test yourself unit 3 foundation as
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Unit 3Unit 3FormulasFormulasto Learnto Learn
FoundationFoundation
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Transformation means Transformation means move or changemove or change
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T for TranslationT for TranslationE for EnlargementE for EnlargementR for RotationR for RotationR for ReflectionR for Reflection
Unit 3
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Translation means slide Translation means slide needs a column vectorneeds a column vector
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Enlargement needs Enlargement needs scale factor and pointscale factor and point
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Rotation needsRotation needs an angle, direction and an angle, direction and
pointpoint
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Reflection needs the Reflection needs the name of a mirror linename of a mirror line
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Area of a triangle isArea of a triangle is base x height ÷ by 2 base x height ÷ by 2
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Area of a parallelogram is Area of a parallelogram is base x heightbase x height
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Area of a trapezium isArea of a trapezium is(a+b) x h ÷ 2(a+b) x h ÷ 2
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Area of circle =Area of circle =radius squared x by radius squared x by ∏∏
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Circumference of a circle Circumference of a circle is diameter x ∏is diameter x ∏
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Volume of cube or cuboid Volume of cube or cuboid isis
the the length x width x heightlength x width x height
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Volume of a prism isVolume of a prism isarea of cross section x area of cross section x
lengthlength
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Volume of a cylinder is Volume of a cylinder is radius squared x ∏ x radius squared x ∏ x
heightheight
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Congruent meansCongruent means exactly the same exactly the same
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Similar meansSimilar means
the same shape the same shape different sizedifferent size
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The quadrilateralsThe quadrilaterals
Square, rectangle, Square, rectangle, parallelogram parallelogram
rhombus, kite and rhombus, kite and trapeziumtrapezium
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To find To find
10 %10 %divide by 10divide by 10
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Estimate meansEstimate meansround and workout!round and workout!
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Perpendicular meansPerpendicular meansat right-angles to!at right-angles to!
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A bearing is an angle A bearing is an angle measured clockwise from measured clockwise from
northnorth
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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
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Speed = distance ÷ timeSpeed = distance ÷ time
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Density = mass ÷ volumeDensity = mass ÷ volume
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Reciprocal meansReciprocal means
one divided byone divided by
reciprocal of 2 is ½reciprocal of 2 is ½
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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
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Length = cmLength = cm
Area = cmArea = cm²²
Volume = cm³Volume = cm³
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Angles in an equilateral Angles in an equilateral triangle are 60ºtriangle are 60º
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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
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Interior angle sum of a Interior angle sum of a polygon ispolygon is
(n-2) x 180°(n-2) x 180°
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For polygonsFor polygonsInterior + Exterior =Interior + Exterior =
180º 180º
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CC for correspondingfor corresponding
I I for Interiorfor Interior
AA for alternatefor alternate
OO for oppositefor opposite
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Corresponding angles are Corresponding angles are equalequal
C
C
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Interior angles add up to Interior angles add up to 180º180º
X
X
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Alternate angles are Alternate angles are equalequal
A
A
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Opposite angles are Opposite angles are equalequal
O
O
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Parallel lines are like Parallel lines are like train trackstrain tracks
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ParallelParallel lines have lines have the same the same gradientgradient
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Equation of a straight line isEquation of a straight line is
y = +/- gradient y = +/- gradient xx +/- +/- InterceptIntercept
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y x y = y²y x y = y²
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y + y = 2yy + y = 2y
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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
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A number in Standard A number in Standard Form is in two partsForm is in two parts
3.6 x 103.6 x 1066
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To add and subtract To add and subtract fractionsfractions
the denominators must the denominators must be the samebe the same
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To multiply fractions we To multiply fractions we multiplymultiply
top by top top by topbottom by bottombottom by bottom
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Negative x negative = Negative x negative = PositivePositive
Positive x negative = Positive x negative = negativenegative
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To divide fractions weTo divide fractions we
invert invert the second fractionthe second fraction
and multiplyand multiply
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Solve meansSolve means
to find the value of to find the value of
x= or y=x= or y=
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Simplify meansSimplify means
collect all the like terms.collect all the like terms.
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Expand meansExpand means
remove the bracketsremove the brackets
2(x – 4) = 2x - 82(x – 4) = 2x - 8
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Factorise meansFactorise means
put the brackets back in.put the brackets back in.
Factor (outside bracket)Factor (outside bracket)
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Change the subjectChange the subjectmeansmeans
rearrange legally!!!rearrange legally!!!
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Expanding double Expanding double bracketsbrackets
( x + 4 )( x - 3 )( x + 4 )( x - 3 )
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Order of OperationsOrder of Operations
BracketsBracketsIndicesIndicesdivisiondivision
MultiplicationMultiplicationAdditionAddition
SubtractionSubtraction
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Inequalities Inequalities
treat like antreat like an
equalsequals
2x + 1 < 52x + 1 < 5
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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, ….
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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
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Pythagoras’ theoremPythagoras’ theorem
a² + b² = c²a² + b² = c²
a
b
C
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Locus meansLocus means
‘the path of a point’‘the path of a point’
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The polygons The polygons
triangletrianglequadrilateralquadrilateral
pentagonpentagonhexagonhexagonheptagonheptagonoctagonoctagonnonagonnonagondecagondecagon
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Plan view meansPlan view means
a birds’ eye viewa birds’ eye view
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The four types of angles The four types of angles areare
AcuteAcuteobtuseobtusereflexreflex
right-angleright-angle
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A perpendicular A perpendicular bisectorbisector
cuts a line in half at cuts a line in half at right-anglesright-angles
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For sequences find the For sequences find the ‘goes up in’‘goes up in’
and adjust.and adjust.
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The four types of triangle The four types of triangle areare
equilateralequilateralisoscelesisosceles
right-angledright-angledscalenescalene