test yourself unit 3 foundation qs
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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