IB Mathematics (HL)



IB Mathematics (HL) – Year 12Term 1ASequences and Series4 lessonsThe Binomial Expansion and Counting Principles4 lessonsIntroduction to Functions8 lessonsPolynomial Functions6 lessonsTerm 1BLogarithms4 lessonsIntroduction to Differentiation7 lessonsThe Chain Rule and Optimisation3 lessonsIntroduction to Integration5 lessonsLearning Review 1Term 2AIntroduction to Trigonometry5 lessonsFurther Trigonometry8 lessonsTrigonometric Identities5 lessonsTerm 2BComplex Numbers14 lessonsCalculus Revisited2 lessonsLearning Review 2Term 3Calculus Revisited (continued)6 lessonsImplicit Differentiation and Volumes of Revolution4 lessonsMathematical Induction2 lessonsIntroduction to Vectors6 lessonsLines and Planes in Space11 lessonsLearning Review 3IB Mathematics (SL) – Year 13Term 1AIntroduction to Statistics2 lessonsProbability5 lessonsProbability Distributions9 lessons**Internal Assessment (Mathematical Exploration)**4 lessons + individual workFurther Calculus4 lessonsTerm 1B Further Calculus (continued)4 lessonsKinematics3 lessonsOption14 lessonsTerm 2AMock ExaminationsOption (continued)15 lessons** REVISION **Term 1A – 4 lessonsSequences and Series (1.1)Prior KnowledgeAlgebraic manipulationUnderstanding of basic sequences and the nth termStudent OutcomesUnderstanding of arithmetic sequences and series and their applicationsUnderstanding of sigma notationAble to sum a finite arithmetic seriesUnderstanding of geometric sequences and seriesAble to sum finite and infinite geometric seriesUnderstanding of recursive function notationApplications of geometric sequences and series, e.g. compound interest (yearly, half yearly, quarterly, monthly), annual depreciation, population growthComing up…Links to (2.4) exponential functionsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of technology to generate and display sequencesHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 4 lessonsThe Binomial Expansion and Counting Principles (1.3)Prior KnowledgeIGCSE algebraic manipulation, particularly the ability to expand multiple bracketsStudent OutcomesUnderstanding of the binomial theorem, and the expansion of (a + b)n, where n is an integerAble to calculate binomial coefficients using Pascal’s triangleAble to calculate binomial coefficients using nr / nCr by hand and using technologyUnderstanding of counting principles, including combinations and permutations (permutations where some objects are identical are not required)Coming up…Links to (5.6) the binomial distributionSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsAble to use the GDC to calculate binomial coefficientsAble to use the GDC to calculate nCr and nPrHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 8 lessonsIntroduction to Functions (2.1 – 2.4)Prior KnowledgeElementary understanding of functions from IGCSE level, including algebraic substitution and basic function notationStudent OutcomesUnderstanding of function notation f:x -> f(x)Able to calculate the domain and range of a function, graphically and analyticallyAble to sketch the graph of a function y = f(x),and investigate its key features: maximums, minimums, intercepts, horizontal and vertical asymptotes, symmetry, domain, rangeUnderstanding of one-to-one and many-to-one functionsUnderstanding of odd and even functionsUnderstanding of composite functions (f o g)(x) = f ( g(x) )Understanding of the identity function, and able to calculate the inverse function f-1(x), including the need for domain restriction in certain casesAppreciation of self-inverse functionsUnderstanding that the graph of y = f-1(x) is the reflection of y = f(x) in the line y = xUnderstanding of basic transformations of graphs: y = f(x) + a ; y = f(x – a) ; y = -f(x) ; y = f(-x) ; y = kf(x) ; y = f(kx) and the composition of these transformationsUnderstanding of the reciprocal function, x -> 1x where x≠0, its graph and its self-inverse natureUnderstanding of the graphs of y = f(x) and y = f(x)Able to sketch the graph of y = 1f(x) given the graph of y = f(x)Able to sketch simple rational functions, x -> ax+bcx+d both analytically and using technology, including identification of all horizontal and vertical asymptotes and interceptsUnderstanding of simple exponential/logarithmic functions, x -> ax, a>0; x -> ex; x -> logax, x>0 including exponential and logarithmic functions as inverses of each otherComing up…The quadratic function and its transformationsPolynomial functions and their graphsFactor and remainder theoremsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to graph unfamiliar functionsUse of GDC to investigate all the above features of a functionHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 6 lessonsPolynomial Functions (2.5 – 2.7)Prior KnowledgeUnderstanding of function notationUnderstanding of key features of the graph of any functionUnderstanding of transformations of graphsStudent OutcomesUnderstanding of polynomial functions and their graphs, including the relationship between the degree of the polynomial and the possible number of x-interceptsUnderstanding of the graphical significance of a repeated rootAble to use the factor and remainder theoremsKnowledge of the fundamental theorem of algebraAble to solve quadratics using the formulaUnderstanding of the use of the discriminantAble to solve polynomial equations graphically and algebraicallyAble to use the formulae for the sum and product of the roots of a polynomial equationComing up…Complex roots of polynomialsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to graph polynomial functions and investigate key featuresUse of the GDC to consolidate understanding of the discriminant and its links to the graph of a quadratic functionHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B – 4 lessonsLogarithms (1.2, 2.6)Prior KnowledgeUnderstanding of exponential functions and their graphs, including exStudent OutcomesUnderstanding of logarithms, including the terms exponent and base, and the ability to change between log form and exponential formUnderstanding of the laws of logarithms and the laws of exponentsUse of the change of base formulaUnderstanding of the graph of logarithmic functions, including the natural log, ln(x) as the inverse of exUse of logarithms to solve exponential equationsComing up…Differentiation of ln(x) and exSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsAble to use the GDC to evaluate logs to an appropriate degree of accuracyHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B – 7 lessonsIntroduction to Differentiation (6.1 – 6.3)Prior KnowledgeUnderstanding of infinite geometric seriesUnderstanding of rational and exponential functions, including asymptotesStudent OutcomesInformal understanding of limits and convergence, including limit notationIncludes the result limx→0sin?(x)x=1Understanding of the use of a tangent to find the gradient of a curveIntroduction of the derivative as the gradient function (including the ability to determine whether a function is increasing or decreasing) and as a rate of changeKnowledge of the definition of the derivative from first principles (see syllabus 6.1)Ability to differentiate polynomials (including fractional and negative powers), ex, and ln(x), including finding the second derivative and higher (including notation for the nth derivative – see syllabus 6.1)Use of the derivative to calculate the gradient at a point, and hence find tangents and normals, using the fact that the gradients of the tangent and the normal should multiply to give -1Use of the derivative to locate local maxima and minimaUse of the second derivative to classify stationary points and points of inflexion, including knowledge of the terms “concave up” and “concave down” (see syllabus 6.3)Knowledge that a point of inflexion may have zero or non-zero gradient, and that at a point of inflexion f”(x) = 0 and f”(x) changes sign (also known as a concavity change)Understanding of the graphical behaviour of functions, including the links between f, f’, and f’’Coming up…The chain rule for differentiating simple composite functionsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of Excel and Geogebra to investigate limitsUse of the GDC to investigate stationary points including points of inflexionUse of technology to display the graph of a derivative without explicitly finding an expression for the derivativeHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B – 3 lessonsThe Chain Rule and Optimisation (6.2, 6.3)Prior KnowledgeUnderstanding of the derivativeAbility to differentiate polynomials, ex, and ln(x)Student OutcomesUnderstanding of the chain rule for differentiating composite functions, e.g. (5x -2)6, 3e(4x + 2), ln(6x – 1)Able to solve optimisation problems using differentiationComing up…Use of the chain rule when differentiating circular functionsThe quotient and product rule for differentiationSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsN/AHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B – 5 lessonsIntroduction to Integration (6.4 – 6.5)Prior KnowledgeIntroductory work on differentiation, including differentiating polynomials, ex, and ln(x)Student OutcomesUnderstanding of indefinite integration as anti-differentiation for polynomials, ex, and 1x including an appreciation of the constant of integrationAble to integrate the composition of any of these functions with a linear function by inspectionAnti-differentiation with a boundary condition to determine the constant of integrationUnderstanding of definite integration as the area between the curve and the x-axis, including a discussion on the derivation from first principlesAble to calculate definite integrals, both analytically and using technologyUsing integration to find the areas between two curvesComing up…Integration by substitutionVolumes of revolutionSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to calculate definite integrals that cannot be found analyticallyHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 2A – 5 lessonsIntroduction to Trigonometry (3.1, 3.7)Prior KnowledgeIGCSE knowledge of right angled trigonometry and Pythagoras’ TheoremStudent OutcomesIntroduction to the radian measure of anglesAble to find the length of an arc and the area of a sector using both degrees and radiansAble to use the sine and cosine rulesUnderstanding of the ambiguous case of the sine ruleAppreciation that Pythagoras’ Theorem is a special case of the cosine ruleAble to find the area of a triangle using ? absinCApplications of the above formulae to solve problems including navigation, 2D and 3D geometrical problems, angles of elevation and depressionComing up…The unit circle and trigonometric graphsReciprocal and inverse trig functionsTrigonometric identities, including the Pythagorean Identity, sin2x + cos2x ≡ 1Suggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsAbility to change between Degrees and Radians on the GDC depending on the problemHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 2A – 8 lessonsFurther Trigonometry (3.2, 3.4 – 3.6)Prior KnowledgeUnderstanding of the applications of sin, cos, and tanUnderstanding of the radian measure of anglesKnowledge of Pythagoras’ TheoremStudent OutcomesUnderstanding of the definition of cosθ and sinθ in terms of the unit circleUnderstanding of the definition of tanθ = sinθcosθApplications of tanθ in terms of the gradient of a straight lineUse of the unit circle to find exact values of trigonometric ratios of 0, π/6, π/4, π/3, π/2 and their multiplesKnowledge of the graphs of sinx, cosx, and tanx including their domains and ranges, amplitude, and their periodic natureKnowledge of the definitions of secθ, cosecθ, cotθ and their graphsUse of transformations of graphs to produce composite functions of the form, e.g. f(x) = asin(b(x+c)) + dUse of the graphs to solve trigonometric equations in a finite interval, including problems that lead to quadratic equations in sinx, cosx, or tanxApplications of the trigonometric graphs, including modelling periodic phenomena such as tidal motion, or the motion of a Ferris wheelKnowledge of the inverse functions arcsinθ, arccosθ, arctanθ; including their graphs, domains, and rangesComing up…Trigonometric identities and their uses in solving more complex equationsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to graph composite trigonometric functions as mentioned aboveUse of the GDC to graph and solve trigonometric functionsUse of the GDC to find the intersection of different graphsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 2A – 5 lessonsTrigonometric Identities (3.2, 3.3)Prior KnowledgeUse of the trigonometric graphs to solve trigonometric equations in a finite intervalKnowledge of Pythagoras’ Theorem and the unit circleStudent OutcomesKnowledge of the Pythagorean Identities, sin2x + cos2x ≡ 1, 1 + tan2x ≡ sec2x , 1 + cot2x ≡ cosec2xKnowledge of the compound angle identities (proof not required)Knowledge of the double angle identities, including their derivation from the compound angle identitiesUse of these identities in solving harder trigonometric equationsUnderstanding of the relationship between the trigonometric ratios, e.g. given cosx = ? and that x is acute, find sin2x without finding xComing up…Links to domain and rangeLinks to quadratic modellingSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to solve harder trigonometric functions that require the knowledge of the above identitiesHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 2B – 14 lessonsComplex Numbers (1.5 – 1.8)Prior KnowledgeBasic algebraic skills including the use of the quadratic formulaUnderstanding of polynomial functions and the relationship between the highest power of the functions and the number of possible rootsGraphing polynomial functionsStudent OutcomesUnderstanding of i = -1Introduction to complex numbers, including the terms real part, imaginary part, conjugate, modulus, and argumentUnderstanding of the Cartesian form z = a + ibKnowledge of sums, products, and quotients of complex numbersAble to use modulus-argument (polar) form; z = r(cosθ = isinθ) = rcisθAble to use Euler form, reiθAble to convert between the different forms of complex numbersUnderstanding of the complex plane and drawing Argand diagramsAble to use de Moivre’s theorem when dealing with powers of complex numbers, and use it to find the nth roots of a complex number (include the nth roots of unity)Understanding that complex roots of polynomials will come in conjugate pairsComing up…Use of mathematical induction in cases including complex numbers Suggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to solve polynomial equationsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 2B/3 – 6 lessonsCalculus Revisited (6.2 – 6.3)Prior KnowledgeIntroductory knowledge of differentiation and integration of polynomials, ex and ln(x)Knowledge of the chain rule and integration by inspection in simple casesStudent OutcomesAble to differentiate and integrate sinx, cosx, and tanxExtension of the chain rule to include the circular functionsUnderstanding of the product and quotient rules for differentiationUsing integration to find the areas underneath trigonometric curvesSimple integration by substitutionFurther use of differentiation to solve optimisation problems and applications of differentiation, e.g. profit, area, volume problemsComing up…Calculus using the reciprocal and inverse trigonometric functionsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to perform definite integrationsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 3 – 4 lessonsImplicit Differentiation and Volumes of Revolution (6.2, 6.5)Prior KnowledgeUnderstanding of differentiation and integrationStudent OutcomesUnderstanding of implicit differentiationUnderstanding of the formulae for volumes of revolutionComing up…Integration by partsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to evaluate integrals when finding volumes of revolutionHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 3 – 2 lessonsMathematical Induction (1.4)Prior KnowledgeAlgebraic manipulationKnowledge of complex numbers, differentiation, sequences and series, trigonometryStudent OutcomesAble to prove results using mathematical inductionThis topic links to many others, for example complex numbers, differentiation, sequences and series, trigonometric identitiesComing up…N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsN/AHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 3 – 6 lessonsIntroduction to Vectors (4.1 – 4.2, 4.5)Prior KnowledgeIGCSE knowledge of vectors, including an understanding of direction, magnitude, and resultant vectorsStudent OutcomesUnderstanding of the unit vectors i, j, k and their link to 3D geometryKnowledge of column vectors and component formSimple applications of IGCSE vector work to solve geometrical problems (see syllabus 4.1)Able to find the magnitude of a vector, vKnowledge of position vectors OA = aAble to use the scalar (dot) product, including its applications to parallel and perpendicular lines (see syllabus 4.2)Able to use the scalar product to find the angle between two vectorsAble to calculate the vector (cross) product, including knowledge of its basic properties and it’s alternative form v x w = vwsinθn (see syllabus 4.5)Understanding of the geometric interpretations of the scalar product (areas of triangles and parallelograms)Coming up…Line and planes in spaceSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsN/AHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 3 – 11 lessonsLines and Planes in Space (4.3 – 4.4, 4.6 – 4.7)Prior KnowledgeUnderstanding of the scalar and vector productsStudent OutcomesAble to use the vector equation of a line: r = a + λb and convert between this form and Cartesian/Parametric formsAble to find the angle between two linesAble to use the vector equation of a line when solving problems involving velocity and time (simple kinematics)Able to distinguish between coincident, parallel, intersecting, and skew lines (including finding any points of intersection)Knowledge of the vector equation of a plane: r = a + λb + μcUse of the normal vector to obtain the form r . n = a . nAble to use the Cartesian equation of a plane: ax + by + cz = dUnderstanding of problems involving the intersections of a line with a plane / two planes / three planesInterpret solutions to systems of equations geometrically (see syllabus 1.9)Able to find the angle between a line and a plane / between two planesComing up… N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsN/AHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 2 lessonsIntroduction to Statistics (5.1)Prior KnowledgeIGCSE knowledge of statistics, including the basics of the data handling cycleUnderstanding of basic graphs and chartsKnowledge of the mean, median, mode, and range, including finding these from both discrete and grouped frequency tablesUnderstanding of the concepts of discrete and continuous dataUnderstanding of the concepts of ‘sampling’ and ‘random sampling’ Student OutcomesKnowledge of statistical measures and their interpretation, specifically the mean, median, and mode as measures of central tendency, and the range and interquartile range as measures of dispersionUnderstanding of the concepts of populations, samples, random samples, frequency distributions of both discrete and continuous dataAppreciation of grouped data: mid-interval values, interval width, upper and lower interval boundariesAbility to calculate the variance and standard deviation of a set of data using both formulae and technologyUnderstanding of the variance and standard deviation as measures of dispersionUnderstanding of the effect of constant changes to the original data, e.g. what happens to the mean and standard deviation if 5 is subtracted from every data item in the list?Applications of the above statistics to real-life situationsComing up…The binomial and normal distributionsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of GDC to calculate the above statisticsUnderstanding that the GDC notation may differ from the IB notationHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 5 lessonsProbability (5.2 – 5.4)Prior KnowledgeIGCSE knowledge up to and including the use of tree diagrams to solve simple probability problemsAn appreciation of the concepts of trial, outcome, equally likely likely outcomes, sample space (U), and eventUnderstanding that the probability of an event A is P(A) = n(A)n(U)Appreciation of the concept of complementary events A and A’ (not A)Appreciation of the difference between experimental relative frequency and theoretical probabilityStudent OutcomesAble to use and interpret Venn diagramsKnowledge of the union, ∪ and intersection, ∩Able to use Venn diagrams, tree diagrams, counting principles, and tables of outcomes to solve problemsAble to find the probability of combined events using the formula for P(A ∪ B)Understanding of mutually exclusive events where P(A ∩ B) = 0Understanding and use of conditional probability P(A | B) = P(A ∩B)P(B)Understanding of the definition of independent events, P(A | B) = P(A) = P(A | B’)Use of P(A ∩ B) = P(A)P(B) to show independenceAble to use Bayes’ theorem for a maximum of three eventsComing up…Probability distributions and probability density functionsThe Binomial, Poisson, and Normal distributionsSuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsN/AHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A – 9 lessonsProbability Distributions (5.5 – 5.7)Prior KnowledgeThe binomial expansionAble to use Venn diagrams, tree diagrams, counting principles, and tables of outcomes to solve probability problemsKnowledge of statistical measures and their interpretation, specifically the mean, median, and mode as measures of central tendency, and the range and interquartile range as measures of dispersionUnderstanding of the concepts of populations, samples, random samples, frequency distributions of both discrete and continuous dataAbility to calculate the variance and standard deviation of a set of data using both formulae and technologyStudent OutcomesUnderstanding of the concepts of discrete and continuous random variables and their probability distributionsAble to define and use probability density functionsAble to calculate the expected value (mean), mode, median, variance, and standard deviation for probability density functions (discrete and continuous)Able to apply this knowledge to real life situations, for example games of chanceUnderstanding of the Binomial and Poisson distributions (including its mean and variance) and the conditions under which random variables have these distributions (formal proofs of the mean and variance are not required)Understanding of the Normal distribution (probabilities and values of the variable must be found using technology)Understanding of standardized normal variables, including an appreciation that the standardize value (z) gives the number of standard deviations from the meanUnderstanding of the properties of the Normal distributionComing up…N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to calculate statistics and probabilities for the above distributionsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 3 – 4 lessonsInternal Assessment (Mathematical Exploration)Prior KnowledgeAny and all mathematical content students have met either in or outside the classroomStudent OutcomesDevelop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematicsProvide opportunities for students to complete a piece of mathematical work over an extended period of timeEnable students to experience the satisfaction of applying mathematical processes independentlyProvide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematicsEncourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical toolEnable students to develop the qualities of patience and persistence, and to reflect on the significance of their workProvide opportunities for students to show, with confidence, how they have developed ing up…N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of technology to support and enhance the explorationHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1A/1B – 8 lessonsFurther Calculus (6.2, 6.4, 6.5, 6.7)Prior KnowledgeAll prior work on differentiation and integrationStudent OutcomesAble to find the derivatives of secx, cosecx, cotx, logax, arcsinx, arccosx, arctanxAble to calculate integrals using these and all prior results from syllabus 6.2, including the use of both standard and non-standard substitutionsAble to use integration by parts to solve problems, including those where repeated integration by parts is requiredComing up…N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to evaluate definite integrals that cannot be done by analyticallyHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B – 3 lessonsKinematics (6.6)Prior KnowledgeAll prior work on differentiation and integrationStudent OutcomesAble to solve kinematic problems involving displacement s, velocity v, and acceleration aKnowledge that v = dsdt, a = dvdt = d2s/dt2 Understanding that the total distance travelled can be found by evaluating t1t2vdtComing up…N/ASuggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to evaluate definite integralsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidenceTerm 1B/2A – 29 lessonsOption (Topic 7 or Topic 9)Prior KnowledgeStudent OutcomesComing up…Suggested ActivitiesCriteria for SuccessIB TextbookPage, chapter, exercise, questionsExisting ResourcesLinks to high quality lesson resources hereESL resourcesLinks to high quality ESL resources hereIDEALS / TOKLinks to interesting TOK themes hereNRICHLink to nrich challenges hereStandards UnitsLink to appropriate standards unit lessons hereInteresting questionsInteresting probing questions to go hereICT skillsUse of the GDC to evaluate definite integralsHomeworkLinks to standardised homework hereAssessmentsLink to any activities that will provide assessment evidence ................
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