UN DERSTA N D TRA N SLA TION VECTORS
DRA W LOCI FROM A POIN T A N D A LIN E
DRA W EQUA L DISTA N CE LOCI FROM POIN TS A N D LIN ES
DESCRIBE A TRA N SLA TION FULLY USIN G VECTORS
TRA N SLA TE A SHA PE BY A GIVEN VECTOR
TRANSLATIONS
LOCI
RELA TION SHIP BETW EEN TRA N SLA TION A N D CON GRUEN CE
DRA W REGION S BOUN DED BY A CIRCLE A N D IN TERSECTIN G LIN E
IDEN TIFY REGION S A S
OR
DESCRIBE A N EN LA RGEMEN T FU L L Y
CON STRUCT A LL DIFFEREN T TYPES OF TRIA N GLES
EN LA RGE A SHA PE BY A GIVEN SCA LE FA CTOR, FROM A POIN T
CON STRUCT A REGULA R HEXA GON IN SIDE A CIRCLE
ENLARGEMENT
CON STRUCT CIRCLES A N D A RCS OF GIVEN RA DII
FIN D CEN TRE OF EN LA RGEMEN T IN 2D SHA PES
CONSTRUCTING SHAPES
RECOGN ISE DIFFEREN CES BETW EEN PROPERTIES OF TRIA N G L E S
CA LCULA TE SCA LE FA CTOR OF A N EN LA RGEMEN T
FOLLOW IN STRUCTION S TO A CCURA TELY DRA W A SHA PE
EFFECT OF EN LA RGEMEN T ON A N GLES
PERPEN DICULA R FROM A POIN T
AND
A LIN E
DESCRIBE REFLECTION S FULLY
OR
PERPEN DICULA R BISECTOR OF A LIN E
EXPRESS MIRROR LIN E A S A SIMPLE EQUA TION
REFLECTION
PA RA LLEL LIN ES
CONSTRUCTING LINES AND ANGLES
BISECTIN G A N GLES
RELA TION SHIP BETW EEN REFLECTION A N D CON GRUEN C E
CON STRUCT A N GLES OF 30, 45, 60 A N D 90 DEGREES
RECOGN ISE A N D DRA W REFLECTION SYMMETRY ON A SHA PE
DESCRIBE A ROTA TION
RELA TION SHIP BETW EEN ROTA TION A N D CON GRUEN C E
ROTATION
SYMMETRY
RECOGN ISE ROTA TION A L SYMMETRY OF 2D SHA PES
FIN D ORDERS OF ROTA TION A L SYMMETRY
FIN D CEN TRES OF ROTA TION OF 2D SHA PES
ROTA TION A ROUN D A POIN T (IN CLUDIN G THE ORIGIN )
COMPLETE SYMMETRY DIA GRA MS
)
EXPRESS LIN ES OF SYMMETRY ON A GRA PH A S A A LGEBRA IC EQUA TION
SUBJECT ON
BOTH SIDES
USE A XES A N D COORDIN A TES IN 3D
INCLUDES
POWER OF THE
SUBJECT
RECOGN ISE A N D PLOT CUBIC FUN CTION S GRA PHS
RECOGN ISE A N D PLOT
CHA N GIN G THE SUBJECT OF A FORMULA
GRA PHS
ADVANCED GRAPHS
RECOGN ISE A N D PLOT
MANIPULATING EXPRESSIONS
GRA PHS
EXPA N DIN G DOUBLE BRA CKET S
SIMPLIFY EXPRESSION S BY CA N CELLIN G, A DDITION , SUBTRA CTION A N D MULTIPL Y I N G
RECOGN ISE A N D PLOT
AND
(-360 o to +360 o )
GRA PHS
FRACTIONAL
USE IN DEX LA W S
POWERS RAISED
TO A POWER
ZERO AND
NEGATIVE
POWERS
USE A LGEBRA TO DESCRIBE TRA N SFORMA TION S
SOLVE USIN G ELIMIN A TION OR SUBSTITUTION
stretch
left shift along
A PPLY SHIFT A N D STRETCH TRA N SFORMA TIONS TO FUN CTION S f(x)
(Linear, Quadratic, Sine and Cosine)
W RITE SIMULTA N EOUS EQUA TION S FOR A PROBLEM
TRANSFORMATION OF FUNCTIONS
DRA W A N D FIN D SOLUTION S U S I N G
SIMULTANEOUS EQUATIONS
IN TERSECTION OF TW O STRA IGHT LIN E GRA PHS
stretch
shift
FIN D A PPROXIMA TE SOLUTION S USIN G
ROTATION
IN TERSECTION OF LIN EA R A N D QUA DRA TIC GRA PHS
USE ELIMIN A TION TO SOLVE COMPLEX SIMULTA N EOUS EQUA TION S
(1 linear, 1 quadratic with one variable)
REFLECTION
A PPLY THE 4 TRA N SFORMA TION S TO FUN CTION S
SOLVE SIMULTA N EOUS EQUA TION S BA SED ON CIRCLES
TRANSLATION
ENLARGEMENT
CON VERT IN EQUA LITIES TO EQUA TIO N S
SHOW INEQUALITIES ON A GRAPH
DRA W GRA PH FOR EA CH EQUA TION
FIN D SOLUTION A N D SHA DE THE REGION
FA CTORISIN G QUA DRA TICS
COMPLETIN G THE SQUA RE
FIN D GRA DIEN T OF STRA IGHT LIN E GRA PH FROM EQUA TION S
QUADRATICS
GRA DIEN TS OF PA RA LLEL LIN ES = SA ME
CA LCULA TE GRA DIEN TS OF PERPEN DICULA R LI N E S
USIN G THE QUA DRA TIC FORM U L A
PLOT A N D DRA W GRA PHS OF QUA DRA TIC FUN CTION S
USE GRA PHS TO FIN D SOLUTION S TO QUA DRA TIC PROBLEMS
GRADIENTS OF LINES
UN DERSTA N D A N D PLOT
GRA PHS
(m = gradient; c = crosses y-axis)
FIN D EQUA TION S OF LIN ES W HICH A RE PA RA LLEL A N D PERPEN DICULAR
TO A STRA IGHT LIN E GRA PH
SET UP EQUA TION S TO SOLVE
CON STRUCT GRA PHS OF SIMPLE LOCI
(including circle)
PROPORTION
GRAPHS OF LOCI
FIN D POIN TS OF IN TERSECTION OF CIRCLES A N D STRA IGHT LIN ES
USE LOCI TO CON STRUCT GRA PHS
(including based on circles and perpendicula r l i n e s)
SET UP EQUA TION S TO SOLVE
UN DERSTA N D A N D USE GRA PHS IN VOLVIN G
W ORD PROBLEMS
W ORD PROBLEMS
AND
PROPORTION
CA LCULA TE LEN GTH OF A N A RC
PROVE THE CON GRUEN CE OF TRIA N GLES USIN G FORMA L A RGUMEN T
(SSS, A SASA
, S
, RHS)
CA LCULA TE A REA OF A SECTOR
CA LCULA TE A REA OF TRIA N GLE US I N G
PROVE THE SIMILA RITY OF TW O TRIA N GLES USIN G FORMA L A RGUMEN T
ADVANCED AREA
CONGRUENCE AND SIMILARITY
UN DERSTAND
IN RULER A N D COMPA SS CON STRUCTION S
FIN D A REA OF SEGMEN T OF A CIRCLE
(when given radius and length of chord)
A DD OR SUBTRA CT TW O VECTORS
MULTIPLY A VECTOR BY A N UMBER
USE PYTHA GORA S' THEOREM IN 3D PROBLEMS
VECTORS
PYTHAGORAS' THEOREM
CA LCULA TE THE RESULT OF TW O VECTORS
CA LCULA TE LEN GTH OF A DIA GON A L OF A CUBOID
USE VECTORS IN GEOMETRICA L PROOF
USE TRIGON OMETRY IN 2D A N D 3D PROBLEMS
FIN D THE A N GLE BETW EEN A
CA LCULA TE SURFA CE A REA OF BA SIC SOLIDS
(cube, cuboid, cone, pyramid, sphere, hemisphe r e )
TRIGONOMETRY
COMPLEX SHAPES AND SOLIDS
FIN D
USE
AND A
AND
TO SOLVE 2D A N D 3D PROBLEMS
CA LCULA TE SURFA CE A REA OF COMPOUN D SOLIDS
USE
CA LCULA TE VOLUME OF COMPLEX SOLIDS
(cones, pyramids, spheres, hemispheres and frustums)
A N GLE IN A
SEMICIRCLE
A LTERN ATE
= 90 o
A N GLES IN SA ME
SEGMEN T
SEGMEN T A RE EQUA L
THEOREM
EN LA RGE BY N EGA TIVE A N D FRA CTION A L SCA LE F A C T O R S
ADVANCED TRANSFORMATIONS
TA N GEN TS FROM
A POIN T A RE
TW O RA DII FORM
DESCRIBE COMBIN ED TRA N SFORMA TION S
EQUA L LEN GTH
A N ISOSCELES
TRIA N GLE
CIRCLE THEOREMS AND PROOFS
OPPOSITE
A N GLES IN A
CYCLIC
QUA DRILA TERAL
= 180 o
A N GLE A T CEN TRE =
DOUBLE THE A N GLE A T
CIRCUMFERENCE
(from the two ends of same
chord)
TA N GEN T A N D RA DIU S
MEET A T 90 o (A T THE
EDGE OF THE CIRCLE)
PERPEN DICULAR
BISECTOR OF A CHORD
PA SSES THROUGH THE
CEN TRE
TO SOLVE 2D A N D 3D PROBLEMS
ANY NUMBER TO POWER OF 0 IS ALWAYS 1
ANY NUMBER TO POWER OF 1 IS ALWAYS JUST ITSELF
CALCULATE EXPONENTIAL DECAY/GROWTH
1 TO THE POWER OF ANYTHING IS ALWAYS 1
CALCULATE IN STANDARD FORM
ADVANCED CALCULATOR
NEGATIVE POWERS = 1/ (turn it upside down)
INDEX LAWS
SIN/COSINE/TAN FUNCTIONS
FRACTIONAL POWERS = ROOTS
POWERS FUNCTIONS
SIMPLIFY AND MANIPULATE SURDS
RATIONALISE A DENOMINATOR
(denominator = integer not surd)
SURDS
USE SURDS IN PROBLEMS WITHOUT A CALCULATOR
POWER (n) =
NUMBER OF PLACES DECIMAL POINT MOVES
PYTHAGORAS AND SURDS
UNDERSTAND AND USE
A x 10 n
STANDARD FORM
IN MEASUREMENTS
IN PERIMETER
POSITIVE AND NEGATIVE POWERS
UPPER AND LOWER BOUNDS
A = BETWEEN 1 AND 10
n+ = BIG NUMBER
n- = SMALL NUMBER
CONVERT BETWEEN STANDARD
AND NORMAL FORM
IN AREA
IN VOLUME
CALCULATE COMPOUND INTEREST
USE DIRECT PROPORTION TO FIND AN UNKNOWN QUANTITY
USE INVERSE PROPORTION TO FIND AN UNKNOWN QUANTITY
PROPORTIONS
COMPOUND GROWTH AND DECAY
CALCULATE REPEATED PROPORTIONAL CHANGE
REPEATED PROPORTIONAL CHANGE USING MULTIPLIERS RAISED TO A POWER
CALCULATE DEPRECIATION
DRA W A FREQUEN CY DIA GRA M FOR GROUPED DISCRETE DA TA
UN DERSTA N D THE A DDITION LA W FOR MUTUA LLY EXCLUS I V E E V E N T S
CA LCULA TE PROBA BILITIES W ITH A N D W ITHOUT REPLA CEM E N T
DRA W A TW O SIDED STEM A N D LEA F DIA GRA M
PROBABILITY OF EVENTS
DRA W CUMULA TIVE FREQUEN CY TA BLES A N D GRA PHS
CHARTS AND DIAGRAMS
UN DERSTA N D THE MULTIPLICA TION LA W FOR IN DEPEN DEN T EV E N T S
DRA W BOX PLOTS FROM RA W DA TA
OR W HEN GIVEN THE MEDIA N A N D QUA RTILES
USE FREQUEN CY DEN SITY TO DRA W HISTOGRA MS
(UN EQUA L CLA SS IN TERVA LS)
FIN D MEDIA N , QUA RTILES A N D
IN TERQUA RTILE RA N GE
USE CUMULA TIVE FREQUEN CY GRA P H S
TO SOLVE PROBLEMS
ESTIMA TE VA LUES
EXPLA IN ISOLA TED POIN TS IN SCA TTER GRA PHS
DRA W A PROBA BILITY TREE DIA GRA M
USE HISTOGRA MS TO SOLVE PROBLEMS
(eg:find the median or size of each group)
INTERPRETING GRAPHS AND DIAGRAMS
PROBABILITY TREES
CA LCULA TE PROBA BILITY OF COMPOUN D EV E N T S
USE HISTOGRA MS TO COMPLETE FREQUEN CY TA BLES
USE BOX PLOTS TO FIN D MEDIA N , QUA RTILES A N D IN TERQUA RTILE RA N GE
COMPA RE DA TA USIN G
UN DERSTA N D THE DIFFEREN CE BETW E E N
AND
SA MPLING
COMPARING DATA
SAMPLING
CA LCULA TE SA MPLE SIZES FOR STRA TIFIED SA M P L I N G
COMPA RE DA TA USIN G
COMPA RE SPREA D USIN G
OR
UNITS OF TIME
READ MAPS USING THE SCALE
READ 12 AND 24 HOUR CLOCKS
TIME
DRAW LINES AND SHAPES TO DIFFERENT SCALES
READ ANALOGUE AND DIGITAL CLOCKS
MAPS AND SCALE DRAWINGS
CONVERT BETWEEN UNITS OF TIME
USE 3 FIGURE BEARINGS TO DESCRIBE DIRECTION
USE FORMULA TRIA N GLE TO CA LCULA TE
SPEED/DISTA N CE/TIME
COMPOUND MEASURES
MEASURING BEARINGS
BEARINGS
USE FORMULA TRIA N GLE TO CA LCULA TE
MA SS/VOLUME/DENSITY
FIN D BEA RIN GS BETW EEN TW O POIN TS
MAKE ESTIMATES OF MEASUREMENTS
USE APPROPRIATE UNITS TO ESTIMATE
ACCURACY AND ESTIMATION
ESTIMATE LENGTHS USING SCALE DIAGRAMS
RECOGN ISE EN LA RGEMEN TS OF 2D A N D 3D SHA PES
USE PROTRACTORS AND RULERS TO CREATE ACCURATE DRAWINGS
ENLARGEMENT
EFFECTS OF ENLARGEMENT ON PERIMETER AND AREA
EFFECTS OF EN LA RGEMEN T ON VOLUME
CONVERT BETWEEN METRIC AND IMPERIAL MEASURES
VOLUME AND CAPACITY
SPEED
METRIC AND IMPERIAL UNITS
A REA
DISTA N CE
CONVERTING BETWEEN METRIC UNITS
UNITS OF MEASUREMENT
EXPECTED FREQUENCIES
EFFECT OF MORE THAN ONE TRIAL
EFFECT OF INCREASED SAMPLE SIZE
MARK EVENTS ON A LIKELIHOOD SCALE
ESTIMATING PROBABILITY
LIKELIHOOD SCALE
ACTUAL FREQUENCIES
IDENTIFY EVENTS AS
COMPARING RESULTS
MARK EVENTS ON A 0-1 PROBABILITY SCALE
GIVE EXAMPLES OF MUTUALLY EXCLUSIVE EVENTS
PROBABILITY SCALE
PROBABILITY TABLES/DIAGRAMS
WRITE PROBABILITIES AS FRACTIONS,
DECIMALS OR PERCENTAGES
MUTUALLY EXCLUSIVE OUTCOMES
ADD SIMPLE PROBABILITIES
DRAW SAMPLE SPACE DIAGRAM TO SHOW ALL
POSSIBLE OUTCOMES OF TWO EVENTS
LIST ALL OUTCOMES FOR ONE OR TWO EVENTS
SAMPLE SPACE DIAGRAMS
FIND PROBABILITIES OF CERTAIN OUTCOMES
USING SAMPLE SPACE DIAGRAMS
LISTING EVENTS
LIST ALL OUTCOMES OF SPECIFIED GROUPS
MEASURE SHAPE TO FIND PERIMETER
USE FORMULAE TO FIND AREA OF TRIANGLES
CALCULATE VOLUME OF A CUBOID
FIND VOLUME OF COMPOUND CUBOIDS
USE FORMULA TO FIND AREA OF A TRAPEZIUM
VOLUME
CA LCULA TE VOLUME OF A CYLIN DER
AREA AND PERIMETER
CALCULATE THE AREA OF OTHER QUADRILATERALS
CALCULATE VOLUME OF DIFFERENT PRISMS
CALCULATE AREA AND PERIMETER OF COMPOUND SHAPES
CA LCULA TE SURFA CE A REA OF PRISMS A N D PYRA MIDS
IDEN TIFY
AND
ON A 3D SHA PE
IDENTIFY DIFFERENT TYPES OF SOLID SHAPES
(eg: cuboid, prism, sphere, cylinder
etc)
DRAW THE NET OF A GIVEN 3D SHAPE
3D SHAPES
RECOGNISE DIFFERENT TYPES OF TRIANGLE
DRAW ELEVATIONS AND PLANS OF SIMPLE SOLIDS
IDENTIFY PROPERTIES OF DIFFERENT TRIANGLES
TRIANGLES
SKETCH A 3D SHAPE WHEN GIVEN THE ELEVATIONS AND PLAN
ANGLES IN A TRIANGLE
FIN D MISSIN G A N GLES IN A TRIA N GLE
USE PYTHAGORAS' THEOREM TO FIND LENGTH OF MISSING SIDE
CORRECTLY USE LETTERS TO LABEL ANGLES AND LINES
IDEN TIFY A N D CORRECTLY LA BEL PA RA LLEL LIN ES
ANGLES ON A STRAIGHT LINE
ANGLES BASICS
RECOGNISE AND NAME DIFFERENT QUADRILATERALS
A N GLES ROUN D A POIN T
QUADRILATERALS
IDENTIFY PROPERTIES OF DIFFERENT QUADRILATERALS
RECOGN ISE CORRESPON DIN G A N D A LTERN A TE A N GLE S
(in parallel lines)
CALCULATE MISSING ANGLES IN A QUADRILATERAL
RECOGNISE VERTICALLY OPPOSITE ANGLES ARE EQUAL
RECOGNISE AND NAME DIFFERENT POLYGONS
(based on number of sides)
LABEL DIFFERENT PARTS OF A CIRCLE USING MATHEMATICAL TERMS
EXTERIOR ANGLES IN A POLYGON = 360
ANGLES AT A VERTEX = 180
RELATIONSHIP OF SIDES TO ANGLES
(in regular polygons)
CALCULATE SUM OF INTERIOR ANGLES
CA LCULA TE IN TERIOR A N D EXTERIOR A N GLES
TESSELLA TION
DRA W A CIRCLE, (USIN G COMPA SSES) TO A GIVEN RA DIUS/DIA METER
ANGLES OF POLYGONS
CIRCLES
FIND CIRCUMFERENCE OF A CIRCLE
FIN D PERIMETER A N D A REA OF SEMI A N D QUA RTER CIRCLES
CALCULATE SURFACE AREA OF CYLINDERS