Unit 3Unit 3FormulasFormulasto Learnto Learn

FoundationFoundation

Transformation means Transformation means move or changemove or change

T for TranslationT for TranslationE for EnlargementE for EnlargementR for RotationR for RotationR for ReflectionR for Reflection

Unit 3

Translation means slide Translation means slide needs a column vectorneeds a column vector

Enlargement needs Enlargement needs scale factor and pointscale factor and point

Rotation needsRotation needs an angle, direction and an angle, direction and

pointpoint

Reflection needs the Reflection needs the name of a mirror linename of a mirror line

Area of a triangle isArea of a triangle is base x height ÷ by 2 base x height ÷ by 2

Area of a parallelogram is Area of a parallelogram is base x heightbase x height

Area of a trapezium isArea of a trapezium is(a+b) x h ÷ 2(a+b) x h ÷ 2

Area of circle =Area of circle =radius squared x by radius squared x by ∏∏

Circumference of a circle Circumference of a circle is diameter x ∏is diameter x ∏

Volume of cube or cuboid Volume of cube or cuboid isis

the the length x width x heightlength x width x height

Volume of a prism isVolume of a prism isarea of cross section x area of cross section x

lengthlength

Volume of a cylinder is Volume of a cylinder is radius squared x ∏ x radius squared x ∏ x

heightheight

Congruent meansCongruent means exactly the same exactly the same

Similar meansSimilar means

the same shape the same shape different sizedifferent size

The quadrilateralsThe quadrilaterals

Square, rectangle, Square, rectangle, parallelogram parallelogram

rhombus, kite and rhombus, kite and trapeziumtrapezium

To find To find

10 %10 %divide by 10divide by 10

Estimate meansEstimate meansround and workout!round and workout!

Perpendicular meansPerpendicular meansat right-angles to!at right-angles to!

A bearing is an angle A bearing is an angle measured clockwise from measured clockwise from

northnorth

The x axis is called y=0The x axis is called y=0

The y axis is called x=0The y axis is called x=0

Speed = distance ÷ timeSpeed = distance ÷ time

Density = mass ÷ volumeDensity = mass ÷ volume

Reciprocal meansReciprocal means

one divided byone divided by

reciprocal of 2 is ½reciprocal of 2 is ½

The opposite of square is The opposite of square is square rootsquare root

The opposite of cube is The opposite of cube is cube rootcube root

Length = cmLength = cm

Area = cmArea = cm²²

Volume = cm³Volume = cm³

Angles in an equilateral Angles in an equilateral triangle are 60ºtriangle are 60º

Angles in a triangle add Angles in a triangle add up to 180°up to 180°

Angles in a quadrilateral Angles in a quadrilateral add up to 360ºadd up to 360º

Interior angle sum of a Interior angle sum of a polygon ispolygon is

(n-2) x 180°(n-2) x 180°

For polygonsFor polygonsInterior + Exterior =Interior + Exterior =

180º 180º

CC for correspondingfor corresponding

I I for Interiorfor Interior

AA for alternatefor alternate

OO for oppositefor opposite

Corresponding angles are Corresponding angles are equalequal

C

C

Interior angles add up to Interior angles add up to 180º180º

X

X

Alternate angles are Alternate angles are equalequal

A

A

Opposite angles are Opposite angles are equalequal

O

O

Parallel lines are like Parallel lines are like train trackstrain tracks

ParallelParallel lines have lines have the same the same gradientgradient

Equation of a straight line isEquation of a straight line is

y = +/- gradient y = +/- gradient xx +/- +/- InterceptIntercept

y x y = y²y x y = y²

y + y = 2yy + y = 2y

The Rules of indicesThe Rules of indices

aa44 x a x a5 5 = a = a99

aa77 ÷ a ÷ a3 3 = a = a44

(a(a66))3 3 = a= a18 18

A number in Standard A number in Standard Form is in two partsForm is in two parts

3.6 x 103.6 x 1066

To add and subtract To add and subtract fractionsfractions

the denominators must the denominators must be the samebe the same

To multiply fractions we To multiply fractions we multiplymultiply

top by top top by topbottom by bottombottom by bottom

Negative x negative = Negative x negative = PositivePositive

Positive x negative = Positive x negative = negativenegative

To divide fractions weTo divide fractions we

invert invert the second fractionthe second fraction

and multiplyand multiply

Solve meansSolve means

to find the value of to find the value of

x= or y=x= or y=

Simplify meansSimplify means

collect all the like terms.collect all the like terms.

Expand meansExpand means

remove the bracketsremove the brackets

2(x – 4) = 2x - 82(x – 4) = 2x - 8

Factorise meansFactorise means

put the brackets back in.put the brackets back in.

Factor (outside bracket)Factor (outside bracket)

Change the subjectChange the subjectmeansmeans

rearrange legally!!!rearrange legally!!!

Expanding double Expanding double bracketsbrackets

( x + 4 )( x - 3 )( x + 4 )( x - 3 )

Order of OperationsOrder of Operations

BracketsBracketsIndicesIndicesdivisiondivision

MultiplicationMultiplicationAdditionAddition

SubtractionSubtraction

Inequalities Inequalities

treat like antreat like an

equalsequals

2x + 1 < 52x + 1 < 5

For sequences find the For sequences find the ‘goes up in’‘goes up in’

and adjustand adjust

2, 5, 8, 11, ….2, 5, 8, 11, ….

ConversionsConversions

1kg ~ 2.2 lbs1kg ~ 2.2 lbs1 L ~ 1.75 pints1 L ~ 1.75 pints8 km ~ 5 miles8 km ~ 5 miles2.5 cm ~ 1 inch2.5 cm ~ 1 inch

Pythagoras’ theoremPythagoras’ theorem

a² + b² = c²a² + b² = c²

a

b

C

Locus meansLocus means

‘the path of a point’‘the path of a point’

The polygons The polygons

triangletrianglequadrilateralquadrilateral

pentagonpentagonhexagonhexagonheptagonheptagonoctagonoctagonnonagonnonagondecagondecagon

Plan view meansPlan view means

a birds’ eye viewa birds’ eye view

The four types of angles The four types of angles areare

AcuteAcuteobtuseobtusereflexreflex

right-angleright-angle

A perpendicular A perpendicular bisectorbisector

cuts a line in half at cuts a line in half at right-anglesright-angles

For sequences find the For sequences find the ‘goes up in’‘goes up in’

and adjust.and adjust.

The four types of triangle The four types of triangle areare

equilateralequilateralisoscelesisosceles

right-angledright-angledscalenescalene