Maths Ks3 Resources

8/8/2019 Maths Ks3 Resources

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Key Stage 3 Mathematics Resources

Verulam School KS3 Mathematics 2010 Page 2

Number Terms to Know (continued):equivalent two fractions that express the same part of a whole. If you multiply the

numerator and denominator of one fraction by a number you get an equivalentfraction. 1/4, 2/8, and 3/12 are all equivalent fractions.

estimate to find an approximate value for a calculation by rounding each of the

numbers.exponent the number that tells you how many times to multiply the base number by

itself.factor a number which divides evenly into another number.factorise to find all the factors of a number.

fraction written as one whole number over another, it describes part of a whole.Ex. 3/4, 1/6, 19/4.

Highest (or Greatest) Common Factor

The greatest (highest, largest) number

that divides into two or more givennumbers.improper fraction A fraction whosenumerator is equal to or greater than its

denominator.index (see exponent) also called a power.index notation when a product is written

as one or more base numbers andexponents.

integers all the whole numbers and theiropposites (the positive whole numbers,the negative whole numbers, and zero) --fractions and decimals are notintegers.

inverse operation the operation thatundoes or reverses an operation. For example,

addition and subtraction are inverse operations.irrational numbers a number that is not an integer and cannot be written as a

fraction. They are infinite, non-recurring decimals.

Least Common Denominator the least common multiple of the denominators of two ormore fractions. That is, the lowest number which is a multiple of both denominators.

Least Common Multiple the smallest number that is divisible by two or more givennumbers.


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Number Terms to Know (continued):lowest termswhen a fractions numerator and denominator have no common factors

mixed number a number composed of a whole number and a fraction. 5

multiple the multiples of a number are the products of the multiplication table.

X 1 2 3 4 5 6 7 8 9 10 11 12

1 1 2 3 4 5 6 7 8 9 10 11 12

2 2 4 6 8 9 12 14 16 18 20 22 24

3 3 6 9 12 15 18 21 24 27 30 33 36

4 4 8 12 16 20 24 28 32 36 40 44 48

5 5 10 15 20 25 30 35 40 45 50 55 60

6 6 12 18 24 30 36 42 48 54 60 66 72

7 7 14 21 28 35 42 49 56 63 70 77 84

8 8 16 24 32 40 48 56 64 72 80 88 96

9 9 18 27 36 45 54 63 72 81 90 99 108

10 10 20 30 40 50 60 70 80 90 100 110 120

11 11 22 33 44 55 66 77 88 99 110 121 132

12 12 24 36 48 60 72 84 96 108 120 132 144

negative numbers The set of numbers less than zero, to the left of 0 on the numberline.

numerator the number above the line in a fraction. It is the number of parts that arebeing taken from the whole.

Order of Operations (BODMAS or BIDMAS): The order in which to carry outoperations when evaluating an expression-- brackets, powers (or indices),

multiplication and division, addition and subtraction.percentage meaning "parts per hundred;" a fraction in which the number to the left

of the % sign is the numerator and 100 is the denominator. 57% = 57/100 =

0.57.place value the value of a digit, based on where it appears in a numeral. The value of each

position in a numeral is ten times the value of the position to its right.prime factorization a number written as the product of its prime factors.

prime number a positive whole number divisible only by 1 and itself. Following are thefirst fifteen prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 .

(Note: 1 is not prime).


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Terms to know (continued):

positive numbers The set of numbers greater than zero, to the right of 0 on the numberline.

power (see exponent)also called an indexproduct the result of multiplying two or more numbersproper fraction a fraction whose numerator is smaller than its denominator.

proportion a statement that compares one part with the whole, such as 12 out of 50.ratio a statement which compares parts with each other, such as 2:1.rational numbers the set of numbers including all the integers, plus all the numbers that

are terminating or repeating decimals.real numbers the set of all the rational numbers and all the irrational numbers.

reciprocal any number multiplied by its reciprocal is 1. The reciprocal of

is

because

recurring decimal see repeating decimalreduced written in lowest terms; written as a fraction whose numerator and denominator

have no common factors.

repeating decimal a decimal that endlessly repeats one number or a group of numbers.round to give an approximate value of a number, for example to the nearest 100, a

specific decimal place, or number of significant figures..

significant digits (or figures) the digits in the number; the closer a digit is to thebeginning of the number, the more significant it is.

square number the outcome when a number is multipled by itself. 5

5 = 5

2

= 25square root the inverse of squaring a number, the number that, when multiplied by itself,the product is a given number. 5 is the square root of 25 (written as )

standard form a short hand way of writing very large or small numbers. Always writtenas A x 10n where A is any number between 1 and 10 and n is a power of 10.

surd a rumber containing a irrational root for example 35 or 7 + 23

terminating decimal a decimal that does not continue after a certain place.

unit fraction a fraction with a numerator of 1, such as1

2.

whole number the set of numbers which includes zero and all the counting numbers--no

fractions or decimals, and no negative numbers.


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Algebra terms to know:algebraic expression a collection of terms separated by + and signs, like .brackets these show that the terms inside should be treated alike, for example:

BODMAS (BIDMAS) the order operations should be performed: Brackets, Order (orIndices), Division or Multiplication, and Addition or Subtraction.

coefficient the number (with its sign) in front of the letter representing the unknown.collect like terms to group together terms of the same variable.common factor factors that are in common for two or more numbers or terms.

constant a number that does not change.coordinates an x- and y-coordinate give the horizontal and vertical positions of a

point.(x, y).

cube number the outcome when a whole number is multipled by itself and thenmultiplied by itself again. Cube numbers are 1, 8, 27, 64, 125, . . .

cube root the number whose outcome when multiplied by itself and then multiplied byitself again gives a cube number. For example, the cube root of 8 is 2,because 2 x 2 x 2 = 8.

equation a statement showing that two expressions are equal, for example,4x + 3 = 23.expand to remove the brackets to create an equivalent expression; the opposite of

factorising.

exponent tells how many times the base number is multiplied by itself. Same as index,power.

factor a number or term that divides exactly into another number or term.

factorise to include brackets by taking out common factor; opposite of expanding.Fibonacci numbers a sequence where each term is the sum of the previous two terms;

for example, 1, 1, 2, 3, 5, 8, 13, 21.

formula an equation showing the relationship between two or more variables.gradient a measure of how steep a line is, the change in y over the change in x.identity two expressions liked by the sign are true for all values of the variable;

for example, .index tells how many times the base number is multiplied by itself. (exponent,power).

index notation when a product like 2 x 2 x 2 x 2 is written as 24, the 4 is the index.

indices the plural of index.intercept the point where a line crosses an axis.

inverse operation the operation that undoes or reverses a previous operation;i.e. subtracting is the inverse of adding and dividing is the inverse of multiplying.


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Terms to know (continued):inverse proportion if two variables are in inverse proportion, their product is a

constant and as one increases the other decreases.linear equation an equation where the highest power of the variable is 1,

such as 4x + 3 = 23.linear expression a combination of terms where the power of the highest variable is 1.

nth term this phrase is used to describe a general term in a sequence and can be usedto find any term by substituting that number for n. (fifth term, substitute 5)

operation a rule for combining two numbers of variables, such as +, -, x or /

power see index or exponent.

proportion if two variables are in proportion, their product is a constant and as oneincreases or decreases, the other does the same.

quadratic expression an expression containing terms where the highest power of thevariable is 2,Such as x2, 3x2, 5y2-3.

sequence the number of ways a shape would fit on top of itself as it is rotated 360.

simplify to make simpler by collecting like terms.solution the value of an unknown in an equation.solve to find the solution of an equation.

square numbers the outcome when a whole number is multiplied by itself; 1, 4, 9, 16

square root the square root of a number such as 16 is a number whose outcome when

multiplied by itself is 16. ( ).

substitute to find the value of an expression when the variable has a specific value.

term a number, variable, or the product of a number and an variable.triangle numbers 1, 3, 6, 10, 15. The nth term rule for trianglenumbers isunknown the letter or letters in an equation.

variable a symbol representing a quantity that can be any number.

Algebra Rules abc = a x b x c

ab = a x b a2 = a x a

5c = 5 x c n2p2 = n2 x p2

= c + c + c + c + c = n x n x p x p5c = 5 x c

c6 = c x c x c x c x c x c= c + c + c + c + c

= n p 2m2 = 2 x m2 = 2 x m x m

= =


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Shape terms to know:acute angle an angle will be acute if it is less than 90, less than a right-angle.arc part of a circumference of a circle.

angle when two line segments intersect at

a point it forms an angle.axis, axes a line, or lines, used to locate a

point on a grid using coordinates.bilateral symmetry when a shape has only

one line of symmetry.

bisector a line segment or plane whichdivides something exactly in half.

centre of enlargement the point around

which the object is enlarged.

centre of rotation the fixed point aroundwhich the object is rotated.

chord a straight line connecting twopoints on the circumference of a circle.

circle a set of points in a plane that are afixed distance from a specifiedpoint in the plane.

circumference the perimeter of a circle.cone a pyramid with a circular base and a

curved surface rising to a vertex.congruent two shapes which are identical in size and shape.

coordinates an x- and y-coordinate give the horizontal and vertical positions of a point.Written as (x, y).

cross section a cut at right angles to a face and usually at right angles to the length of aprism.

cube a solid with six identical square faces.cuboid a solid with six rectangular faces, two or four of which are squares.cylinder a prism with a circle as a cross-sectional face.

decagon a polygon with ten sides.diameter a line segment passing through the center of a circle; equal to twice the radius.edge a line segment that joins two vertices of a solid.

enlargement a transformation that changes the size but not the shape by a scale factor.

equilateral triangle a triangle with three equal sides and three equal angles,each angle = 60

face one of the flat surfaces of a solid.


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Shape terms to know (continued):gradient a measure of how steep a line is.hemisphere a half-sphere.heptagon a seven-sided polygon.

hexagon a six-sided polygon.

horizontal from left to right, parallel to the horizon.hypotenuse the longest side of a right-angled triangle.

image the shape after it undergoes a transformation.intercept the point where a line crosses an axis.interior angle an angle inside a polygon.

irregular polygon a polygons whose sides and angles are not all equal.isosceles trapezium a quadrilateral with one pair of parallel sides. Non parallel sides are

equal.

isosceles triangle a triangle with two equal sides and two equal angles.

kite a quadrilateral with two pairs of equal adjacent sides.line the shortest distance connecting two points, it continues infinitely in both directions.line of symmetry goes through the centre and divide a shape into two identical parts.

locus a curve defined by a particular property.

net a 2D shape made of polygons that can be folded to make a 3D solid.nonagon a polygon with nine sides.obtuse an angle that is more than 90 but less than 180.

octagon a polygon with eight sides.order of rotational symmetry the number of ways a shape would fit on top of itself as it

is rotated through 360.origin the point where the x- and y-axis cross, it has the coordinates (0,0).

parallel two lines which do not meet and are exactly the same distance apart for theirentire length.

parallelogram a quadrilateral with opposite sides equal and parallel.pentagon a five-sided shape.

perimeter the distance around an enclosed shape.perpendicular two lines are perpendicular if they cross at right angles to each other.polygon a closed 2D shape made from straight sides.

prism a 3D solid with two cross-sectional faces that are the same polygon, parallel to eachother. All other faces are either parallelograms or rectangles.

pyramid a solid with a polygon as the base and one other vertex; the vertices of the baseare jointed to this vertex and make triangle-shaped faces.

Pythagoras Theorem In a right triangle, the square of the hypotenuse is equal to the sumof the squares of the other two sides.

quadrilateral a polygon with four sides


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Shape terms to know (continued):radius, radii a straight line from the centre of a circle to a point on the circumference.rectangle a quadrilateral with four right angles and opposite sides equal in lengthreflex angle an angle that is more than 180 but less than 360.

regular polygon a polygon with all sides and all angles equal.

reflect, reflection a transformation involving a mirror line. The size of the shape does notchange, and all points are the same distance from the line as they were in the

original location. The line connecting the shape to its image is perpendicular.Described by giving the equation of the mirror line.

rhombus a quadrilateral with four equal sides and opposite sides parallel.

right angle an angle that is a quarter of a turn, or 90.rotate, rotation a transformation that spins a shape around a given point. Size of the

shape does not change. Described by giving the centre of rotation, angle, and

direction of rotation.

sector area of circle bisected by two radii.segment the area of part of a circle bounded by an arc and a chord.semicircle half of a circle.

scale factor how much a shape is enlarged by. A scale factor of 2 means the vertices of

the image are 2x the distance from the centre of enlargement as they were in theoriginal shape.

shape an enclosed space.

solid a 3D shape.sphere a shape where all the points are the same distance from the centre (a ball).

square a quadrilateral with four equal sides and four right angles.symmetrical a shape that has symmetry.

symmetry (reflection) if a line passing through the centre produces two identical shapes.

symmetry (rotation) if rotating the shape around its centre gives an identical shape.

tangent the straight line that touches the circle at one point.tessellation an infinitely repeating pattern where one or more shapes are fitted together.

transformation an action that changes the position and/or the size of a shape.translate, translation a transformation that changes the position of a shape in either the

x or y axis or both. Described using a vector.

trapezium a quadrilateral with one pair of parallel sides.triangle a polygon with three sides.vector a measurement of the translation of a shape. The top number is the movement in

the x-axis and the bottom is the movement in the y-axis.

vertex (vertices) the point where two or more edges meet. The corner of a shape.vertical directly up and down, perpendicular to the horizontal.

volume a measure of how much space fills a solid, measured in cubic units (cm3, m3).


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Shape

Angle

Property

Length

Property

Parallel

Sides

Diagonals

SQUAREAll fourare 90

All sides

are thesame

length

Opposite

sides areparallel

Equal

lengths.Bisect at

90

RECTANGLE

Opposite

angles areequal

Opposite

sides arethe same

length

Opposite

sides areparallel

Equal

lengths.Bisect, not

at 90

PARALLELOGRAM

Oppositeangles are

equal

Oppositesides arethe same

length

Oppositesides areparallel

Not equallengths.

Bisect, not

at 90

TRAPEZIUM

They can

all bedifferent

They can

all bedifferent

One pair of

oppositesides areparallel

Not equal.

Do notbisect

RHOMBUSOppositeangles are

equal

All sidesare thesame

length

Oppositesides areparallel

Not equal.Bisect at90

KITE

One pair of

oppositeangles are

equal

Two pairs

of adjacentsides are

equal

No sidesare parallel

One

diagonalbisected at

90

ISOSCELESTRAPEZIUM

Two pairs

of adjacentangles are

equal

One pair of

oppositesides are

equal

One pair of

oppositesides are

parallel

Equal

length.Do not

bisect.


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Data Handling Terms to Know:

average a single value that is used to represent a set of data

bias favouring one outcome over another

box plot used to show how the data is distributed

certain when something is definitely going to happencontinuous data data that can be measured and take any value; length, weight, temp.

convenience or opportunity sampling a survey conducted using convenient people, such

as the first people who come along or friends/family of the investigator.

correlation a measure of the relationship between two sets of data; measured

according to type and strength. The closerthe points lie to a straight line, the

strongerthe correlation. Inpositivecorrelation, an increase in one variable results

in an increase in the other. In negativecorrelation, an increase in one variable

results in a decrease in the other.cumulative frequency diagram a cumulative frequency diagram can be used to find the

estimate for the mean and quartiles of a set of data; find the cumulative

frequency by adding the frequencies in turn to give a running total.

data information that has been collected.

data collection sheet used to record questionnaire responses/results of experiment.

direct observation collecting data first hand, such as by counting or measuring.

discrete data data that can only be counted and take certain values, such as number

of cars.equally likely 50% chance of an event happening.

frequency density in a histogram, the height of the bar. The area of the bar is the

frequency. frequency densityfrequency

class width

frequency diagram similar to a bar chart but used for continuous data. No gaps

between bars.

frequency polygon drawn from a histogram or a bar chart by joining midpoints at the

tops of bars with straight lines to make a polygon.

frequency table a table showing how often something occurs.

grouped data data that has been grouped into specific intervals, or classes.

histogram similar to a bar chart except the area of the bar represents the frequency.

interquartile range the difference between the upper and lower quartiles.

likely greater than 50% chance of something happening.

line graph a line graph is a series of points joined with straight lines.


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Terms to know (continued):

line of best fit a line drawn to represent the relationship between two sets of data.

lower quartile the value 25% of the way through the data.

mean found by calculatingthe sum of all data

the number of values.

median the middle value when all the numbers have been lined up in order; for an even

set of numbers, the median is in the middle of the two middle values.

modal class the class that contains the mode.

mode the value that occurs most often.

moving average used to smooth out the fluctuations in a time series. Found by

averaging groups of readings from the data in sets of 2, 3 or more points.

outlier a value that does not fit the general trend.

probability scale goes from 0 to 1, with 0 being impossible and 1 being certain.

qualitative data data that cannotbe counted or measured using numbers, such as

colour, taste.

quantitative data data than can be counted or measured using numbers, like age, height.

quota sampling choosing a sample with specific characteristics, like 10 adult men.

random sampling each member of population is assigned a number and chosen at random.

range a measure of the spread of the data; difference between highest and lowest value.

scatter graph a graph used to show the relationship between two sets of variables.

secondary data data someone else has collected, such as data from newspapers or the

internet.

stem and leaf diagrama way of arranging data using a key to explain the stem and

leaf so that 34 represents 34.

stratified sampling when the sample is divided into groups or strata and the sample is

representative of the whole.

survey a way of collecting data by asking questions.

systematic sampling similar to random sampling, except every nth person is surveyed.

n is found by dividing the population size by the sample size.

tally chart a useful way of organising raw data.

time series a graph of data recorded at regular intervals.

two-way table combination of two sets of data presented in table form, such as men

and women and left and right handed.

unlikely less than 50% chance of something happening

upper quartile the value 75% of the way through the data.


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HOW TO SET UP GRAPHS AND CHARTS

You must draw your graph/chart in pencil and use a ruler for all straight lines

Setting up your axes

o Choose the units of your axisare you going up/across by 1s? 2s? 5s? 10s?o Make sure you have enough space for all your data (but not too much space)o The x axis is the horizontal line (goes across) the y axis is vertical (goes up and

down)

o Where the axes intersect is 0 on both the x and the y.o Use the lines, not the spaces for the numbers on each axiso Use the spaces across the bottom for bar charts, frequency diagrams, and

histogramso Make sure your scale goes up evenlydont skip spaces or numbers.o Use the zig-zag if you need to skip numbers at the beginning (see the cumulative

frequency graph as an example)Drawing your graph

o Use a sharp pencil. If you are plotting points, use little xs to mark them.o For a line graph, plot the points and draw a straight line through all the points.o For a time series graph, connect the points using line segmentso For scatter graphs, draw your line of best fit through the middle of the data and

showing the trend; you do not need to go through any of the points, and ignoreoutliers.

o For cumulative frequency graphs, connect the points with a smooth curve.Finishing touches

o Make sure that you give your graph a title that explains what it is showingo Label each axis with what it is measuring


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Types of Graphs and Charts

Cumulative Frequency Graph Box Plot

Time Series Graph

Number of Staff per Year

Stem and Leaf


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