for b and B, c and C

(The Cosine of the included angle)It is used to calculate the third side of a triangle if two sides and the included angle are known, or to calculate the size of an angle when the lengths of three sides are known.

cube A regular solid figure with six congruent square faces.

cube root A number that when cubed (index 3) gives the original number.The cube root of

cyclic quadrilateral A quadrilateral with all vertices on the circumference of a circle.Opposite angles of a cyclic quadrilateral are supplementary (add to 180).

cylinder A rounded three-dimensional solid that has a flat circular face at each end. Ddata Facts or opinions from which conclusions can be drawn. (Facts that have been

collected but not yet interpreted) decagon A polygon with 10 sidesdecimal numbers Addition and Subtraction line up the decimal point.

Multiplication the number of decimal places in the answer is equal to the number of decimal places in the question. ∙3 × ∙2 = ∙06 Division move the decimal point in the divisor (dividing number) and the question the same number of places until the divisor is a whole number. ∙126 ∙03 =12∙6 3 = 4∙2

N

E

20

N

E

S

W

42

m

d v

NumeratorDenominator

deduct /deduction Is the same as subtract.denominator The name of a fraction. It is below the line. It must be the same for addition and

subtraction but does not get added or subtracted.

density Compares the masses of objects and the volume they occupy. The formulae are

In the cover the one variable and the other two variables are in the correct position for the formula.

dependent events Events whose outcomes affect each other.

diagonal A line segment joining two non-adjacent (not next to each other) vertices of a convex polygon. It is customary to use n for the number of sides.

The formula to calculate the Number of diagonals of a polygon is

diameter A chord that passes through the centre of a circle.

difference The answer to a subtraction problem.

difference of two perfect squares. This is mainly used in factorisation in algebra but can also be used in number.

directed number Positive (gain, increase or profit) and negative (loss or decrease) numbers.

direction Uses the four main directions and the amount of turn away from North and South. 1) N 20 0 E Means face NORTH then turn 20 degrees towards EAST2) S 42 0 W Means face SOUTH then turn 42 degrees towards WEST.

discount A percentage or amount taken from the marked price to obtain the actual selling price.discreet data Numerical data with exact distinct values.

discriminant Part of the quadratic formula = It determines the number of solutions to a quadratic equation.. If the answer is Positive 2 solutions, if zero 1 solution, if negative no solutions.When sketching a parabola it indicates the number (if any) of x intercepts.

distributive law The formula used to remove brackets .Everything in the bracket is multiplied by the outside of the bracket. (sign included)

dodecagon A polygon with 12 sides.

E earnings Money earned as wages, salary, commission or piece work.

Gross Earnings – Income tax = Net Earnings

edge The line segment where two faces of a polyhedron meet.

equation A mathematical sentence containing an equal sign. To solve an algebraic equation whatever changed the pro-numeral (letter) must be undone by using the mathematical inverse of each operation on both sides.

All equations where the pro-numeral occurs once are a combination of the four mathematical operations.

1) 2)

xy

x+y

If the pro-numeral occurs more than once either on the same side of the equal sign or on opposite sides of the equal sign they must be gathered together first.

equiangular Having equal angles.equilateral Having equal sides.equilateral triangle A triangle with three equal sides and all angles equal to 60 degrees.

estimation An approximate amount, value or size of something.evaluate To find a numeric answer. The answer is a number.

event One or more outcomes of a probability experiment.

expand Multiply factors

Distributive Law FOILexperimental probability This is determined by observing long term trends e.g. tossing a coin, rolling dice,

picking a card etc. The experiment must be repeatable and have results which can be listed.

exponent / index A number that indicates the number of times the base appears as a factor. 63 = the exponent is 3 and the base is 6. The entire term is called a power. The index laws are

Add the indicesTake the indicesMultiply the indices

Both get index.

Both get index.

Index of 0 answer always = to 1

Reciprocal index is positive

expression A group of symbols representing numbers and operations. exterior angle of a polygon The angle outside a polygon formed by extending one of its sides.

The sum of all the exterior angles of any polygon is always

exterior angle of a triangle Is equal to the sum of the two interior opposite anglesIf x is 60 and y is 80 the exterior angle is 140.60+ 80 = 140 (exterior angle of Δ )

Fface Any of the flat sides of a polyhedron.

factor One of the numbers that make up a number by multiplication. E.g. 3 is a factor of 6 because 6 = 3×2.

0

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≤5 6-10 11-15 16-20 ≥ 21

012345678

1 2 3 4 5 6 7 8 9 10 11

02468

101214

02468

101214

012345678

1 2 3 4 5 6 7 8 9 10 11

f (x)

x2 4 6-2-4-6

246

-2-4-6

f (x)

x2 4 6-2-4-6

246

-2-4-6

y=3x+2 y=x+2

(x +3) (x-5)F

O O

F

II

LL

factorise Finding the factors is the opposite of expanding. The factors when multiplied equal the original expression.

(factor is 5 The Distributive law backwards)

(Factors of 18 which differ by +7 FOIL backwards)

factor tree A diagram representing a systematic way of determining all the prime factors of a number. e.g.

fraction Any number that can be written in the form where a and b are integers

Addition and Subtraction the denominator must be the same.

The denominator is the name and does not get added.

Multiplication: numerator times numerator and denominator times denominator.

Division: the fraction (s) immediately to the right of a dividing sign is inverted (turned upside down) and the dividing sign becomes multiply.

frequency polygon A polygon formed by joining the centre of the columns of a histogram.The polygon must start and finish at zero-----joining the imaginary centres of the zero columns on either sides.

FOIL A word to help remember how to multiply factors of a quadratic.

FOIL Multiply the two that are FIRST in each bracket x × x = x2

Multiply the two that are on the OUTSIDE of each bracket x × -5 = -5xMultiply the two that are on the INSIDE of each bracket +3 × x = +3xMultiply the two that are LAST in each bracket. 3 × -5 = -15

formula A statement expressing the relationship between two or more quantities. e.g. (area of a circle) distance= speed × time

frequency diagram /table Used in statistics as a method of recording the data collected. A tally is often used in the frequency diagram to keep track of the number of times something occurs. A graph can then be drawn.

function A set of ordered pairs where each first element is paired with one and only one second element and no element in either pair is without a partner.

Ggradient /slope Vertical movement compared to the horizontal movement.

The gradient of a linear function is if 2 points are known.

The gradient of a linear function is m in the equation (x coefficient)y =3x+2 gradient is 3 the y intercept is 2. y =x+2 gradient is 1 y intercept is 2

grid/ table/ lattice A method of listing all possible outcomes in a two stage problem. E.g. two dice

Range Tally FrequencyCumulative Frequency

Relative FrequencyAngle

≤5 4 4 4/40 =1/10 =10% 366-10 8 12 8/40 = 1/5 =20% 7211-15 9 21 9/40 =22∙5% 8116-20 12 33 12/40 = 3/10 =30% 108≥21 7 40 7/40 =17·5% 63

Total 40 360

0

2

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12

14

A B C D E F

dr i nks per week

I

P R T

xx

y y

z z

H hectare (hm2) A unit of area that is 100 m by 100 m. It is equivalent to 10 000 m2.

The prefix hecto- means 100 or 102.

height The perpendicular length from a vertex of a triangle to the line opposite. The perpendicular distance between two parallel lines is the height of a parallelogram.

is the symbol for perpendicular

heptagon A polygon with 7 sides.

hexagon A polygon with 6 sides.

histogram A type of statistical graph that uses bars, where each bar represents a range of values and the data is continuous. The columns touch each other.

horizontal Parallel to the horizonhypotenuse The side opposite the right angle in a right triangle.

It is always the longest side of the triangle. I improper fraction A fraction whose numerator is greater than or equal to its denominator. e.g. in-centre The point where all the bisectors of the angles of a triangle intersect.

It is the centre of the circle that has the sides of the triangles as tangents.

index / exponent A number that indicates the number of times the base appears as a factor. (7 is the base, 5 is the index)

inequality A mathematical sentence including one of the symbols >,<, or (greater or less than, greater or equal to, less than or equal to) the symbol points to the smaller value.

infinitely large Larger than any integer. Division by zero is an infinitely large and is undefined. The gradient of a line parallel to the Y axis is infinitely large and undefined.

integer Any number in the set

interior angles of a polygon Angles within a polygon formed by the intersection of two sides. The interior angles of a triangle add up to

  The interior angles of a quadrilateral add up to The interior angles of an n sided polygon add up to (Number of sides minus 2 then multiplied by 180)

interest (Simple) Money paid for the use of someone else's money. Simple Interest is calculated using the formula (A = P + I)

P = Principal (amount of the loan) R = Rate is the percentage (as a decimal) per yearT= Time in years.To change the formula to calculate the Principal, Rate or Time use the SI triangle cover the one that has to be found and the remainder is the formula required.

interest (Compound) See compound.

interest free Money borrowed to purchase goods where, for a specified time no interest has to be paid. If the item is not fully paid by the end of the specified time a high rate of interest is charged for the full amount for the entire duration of the loan.

Die 1

Die 2

1 2 3 4 5 61 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,1)5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

AB A B

x-4 -2 2 4

y

-10

-8

-6

-4

-2

2

4

x-4 -2 2 4

y

-4

-2

2

4

E F

median

inverse operations Mathematical operations which undo each other. etc

invert Turn upside down.

intersect To meet or cross.

inter-quartile range The value of the upper quartile minus the value of the lower quartile.

isosceles A polygon with two sides equal in length. Refers to either a triangle or a trapezium. In the triangle the angles opposite the equal sides are equal.

kite A quadrilateral with two pairs of adjacent sides equal. To find the area of a kite multiply the diagonals together and divide by two. The diagonals cut at right angles and the shorter diagonal is bisected.

kilo Prefix meaning thousand. 1000 grams = 1 kilogram1000 metres = 1 kilometre1000 litres = 1 kilolitre

Llike terms Terms that have the same variables (pro-numerals) raised to the same exponent. e.g.

3x2 and -2x2. (in both the variable is x2) Remember that xy is the same as yx. But are not the same and cannot be added or subtracted.

line A set of connected points without an end. E Flinear equation An equation whose graph is a line. The exponents have to be one. e.g.

(neither x nor y can be squared or cubed etc)Slope and Intercept form

m is the gradient (slope) and +c is the y interceptIn y = 2x - 4The y axis is cut at -4 (y intercept)

The gradient is (move from the y intercept)

The General form

In the graph 2x+3y=6 (use the cover up method)Both the y and x intercepts can be calculated by substituting x = 0 for the y intercept and y = 0 for the x intercept. y = 0 2x = 6 x=3 x=0 3y =6 y =2 This gives both intercepts which can be used to sketch the graph.

To find the gradient either get y by itself gradient =

Or the gradient can be calculated using the formula

linear growth Linear growth means that a quantity grows by the same amount in each step.

line of symmetry A line that divides a figure into two parts, each the mirror image of the other.

line segment A part of a line with two end pointsM mean In statistics, the measure of a central tendency calculated by adding all the values and

dividing the sum by the number of values. (the average.) The Mean of 3,7,9,2,5,4 = 3+7+9+2+5+4=30

median In statistics the middle value when the values are arranged in order of size. If there is an even number of data items, the median is the average of the middle two. 2,3,4,5,7,9 the middle is half way between the 4 and 5 = 4.5

metric units of length 1 kilometre = 10 3 metres 1 metre = 10 2 centimetres 1 centimetre = 10 1 millimetres kilometre metre centimetre millimetre

length (units1 ) 1 103 1 102 1 101

x-2 2 4 6 8 10

y

-2

2468

10

145°

f(x)

x2 4 6-2-4-6

246

-2-4-6

(2,-4)

(-4,2)

y

x2 4-2-4

510152025

-5

y

x2 4-2-4

510152025

-5

y

x2 4-2-4

510152025

-5

y

x2-2-4-6-8

510152025

-5

y

x2-2-4-6-8

510152025

-5

y

x2-2-4-6-8

51015

-5-10

y

x2 4-2-4

5

-5-10-15-20-25

y

x2 4-2-4

510152025

-5

area (units2 ) 1 106 1 104 1 102

volume (units3 ) 1 109 1 106 1 103

kilometre metre centimetre millimetrelength (units1 ) 1 1000 1 100 1 10area (units2 ) 1 1000000 1 10000 1 100volume (units3 ) 1 1000000000 1 1000000 1 1000

midpoint The midpoint of a line segment in coordinate geometry is at the average of the x coordinates and the average of the y coordinates.

If A (3, 5) and B (7,9) the mid point is

milli Prefix meaning a thousandth part. 1 kilogram =1000 milligrams: mixed number A number consisting of a whole number and a fraction. e.g.

mode In statistics the value that appears most frequently in a set of data. 2,4,3,5,4,7,4,2,4 the mode is 4. 2, 2, 3, 4, 4, 4, 4, 5, 7 (the 4 occurs more often than any other number)

mutually exclusive Outcomes which have no common elements e.g. drawing from a deck of cards- drawing a club is mutually exclusive to drawing a diamond because there are no ‘diamonds-clubs’ cards. However drawing a club is not mutually exclusive to drawing a king. Because a card exists that is both a club and a king.

Nnet A plane figure obtained by opening and flattening a 3-D object.

numerator Numerator The size of the fraction. It is above the line.Denominator

O obtuse angle An angle whose measure is between 90o and 180o.

obtuse triangle A triangle with one obtuse angle.

odds The ratio of the probability that an event will not occur compared with the probability of it occurring. (Fail : Success or Loss : Win ) The odds that should be placed on drawing a heart from a deck of cards is 39/13 =3/1.

ordered pair A pair of numbers for which the order is important. e.g. a pair of numbers that gives the location of a point in a plane such as (-4,2). The order is important because the point (-4,2) is not the same as (2,-4). It is always (horizontal, vertical)

ordinal data Based on a characteristic or opinion but can be ranked e.g. Excellent → Very poor.

ordinal numbers A whole number that indicates position. First, second, third fourth etc

outcome Results of a probability experiment.

outlier A data item which is much greater or smaller than the rest of the data. It may be genuine data and must be included in calculations. It affects the mean and standard deviation but not the median and inter-quartile range.

Pparabola The shape of the graph of a quadratic. y = x2, y = 3x2, y = (x+3)2, y = x2 – 5

y = x2 +4x – 5, y = (x+3)2–5

A

BM

y = x2 y = 3x2 y = (x+3)2 y = x2 – 5 y = x2 +4x – 5 y = (x+3)2–5 y = –x2 basic shape steeper 3 to the left 5 down 2 left (-½ x coordinate) 3 left 5 down inverted

To sketch a Quadratic the following must be listed.The x intercept/s if they exist. Solve the quadratic for y=0 The y intercept by substituting x = 0The turning point by 1) Inspection y = (x + 4)2 + 3 TP = (– 4,+3)

2) Using the formula and substitution. y = ax2 + bx + c TP x =

For the graph y = x 2 + 8x + 19 (a=1 b=8 c=19)

3) Completing the square

parallel lines Lines in the same plane that are always the same distance apart and never intersect.

parallelogram A quadrilateral with 2 pairs of parallel sides The properties areOpposite angles are equal. Opposite sides are equal. Diagonals bisect each other.

pentagon A five sided polygon.

perimeter The distance around the boundary of a plane (flat) figure. Triangle Square Rectangle

Circle Parallelogram Trapezium

percentage A ratio where the second term is 100. (Hundredths parts) 25% = 25:100To change a percentage to a decimal or fraction divide the percent by 100.

To change a fraction or a decimal to a percent multiply by 100.∙45 = 45 % (move the decimal two places to the right) 1/8 =12½ %

perfect square A whole number that is the square of an integer. Perfect squares to know (memorize)

In algebra perfect squares to know are

Square the first, square the last then double the first times last.Difference of two perfect squares.

perpendicular Two lines that intersect to form right angles. The small box in the corner is the symbol for right angle

x 2 3 4 5 6 7 8 9 10 11 12 13x2 4 9 16 25 36 49 64 81 100 121 144 169

wlP widthslengthsP

2222

12

3 4

Y

X

Pi The ratio of the circumference to the diameter of any (every) circle. The approximate

value is 3.142 or

point An exact location in space represented by a dot. It has no size.place value Digits have a particular value in the number system.

The number 98524∙76831

plane A flat surface that extends infinitely in all directions.

polygon A closed figure made up of line segments. (no beginning or end)

polyhedron A 3-D object that has polygons as its faces. The intersection of any two faces forms an edge.

polynomial An expression of one or more terms, including some variable(s). e.g. .

population In statistics, population refers to the entire group about which data is being collected.

power A number made up of a base and an index

prime number An integer greater than 1 whose only positive factors are itself and one.The first few are 2,3,5,7,11,13,17,19,23,29,31

prism A geometric solid with two equal bases that are, parallel polygons and the faces are rectangles. A prisms is named according to the shape of its bases. e.g. triangular prism

probability The likelihood of an event occurring. Experimental probability—an event is repeated many times e.g. tossing a coin 100

times the results are recorded e.g. H = 53 T = 47

Theoretical probability is based on the outcomes that could occur.

If finding the probability of event A or event B add the probabilities.If finding the probability of event A and event B multiply the probabilities.P (A or B) =P (A) +P (B) P (A and B) =P (A) × P (B)

product The answer to a multiplication problem.pro-numeral / variable Usually a lower case letter used to represent numbers. It can be a symbol.

proper fraction A fraction whose numerator is less than its denominator.

Pythagoras Theorem In any right angled triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other 2 sides.To find hypotenuse To find another side

pyramid A geometric solid with one base that is a polygon and all other faces are triangles with a common vertex.

Q quadrant When the axes are drawn in a coordinate plane, the plane is divided into 4 sections

called quadrants. They are numbered from 1 to 4.

quadrilateral A four sided figure. (polygon)Special quadrilaterals with specific properties are

Square Rectangle Parallelogram

9 8 5 2 4 7 6 8 3 19×10000 8×1000 5×100 2×10 4 7×1/10 6×1/100 8×1/1000 3×1/10000 1×1/1000009×104 8×103 5×102 2×101 4×100 7×10-1 6×10-2 8×10-3 3×10-4 1×10-5

rr

rradian

Rhombus Kite Trapezium

quartile Any one of the values in a frequency distribution that divides the distribution into four parts of equal frequency. The first quartile is the number below which ¼ of the values are found. (1st or lower Quartile, 3rd or upper Quartile the 2nd Quartile is the Median. ) 1, 3, 4, 4, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 14, 15.

Min LQ Median UQ Max1 5 8.5 11 15

quotient The answer to a division problem.

radian Defined as the angle between 2 radii (radiuses) of a circle where the arc between them has length of one radius.

radius (plural: radii) The distance from the centre of a circle to any point on the circumference of the circle.

range In statistics, the difference between the least and the greatest values in a set of data.

ratio A ratio compares two or more quantities of the same kind (units of measure.) 5 : 8A ratio can be written as a fraction or a decimal. Because a ratio is really a fraction, equivalent ratios are obtained by dividing or multiplying all parts of the ratio by the same number. 12 : 15 = 4 : 5 (12÷3 and 15÷3) 3 : 7 = 6 : 14 ( 3×2 and 7×2) To change a ratio to a fraction or a decimal divide the 1st by the 2nd.

To use a calculator to simplify a ratio either divide the 1st by the 2nd and change the answer to a fraction or use the fraction button for

For every ratio question the following information can be written:-

ratio (decimal)

rational number Any number that can be written in the form where a and b are integers

Five Number Summary.

Regents Scor e

0

20

40

60

80

100

120

0 2 4 6 8

H

T

H

T

H

T

HT

HTHT

HT

195° 300°

ray AB A B Half a line (has a beginning but no end) the part of a line on one side of a point

reciprocals Two numbers whose product is one.

(If the number is a fraction it is turned upside down to get its reciprocal.

rectangle A parallelogram with four right angles.All the properties of a parallelogram plus:-Diagonals are equal in length and bisect each other.

recurring decimal A decimal number that contains a digit or digits that repeat. e.g. the line above the digits shows which digits recur.

reflex angle An angle whose measure is between 1800 and 3600.

regular polygon A polygon with all sides and all angles equal. An equilateral triangle and a square are regular polygons.

rhombus A parallelogram with all sides equal in length. A rhombus has all the properties of a parallelogram. The extra properties are:-Diagonals bisect each other at right angles and bisect the angles of the rhombus.

right angle Measures exactly 900

right triangle Triangle with one angle equal to 900

Ssample In statistics refers to a representative portion of the population from which

information is gathered. It is generally accepted that

The information is used to draw conclusions about the behaviour of the population as a whole. The sample should be random and representative of the group.

sample space In probability a list of all possible outcomes.Three coins sample space is

Each branch of the tree diagram is a possible outcome.

Scale /(Map or Drawing) The ratio of a distance measured on a scale drawing to the corresponding distance measured on the actual object.

scale factor A scale ratio must be in the same units -- convert to the smaller units.1cm : 5m = 1 cm : 500 cm Scale Factor is 500.Distance on Drawing × Scale Factor = Real SizeReal Size ÷ Scale Factor = Distance on Diagram

scalene triangle A triangle with all sides of different lengths.

scatter plot A graphical method used in statistics to show the relationship between two variables. The values of the two variables form ordered pairs that are graphed on the coordinate plane. Scatter plots will often show at a glance whether a relationship exists between two sets of data.

scientific notation A number written as the product of a number between 1 and 10 and the appropriate power of ten. (one number to the left of the decimal point) e.g. 118 000 = 1.18 X 105.

secondary data Data obtained indirectly from sources such as a book or computer database.

I

P R T

x

hypotenuse opposite

adjacent

16 8

189

35 35

454545

45

A

B

C

bc

sector Part of a circle bounded by two radii and an arc.

segment Part of a circle bounded by a chord and an arc.

semi circle Half a circleThe angle in a semi circle is 900

sign rules Addition and Subtraction basically common sense is used (no rules.)−3 × − 5 = + 15 − 3 + 5 = +2 −10 + 4 = − 6 − 5 − 7 = −12 +3 + 4 = +7+3 × + 5 = + 15 Note ( −−5 is the same as (−1 × −5 ) and −+6 is the same as (−1 × +6) −3 × + 5 = − 15 Signs that are next to each other + + − − + − −+ follow the rules for multiplication.+3 × − 5 = −15 Multiplication and Division (same rules).

If the two signs are the same the answer is positive. If the two signs are the different the answer is negative.

similar polygons Polygons that have the same shape but not necessarily the same size.

similar triangles Similar triangles have the same shape and their corresponding sides are in the same ratio. Triangles are similar ifTheir angles are equal (AAA) Their corresponding sides are in the same ratio. Two sides are in the same ratio and an angle in a corresponding position is equal.

simple interest (see interest) I=PRT P is the amount borrowed R is percentage as a decimal per year T is time in years.

simplest form (lowest terms) A fraction is in simplest form if both its numerator and denominator are whole numbers and their only common factor is 1.

simultaneous equations Equations with two or more variables that must be true at the same time.One of the variables must be removed either by substitution or elimination.

simplify To make an expression as short or compact as possible. To make it simpler, or to reduce the number of symbols used.

sine A trigonometry ratio equal to the opposite side over hypotenuse. SOH

sine rule Used if two angles and a side are known or two sides and a NON included angle are known.

square A rhombus with right angles.A square has all the properties of a parallelogram, rectangle and rhombus.

squaring Multiplying a number or pro-numeral by itself.

square root A number that when squared gives the value of the original number. e.g. The square root of 25 is 5 because 52 = 25. The symbol can be replaced by using fraction indices.

)2,1(1x2y11x11

0y2)add(11y4x3substitute0yx20y4x8

equals'yofnumberthemaketo(4

equation other undermove 11y4x30yx2NELIMINATIO

)2,1(1x2x2y

11x11Substitute11x8x3x2y11y4x30yx2

ONSUBSTITUTI

x

hypotenuse opposite

adjacent

baseb

altitude

r

s

radius

side

180°

radius

height

circumference

straight angle An angle whose measure is 180o. (Straight line)

stem-and-leaf plot In statistics, a way of recording, organizing and displaying numerical data so that the original data remains intact. e.g. In this plot, the last row represents the numbers 90, 92 and 95. A stem and leaf plot should always be an ‘ordered’ stem and leaf plot. Mode 75 Median 72 Q1 58+61→119 2 = 59∙5 Q3 = 77+83→1602 = 80

subtend A line, two points, an arc, a chord, can subtend an angle. i,e. the start and finish of the angle but not the actual position of the angle.

sum The answer to an addition problem. The symbol for sum is .

supplementary angles Two angles whose measures total 180o.

surd An irrational number (cannot be written as a fraction.) It exists but is not a precise number.It is the square root of a non-perfect square. There is no exact answer.To multiply surds

To divide surds

Surds can only be added or subtracted if they are the same. Entire surd means everything is under the square root sign

The 3 goes back under the square root sign as a 32 =9.To simplify a surd means get as much as possibly from under the square root sign. Factors that are perfect squares can be moved from underneath the square root sign.

The 4 comes out as a 2.`

surface area The sum of the areas of all the faces, including the bases, of a 3-D object.

Cube Six equal squares.

Pyramid A square plus 4 equal triangles

Cone (learn formula)

Sphere (learn formula)

Cylinder

Ttangent A trigonometry ratio equal to the opposite side over the adjacent side. TOA

Tan x =

tens units

tangent

tangent

1/2

R

B

R

R

B

B

1/2

1/2

1/2

1/2

1/2

1/2

1/2 1/2

1/2

1/2

1/2

1/2

1/2

R

R

R

R

B

B

B

B

R

B

R

R

B

B

R

R

R

R

B

B

B

B

2/53/5

3/5

3/5

3/5

3/5

3/5

3/5 2/5

2/5

2/5

2/5

2/5

2/5

R

B

B B

RR

R

R

RB

B

B RB

3/5

2/5

2/4

3/4

1/4

2/4

1/3

2/32/3

1/32/3

1/33/3

0/3

transversal180

& are cointerior

OPP

OSI

TE

HYPOTENUSE

37°ADJACENT

A

B

C

bc

tangent A straight line that touches the circumference of a circle at one point. The tangent is at right angles to the radius at the point of contact.Two tangents from a common point are equal in length.

A tangent is a straight line that touches a curve once.

term Any expression written as a product or quotient. e.g. 3xy, 2m3, or -5x3y2z

theoretical probability Probability that is determined on the basis of reasoning, not through experimentation.

e.g. Since a regular die has 6 sides, the theoretical probability of tossing a 3 is

time (24 hour clock) Midnight is 0000 hours. The rest of the time before 12 noon does not change except four digits must be used and the word hours is used instead of o’clock. E.g.0230 hoursFrom 12 pm to 12 .59 nothing changes except the word hours is used.For all other p.m. time 12 hours must be added. 1 pm = 1300 hours.

transversal A line that intersects 2 or more other lines in the same plane.

trapezium A quadrilateral with exactly one pair of parallel sides. Co-interior angles add up to 180 (parallel lines)Interior angles add to 360 (quadrilateral)

tree diagram A diagram representing a systematic way of determining all possible outcomes in a probability experiment. e.g. if you draw three marbles from a bag:-Three marbles 3 black 3 red. (replaced).Two equally possible outcomes P (B) = ½. P(R) = ½. P (RRR) = ½× ½ × ½ = 1/8 P (BRR) = ½× ½ × ½ = 1/8

P (RRB) = ½× ½ × ½ = 1/8 P (BRB) = ½× ½ × ½ = 1/8

P (RBR) = ½× ½ × ½ = 1/8 P (BBR) = ½× ½ × ½ = 1/8

P (RBB) = ½× ½ × ½ = 1/8 P (BBB) = ½× ½ × ½ = 1/8

Three marbles 2 black 3 red (replaced).Two different possible outcomes. P (B) = 2/5. P(R) = 3/5. P (RRR) = 3/5 × 3/5 × 3/5 = 27/125 P (BRR) = 2/5 × 3/5 × 3/5 = 18/125

P (RRB) = 3/5 × 3/5 × 2/5 = 18/125 P (BRB) = 2/5 × 3/5 × 2/5 = 12/125

P (RBR) = 3/5 × 2/5 × 3/5 = 18/125 P (BBR) = 2/5 × 2/5 × 3/5 = 12/125

P (RBB) = 3/5 × 2/5 × 2/5 = 12/125 P (BBB) = 2/5 × 2/5 × 2/5 = 8 /125

Three marbles 2 black 3 red ( NOT replaced). Dependent eventsP (RRR) = 3/5 × 2/4 × 1/3 = 1/10 P (BRR) = 2/5 × 3/4 × 2/3= 1/5

P (RRB) = 3/5 × 2/4× 2/3 = 1/5 P (BRB) = 2/5 × 3/4 × 1/3 = 1/10

P (RBR) = 3/5 × 2/4 × 2/3 = 1/5 P (BBR) = 2/5 × 1/4 × 3/3 = 1/10

P (RBB) = 3/5 × 2/4 × 1/3 = 1/10 P (BBB) = 2/5 × 1/4 × 0/0 = 0

trigonometry The three trigonometry ratios sine θ, cosine θ, and tangent θ are defined as follows (the shortened form is written as sin θ, cos θ, and tan θ)

To remember these, use SOH CAH TOA, that is:Sin θ = Opposite/Hypotenuse, SOHCos θ = Adjacent/Hypotenuse, CAH

BaseHeight

BaseHeight

Base

Height

Base

height

Base

height

Radius

Base

height

radius

A B

C

1

3

24

56 7

Tan θ = Opposite/Adjacent TOA

Area of a triangle is (the included angle)

turn / revolution A 360 degree angle.U unit price The price of a single item or the price per kilogram or gram.

unlike terms Terms with different variables or the same variables raised to different exponents. e.g..

Vvariable / pro-numeral A symbol, usually a small case letter, used to represent numbers. e.g. In the expression

2 + 3, the variable is . The 3 is called a constant because its value never changes.

venn diagram A diagram to illustrate the relationship between groups. Can be used in probability.The areas of are 1, 2, 3 members of A, B, C only1) 1, 2, 3 members of A, B, C only2) Members of:- A and B but not C (4), B and C but not A (5), A and C but not B (6)3) A member of A, B and C (7)

vertex (plural: vertices) The point of intersection of two rays that form an angle, two sides of a polygon or two edges of a solid.

vertical At right angles to the horizon.

vertically opposite angles Two angles formed by the intersection of two lines. They share a common vertex but no sides or interior points. e.g. Vertically opposite angles, a and c, are equal and angles b and d, are equal

volume The amount of space occupied by an object.

Volume of a prism → Area of the base times height. V= A× He.g.

Volume of a pyramid and cone (pointy shape) = Area of the base × height ÷ 3.

Volume of a sphere

Volume of a cylinder (Same idea as a Prism—Area of base × Height)

W whole number A number without fractions.