SEC Syllabus (2019): Mathematics SEC SYLLABUS (2019) MATHEMATICS SEC 23 SYLLABUS

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1 SEC SYLLABUS (2019) MATHEMATICS SEC 23 SYLLABUS 1

2 Mathematics SEC 23 Syllabus Available in September (Paper I and Paper IIB nly) Paper I: Sectin A (20 minutes) & Sectin B (1 hr 40 minutes) + Paper II (2 hurs) Intrductin Mathematics furnishes the prime means by which infrmatin can be rganised, cmmunicated and manipulated. It is als an ever-expanding bdy f facts, skills, cncepts and strategies used in the slutin f a wide range f prblems. As a cnsequence, when implementing this syllabus, teachers f Mathematics shuld emphasize tw imprtant aspects f the teaching and learning f mathematics: (i) (ii) Utilitarian Aspect f Mathematics Teaching and Learning Mathematics is useful. It equips individuals with the necessary knwledge t help them understand and interact with the wrld arund them. Mrever, it frms the basis f science, technlgy, architecture, engineering, cmmerce, industry and banking. It is als increasingly being used in the medical sciences, bilgical sciences, ecnmics and gegraphy. This pervasiveness makes Mathematics ne f the mst imprtant subjects in the schl curriculum. Aesthetic Aspect f Mathematics Teaching and Learning Mathematics is an evlving bdy f knwledge that is characterised by its rder, precisin, cnciseness and lgic. It shuld ffer the individuals intellectual challenge, excitement, satisfactin and wnder. Aims When implementing this syllabus, teachers shuld aim t enable candidates t: Understand and appreciate the place and purpse f Mathematics in sciety and apply mathematical cncepts t situatins arising in their wn lives; Apply mathematical knwledge and understanding t slve prblems; Think and cmmunicate mathematically - precisely, lgically and creatively; Develp a psitive attitude t Mathematics, including cnfidence and perseverance; Develp an ability t wrk independently and c-peratively when ding Mathematics; Appreciate the interdependence f the different branches f Mathematics; Acquire a secure fundatin fr the further study f Mathematics; Use Mathematics acrss the curriculum; and, Make efficient, creative and effective use f apprpriate technlgy in Mathematics. Assessment Objectives The examinatin will, in general, test: The candidate s ability t recall, understand and apply mathematical knwledge in a wide cntext; The candidate s ability t understand and analyse a prblem, select an apprpriate strategy, apply suitable knwledge and techniques t slve it, verify and interpret the results; and, The candidate s ability t understand, interpret and evaluate mathematical ideas that are presented in ral, written and visual frms. In particular, the candidate will be required t demnstrate the ability t: Cmmunicate, cnjecture, reasn and prve mathematically; Understand the nature f numbers and make use f them; Understand the nature f algebraic relatinships and make use f them; Understand the nature and prperties f shape, space and measures and make use f them; Understand the nature f statistics and prcess, represent and interpret data; and, Understand the nature f prbability and calculate the prbabilities f events. 2

3 During the curse candidates shuld be given pprtunities t: Use calculatrs and cmputer sftware including spreadsheets, LOGO, a dynamic gemetry package and cmputer algebra system; Use cmputers as a surce f large samples, as a tl fr explring graphical representatins, and as a means fr simulating events; Develp a feel fr numbers; Develp and use a range f methds f cmputatin, namely, mental, pencil-and-paper, calculatr and cmputer methds, and apply these t a range f prblems; Develp and use a range f methds fr apprximatin f numbers and apply these t a range f prblems; Develp and use a range f methds fr estimatin f measures and apply these t a range f prblems; Explre a variety f situatins which lead t the expressin f relatinships; Cnsider hw relatinships between number peratins underpin the techniques fr manipulating algebraic expressins; Cnsider hw algebra can be used t mdel real-life situatins and t slve prblems; Explre shape and space thrugh drawing and practical wrk; Use cmputers t generate and transfrm graphic images and t slve prblems; Frmulate questins that can be slved using statistical methds; Undertake purpseful inquiries based n data analysis; Engage in practical and experimental wrk in rder t appreciate principles which gvern randm events; and, Lk critically at sme f the ways in which representatins f data can be misleading and cnclusins can be uncertain. Scheme f Assessment The examinatin will cnsist f tw papers, Paper I and Paper II, each f 2 hurs duratin. There will be tw versins f Paper II: Paper IIA and Paper IIB. Candidates wh intend t further their study in Mathematics and Science subjects at Intermediate Level and Advanced Level are STRONGLY advised t sit fr Paper IIA. Questins will be set in English and must be answered in English. Candidates are expected t abide by the fllwing principles f gd mathematical practice: inclusin f justificatins in slutins whenever apprpriate; specificatin f the number f decimal places/significant figures being used whenever numbers are runded up r dwn, and inclusin f all apprpriate steps in slutins t prblems. Paper I This paper is t be taken by all candidates and will cver the Cre Syllabus cntent nly. It will be divided int tw Sectins, A and B. Sectin A (Nn-Calculatr Sectin) It will cnsist f eighteen t twenty shrt questins t be answered in 20 minutes. The paper will carry a ttal f 20 marks. Calculatrs and prtractrs are nt allwed. Questins will typically invlve numerical calculatins, apprximatins, estimatins, data and graphical interpretatins, applicatin f frmulae, recall and applicatins f prperties f shapes, recall and applicatins f mathematical facts T answer these questins, particularly thse invlving numerical calculatins, candidates are advised t chse and use the mre efficient techniques (mental and pencil-and-paper). They are expected t have a range f strategies t aid mental calculatins f unknwn facts frm facts that can be rapidly recalled. 3

4 Sectin B (Calculatr Sectin) It will cnsist f nine t eleven cmpulsry graded questins t be answered in ne hur and frty minutes. The questins may have different mark allcatins which will be stated n the paper and will carry a ttal f 80 marks. Candidates are allwed t use mathematical instruments and scientific calculatrs with statistical functins. Prgrammable calculatrs are nt allwed. Candidates are allwed t use transparencies fr drawing transfrmatins. Paper II There will be tw versins f this paper (IIA r IIB). Candidates will be required t indicate n the registratin frm which versin they wish t sit fr. N change in the chice f paper will be allwed after the registratin perid. In the September supplementary sessin nly Paper I and Paper IIB will be ffered. Candidates are allwed t use mathematical instruments and scientific calculatrs with statistical functins. Prgrammable calculatrs are nt allwed. Candidates are allwed t use transparencies fr drawing transfrmatins. Paper IIA will cnsist f nine t eleven cmpulsry questins with varying mark allcatins per questin which will be stated n the paper, carrying a ttal f 100 marks. The questins in this paper will cver the cntent in bth the Cre and the Extensin parts f the syllabus. A typical prblem in this paper will be mre difficult t slve than a typical Paper I prblem. The time allwed fr this Paper is tw hurs. Paper IIB will cnsist f twenty t twenty-eight questins with varying mark allcatins stated n the paper and will carry a ttal f 100 marks. The questins in this paper will cver the cntent in that part f the syllabus indicated as Cre. A typical prblem in this paper will be easier t slve than a typical Paper I prblem. The time allwed fr this Paper is tw hurs. The verall weighting (5%) fr each f the fur main cmpnents f the syllabus is shwn belw: Paper I and Paper IIA Paper I and Paper IIB Number Algebra Shape, Space & Measures Data Handling 25% 35% 30% 10% 35% 20% 35% 10% Results Candidates sitting fr Paper I and Paper IIA may qualify fr Grades 1, 2, 3, 4 r 5. The results fr candidates wh d nt btain at least a Grade 5 shall remain Unclassified (U). Candidates sitting fr Paper I and Paper IIB may qualify fr Grades 4, 5, 6, r 7. The results fr candidates wh d nt btain at least a Grade 7 shall remain Unclassified (U). Grade Descriptins The fllwing descriptins are meant t prvide a general indicatin f the standards f achievement nrmally shwn by candidates earning particular grades. Hwever, the final grade awarded will reflect the extent t which the candidates have met the assessment bjectives verall. Grade 1 is awarded t candidates whse answers exhibit: An understanding f cmplex nn-rutine prblems; Lgical reasning and valid cnclusins; An verall high perfrmance in all areas f the syllabus; 4

5 A high level f presentatin (prviding evidence f effective and clear cmmunicatin thrugh writing and diagrams); and, Crrect cmputatins and slutins. Grade 5 is awarded t candidates whse answers exhibit: An understanding f rutine prblems; An acceptable amunt f reasning and valid cnclusins; An average perfrmance in mst areas f the syllabus; and, An adequate level f presentatin and cmmunicatin. Grade 7 is awarded t candidates whse answers shw: An understanding f simple rutine prblems; A pr perfrmance in all areas f the syllabus; and, Sme attempt at cmmunicatin. Table f Frmulae A table f the frmulae reprduced belw will be prvided fr the use f the candidates. These frmulae will be prvided fr Paper IIA nly. Area f a Triangle 1 absin C 2 Curved Surface Area f Right Circular Cne rl Surface Area f a Sphere Vlume f a Pyramid /Right Circular Cne Vlume f Sphere Slutins f ax 2 + bx + c = 0 Sine frmula Csine frmula Syllabus The syllabus is divided int fur main areas: r base area perpendicular height 4 3 r 2 b b 4ac x 2a a b c sin A sin B sin C a 2 = b 2 + c 2 2bcCs A 3 Number Algebra Shape, Space and Measures Data Handling Candidates taking Paper IIB need nly cver the Cre cntent (shwn in nrmal type). Candidates taking Paper IIA have t cver the Cre cntent (shwn in nrmal type) and the Extensin cntent (shwn in bld type). Examples are shwn in italic. Althugh the syllabus is divided int fur areas, it is very imprtant that candidates see and make cnnectins between these different areas. 5

6 Area 1: Number Ref. N. Cre Extensin Integers Recgnise, understand and use - integers - factrs (divisrs), multiples, least cmmn multiple, prime numbers and prime factr decmpsitin. Understand and use psitive and negative numbers in real life cntexts (e.g. t find the temperature difference between temperatures belw zer) Integers Recgnise, understand and use highest cmmn factr Sequences Generate number sequences Fractins Understand and use fractins in real life cntexts. Recgnise equivalent fractins. Simplify fractins. Order fractins. Cnvert fractins t decimals and vice-versa. Understand that simple fractins can be represented as recurring decimals. Understand that fractins which in their lwest terms are f the frm m/(2 p 5 q ) are nn-recurring (m, p, and q are nn-negative integers r zer) Decimal Numbers Understand and use decimals in real life cntexts. Recgnise recurring and nn-recurring decimals. Order decimals by using place value and by their psitin n the number line Numerical Operatins Use the fur peratins (+,,, ) in calculatins with integers, decimals and fractins. Identify the precedence f mathematical peratins (BIDMAS) Indices Understand that the reciprcal f a number is its multiplicative inverse. Understand and use index ntatin (e.g. 7 3, 7 2 ) Understand and use the terms: square, square rt, cube and cube rt. Understand and use the index laws fr multiplicatin and divisin f integer pwers Standard frm Understand and use the standard index frm expressed in cnventinal ntatin Indices Use the index laws fr psitive and negative fractinal pwers. 6

7 Percentages Understand and use percentages in real life cntexts. Interpret percentage as number f parts per hundred. Cnvert simple fractins t percentages and viceversa (e.g. Interpret 10% f 40 as 10/100 40). Express a quantity as a percentage f anther. Calculate percentage increase and decrease (e.g. a 15% increase in value f C = 1.15 C; a 20% discunt n 250 = ). Determine the riginal value given the final value and the percentage change. (e.g. t find the cst price given the selling price and percentage prfit) Percentages Make repeated use f a multiplier raised t a pwer (grwth r decay factr) Rati Use rati ntatin in practical situatins (e.g. in maps and scale drawings). Recgnise the cnnectin between ratis and fractins. Reduce ratis t their simplest frm. Divide a quantity in a given rati Prprtin Understand and use the elementary ideas and ntatin f direct and inverse prprtin. Calculate an unknwn quantity frm quantities that vary in direct r inverse prprtin Rates f Change Understand and use the elementary ideas f cmmn measures f rates f change (e.g. t calculate the average speed) Measures Understand and use metric units f mass, length, area, vlume and capacity in practical situatins. Express quantities in terms f larger and smaller units. Calculate time in terms f the 12-hur and 24-hur clck. Read and interpret clcks, dials and time-tables Scales Read and use scales in practical situatins (e.g. read a thermmeter scale) Mney Understand and use mney in practical situatins. Cnvert frm ne currency t anther. Slve prblems n persnal and husehld finance invlving earnings (e.g. stcks), simple interest, tax and insurance Mney Make repeated use f a multiplier raised t a pwer t cmpute cmpund interest (including brrwing and repayment), appreciatin r depreciatin. Use a calculatr and spreadsheet t investigate factrs affecting these. 7

8 Determine, by trial and errr, the number f years by means f a calculatr Estimatin and Apprximatin Make estimates f measures, runding t a specified number f significant figures and decimal places t reasnable accuracy in the cntext f a given prblem Make sensible apprximatins in calculatins invlving multiplicatin and/r divisin Estimatin and Apprximatin Understand and use limits f accuracy. Give apprpriate upper and lwer bunds fr data given t a specified accuracy (e.g. measured lengths). Obtain apprpriate upper and lwer bunds t slutins f simple prblems (e.g. the calculatin f the perimeter r area f a rectangle given data t a specified accuracy) The Calculatr Use the calculatr efficiently and effectively. Knw hw t enter cmplex calculatins. Understand the calculatr display, interpreting it apprpriately. Knw when nt t rund during intermediate steps f a calculatin. Knw hw t interpret numbers displayed in standard frm. Knw hw t enter numbers in standard frm. Apply apprpriate checks f accuracy (e.g. wrking backwards frm a slutin; making apprximatins t check the reasnableness f the result r rewrking calculatins). 8

9 Area 2: Algebra Ref. N. Cre Extensin Algebraic representatin Use letters t represent generalised numbers. Understand that algebraic entities can be transfrmed accrding t well-defined prperties f generalised arithmetic. Use input/utput functin (number) machines t define functins. Understand and use functin ntatin (e.g. f(x) = 3x 5). Manipulate algebraic expressins by: cllecting like terms, multiplying a single term ver a bracket, taking ut a single term cmmn factr, simplifying ratinal expressins with numeric denminatrs (e.g. write 2 z 3 z 5 as a 5 2 single fractin) Algebraic representatin Use utput/input inverse functin (number) machines. Use inverse functin ntatin (e.g. if f(x) = 3x 5, then f 1 (x) = (x + 5)/3). Expand the prduct f tw linear expressins (e.g. (x + 1)(x 2) = x 2 x 2) Factrise expressins invlving difference f tw squares and trinmials (e.g. 2x 2 +5x-12 = (2x-3)(x+4)). Use ratinal expressins with algebraic 1 x denminatrs (e.g. write 2 x 2 x 4 as a single fractin) Equatins and Inequalities Cnstruct simple linear equatins frm given situatins. Slve linear equatins. Slve simultaneus linear equatins in tw unknwns: - Graphically by interpreting the cmmn slutin as the pint f intersectin, - Algebraically by eliminatin and by substitutin Equatins and Inequalities Slve simple linear inequalities in ne variable and represent the slutin set n a number line (e.g. 2x 3 > 7). Determine the slutin t an inequality r set f inequalities n a graph by shading the apprpriate regin(s) (e.g. y 3x, y 5 and x + y > 4) Slve quadratic equatins, by factrisatin, by cmpleting the square and by frmula. Slve a linear equatin and a quadratic equatin simultaneusly. Use trial and imprvement methds invlving calculatr and cmputers t find apprximate slutins f equatins fr which there is nt a simple methd f slutin (e.g. slve x 3 x = 80) Frmulae Use frmulae arising in mathematics and in ther subjects. Substitute numbers in a frmula. Derive a frmula and change the subject f the frmula. Cnstruct a frmula n a spreadsheet Frmulae Transfrm mre cmplicated frmulae Graphs Understand and use Cartesian crdinates in tw dimensins. Recgnise that equatins f the frm y = mx + c represent straight lines. Cnstruct table f values fr linear and quadratic functins Graphs Cnstruct tables f values fr cubic functins and reciprcal functins f the type f(x) = a/x, using pencil and paper, a spreadsheet r a graphing package t generate pints and plt the graphs. Slve graphically linear, quadratic, cubic 9

10 Plt and draw graphs f such functins by making use f pencil and paper methds, a spreadsheet and a graphing package. Read ff values frm graphs. This includes reading values f x frm the graph f the functin f(x) t slve an equatin f(x) = k where k is a real number. Understand, interpret and calculate the gradient f a line frm the crdinates f tw pints n it. Find the gradient f a line frm its equatin. Obtain the equatin f a straight line in the frm y = mx + c. Knw and understand that parallel lines have equal gradients. and reciprcal functins simultaneusly (e.g. find graphically cmmn slutins fr y = 2x 1 and y = x 3 ) Infrmatin Graphs Interpret infrmatin presented in a variety f linear and nn-linear graphs (e.g. distance-time and velcity-time graphs, cnversin graphs, graphs f height against age) Indices Use and interpret psitive and negative integral indices, including zer. Use the index laws in simple instances. Slve simple expnential equatins by inspectin (e.g. 2 x = 16) Indices Use and interpret fractinal indices Sequences Generate a sequence using term t term and psitinterm definitins f the sequence. Use expressins t describe the nth term f a simple sequence. Generate terms f a sequence frm the nth term Variatin Slve prblems invlving direct and inverse variatin t determine unknwn quantities restricted t y x n, where n = 1, 2, 3. 10

11 Area 3: Shape, Space and Measures Ref. N. 3.1 Euclidean Gemetry Cre Extensin Angles Understand and use prperties f angles at a pint, angles n a straight line, vertically ppsite angles. Distinguish between acute, btuse and reflex angles. Estimate the size f an angle in degrees Lines and Line Segments Distinguish between lines and line segments. Use parallel lines, alternate angles, crrespnding angles and interir angles n the same side and between the same parallel lines Triangles Understand a prf that the angle sum f a triangle is 180. Understand a prf that the exterir angle f a triangle is equal t the sum f the interir angles at the ther tw vertices. Use the angle prperties f equilateral, issceles and right-angled triangles. Understand a prf f Pythagras Therem. Understand the cnverse f Pythagras Therem. Use Pythagras Therem and its cnverse in 2-D situatins Triangles Use Pythagras Therem in 3-D situatins (e.g. t determine lengths inside a cubid) Quadrilaterals Understand a prf that the angle sum f a quadrilateral is 360. Understand and use the prperties f the square, rectangle, parallelgram, trapezium, rhmbus and kite. Classify quadrilaterals using their gemetric prperties Plygns Calculate and use the sums f the interir and exterir angles f regular and irregular plygns. Use a frmula, such as (2n 4) right angles r (n 2) 180, fr the sum f the interir angles f a plygn with n sides Circles Understand the meaning f terms related t the circle: centre, radius, chrd, diameter, circumference, tangent, arc, sectr and segment. Understand and use the angle prperties f the circle t calculate unknwn angles: The angle in a semicircle is a right angle. The angle at the centre is twice the angle at the circumference Circles Understand the prfs f the angle prperties f a circle. Understand the prf f the alternate segment prperty. 11

12 Angles in the same segment are equal. Angles in ppsite segments are supplementary. The angle between the radius and the tangent at the pint f cntact is a right angle. Reasns justifying the use f these angle facts in simple riders are expected Cnstructins Carry ut cnstructins based n measurement. Estimate, measure and draw lines and angles. Cnstruct parallel lines. Cnstruct angles f 60 and 90 using cmpasses. Cnstruct simple 2-D gemetric figures frm given data. Use straight edges and cmpasses t cnstruct the perpendicular bisectr f a line segment, the perpendicular frm a pint t a line, the bisectr f an angle. Read and make scale drawings (e.g. t slve rightangled triangles). 3.3 Mensuratin Flat (2-D) Shapes Find the perimeter and area f rectangles and triangles by cunting unit measures and by frmula. Find the area f a parallelgram. Find the area f a trapezium. Find the area f cmpund flat shapes. Find the circumference and area f a circle. Find the length f arc as a fractin f the circumference. Find the area f sectr as a fractin f the area f a circle Slid (3-D) Shapes Find the surface area f a cube, cubid, cylinder and pyramid. Find the surface area f simple cmpund slid shapes invlving cubes, cubids, cylinders and/r pyramids. Find the vlumes f cubids by cunting unit measures and by frmula. Find the vlume f a prism and cylinder. Find the vlume f simple cmpund slid shapes invlving cubes, cubids and prisms Flat (2-D) Shapes Find the area f acute and btuse angled triangles using 1 absin C. 2 Find the area f segments in a circle Slid (3-D) Shapes Find the surface area f a right circular cne. Find the surface area f a sphere. Find the vlume f a pyramid and a frustum f a pyramid. Find the vlume f a right circular cne and a frustum f a right circular cne. Find the vlume f a sphere Symmetry and Cngruency Use prperties f shapes in tessellatins. Understand and knw when shapes are cngruent. Appreciate the uniqueness f triangles satisfying SSS, SAS, ASA and RHS. Understand and use SSS, SAS, ASA and RHS cnditins t prve the cngruence f triangles. Understand and knw when shapes are similar. Understand and use AAA, the cmmn rati prperty Symmetry and Cngruency Prve the symmetry prperties f the circle thrugh cngruency. Understand and use the relatinship between lengths, areas and vlumes f similar shapes. 12

13 f sides, and, tw cmmn ratis and the included angle t prve similarity f triangles. Appreciate that all cngruent shapes are similar but similar shapes are nt necessarily cngruent. Appreciate that any tw circles and any tw squares are mathematically similar, whereas, in general, tw rectangles are nt. Recgnise line and rtatinal symmetry in tw dimensins. Recgnise the rder f rtatinal symmetry. Recgnise prperties f triangles, quadrilaterals and circles related t their symmetries. Use the symmetry prperties f the circle and their cnverse t prve that: Equal chrds are equidistant frm the centre. The perpendicular bisectr f a chrd passes thrugh the centre. Tangents frm an external pint are equal. 3.5 Trignmetry Trignmetric ratis Understand, recall and use the trignmetric relatinships in right-angled triangles, namely, sine, csine and tangent. Use the trignmetric ratis t slve prblems in simple practical situatins (e.g. in prblems invlving angles f elevatin and depressin). Trignmetry Trignmetric ratis Extend the use f the sine and csine functins t angles between 90 and 180. Slve simple trignmetric prblems in 3- D. (e.g. find the angle between a line and a plane and the angle between tw planes) Sine and csine rules Use the sine and csine rules t slve any triangle Bearings Interpret and use three-figure bearings measured clckwise frm the nrth. Use scale drawings and trignmetrical ratis t slve prblems invlving bearings Transfrmatin Gemetry Recgnise, describe and cnstruct translatins and reflectins f plane figures. Recgnise, describe and cnstruct rtatins and enlargements abut the rigin f plane figures. Recgnise that reflectins, rtatins and translatins preserve length and angle, s that figure is cngruent t its image under any f these transfrmatins. Recgnise that enlargements preserve angle and nt length. Understand and use the effect f enlargement n the perimeter f 2-D shapes. (In questins requiring candidates t cnstruct transfrmatins n the Cartesian plane, the mirrr lines f cnstructing reflectins will be restricted t the axes, y x, y c, x c.the angles f rtatin fr cnstructing rtatins will be restricted t multiples f Transfrmatin Gemetry The scale factr fr cnstructing enlargements will be extended t include negative numbers. Transfrm plane figures by a cmbinatin f transfrmatins. Find the centre f rtatin fr rtatins thrugh 90. Understand and use the effect f enlargement n the perimeter f plane figures. 13

14 90.The scale factr fr cnstructing enlargements will be restricted t a psitive integer r a fractin.clumn vectrs will be used t describe translatins) Lci Apply the fllwing lcus prperties in tw dimensins in practical situatins: The lcus f pints which are at a fixed distance frm a given pint. The lcus f pints which are equidistant frm tw given pints. Devise instructins fr a cmputer t prduce the desired shapes and paths (e.g. equilateral triangles and hexagns) Lci Use the fllwing lci in tw dimensins: The lcus f pints which are equidistant frm a straight line. The lcus f pints which are equidistant frm tw intersecting straight lines. Use intersecting lci. 14

15 Area 4: Data Handling Ref. N. Cre Extensin Statistics Cllect, classify and tabulate statistical data (e.g. gather data frm Infrmatin and Cmmunicatin Technlgy (ICT) surces). Read, interpret and draw simple inferences frm tables and statistical diagrams. Understand, use and cnstruct, by bth pencil and paper and ICT methds, bar charts, pie charts, simple frequency distributins and histgrams with equal intervals. Calculate and interpret the range, mean, median and mde fr discrete and cntinuus data. Use apprpriate statistical functins n a calculatr and a spreadsheet t calculate these statistics Prbability Calculate the prbability f a single event. Cnstruct simple pssibility space diagrams (e.g. fr the thrw f a cin and a die). Wrk ut the cmbined prbability utcmes f tw independent events Statistics Understand and use histgrams with unequal intervals. Interpret and cnstruct cumulative frequency curves. Interpret and cnstruct bx plts t illustrate r cmpare distributins with large data sets. Estimate the median, the lwer and upper quartiles and the interquartile range frm cumulative frequency curves. Calculate the mean, median and mde fr gruped data. Identify the mdal class frm a gruped frequency distributin Prbability Calculate the prbability fr cmbined events, using pssibility space diagrams and tree diagrams where apprpriate. (In tree diagrams utcmes will be written at the end f the branches and prbabilities by the sides f the branches). 15