IB Mathematics+Autograph
IB Mathematics+Autograph
IB Mathematics+Autograph
In BOLD and RED: suitable for AUTOGRAPH ============================================================ AUTOGRAPH PAGE =================
Studies TOPIC 1: INTRODUCTION TO THE G. D. CALCULATOR 1.1 Arithmetic calculations; data; lists Natural Numbers:; Integers:; Rational numbers: ; Real numbers: Approximation; sig. fig. Standard form SI units Arithmetic sequences Geometric sequences Two simultaneous equations; solving quadratic equations
Studies TOPIC 2: NUMBER AND ALGEBRA 2.1 2.2 2.3 2.4 2.5 2.6 2.7
2D
Studies TOPIC 3: SETS, LOGIC AND PROBABILITY 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Set theory; prime numbers Venn diagrams Sample space Symbolic logic Compound statements Truth tables Logical equivalence Probability Venn diagrams; tree diagrams; cards, 2-dice Combined events/conditional probability
Extras: 2-dice
Studies TOPIC 4: FUNCTIONS 4.1 4.2 4.3 4.4 4.5 4.7 4.8 Functions: domain and range Linear functions, y = mx + c Quadratic functions: vertex, symmetry x = b/(2a) x x x y = a , a , ka + c; exponential growth and decay Trig (degrees): y = asin(bx) + c; y = acos(bx) + c Graph sketching; rational graphs Solving equations and intersections 2D 2D 2D
Studies TOPIC 5: GEOMETRY AND TRIGONOMETRY 5.1 5.2 5.3 5.4 5.5 Coordinate geometry; distance, mid points Straight lines: y = mx + c and ax + by + d = 0; perpendicular lines Right-angled trig Sine and cosine rules 3D shapes: surface area and volume; New shapes from mid-points
2D
Studies TOPIC 6: STATISTICS 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Discrete, continuous Frequency polygons Grouped data, histogram (equal classes); stem and leaf diagrams Cumulative Frequency, box plots, percentiles, quartiles Mean, median, mode, percentile Inter-quartile range, standard deviation; population and sample Scatter diagrams, line of best fit; correlation Regression line (y on x) Hypothesis testing; contingency tables. Chi-squared test STATISTICS STATISTICS
2D
Studies TOPIC 7: INTRODUCTORY DIFFERENTIAL CALCULUS 7.1 7.2 7.3 7.4 7.5 Gradient of chord PQ and P => Q; tangent to a curve n Basic principles for ax : f(x) and f(x) Gradient of a curve; equation of tangent Increasing and decreasing functions Max and min; point of inflexion with zero gradient 2D 2D
Studies TOPIC 8: FINANCIAL MATHEMATICS 8.1 8.2 8.3 8.4 Currency conversions Simple interest Compound interest Tables; inflation
Studies PROJECT (20%) involving the collection of information or the generation of measurements, and the analysis and evaluation of the information or measurements. STATISTICS 2D
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SL TOPIC 1: ALGEBRA 1.1 1.2 1.3 APs, GPs; population growth Exponents and logarithms; change of base Binomial Theorem; Pascals Triangle
SL TOPIC 2: FUNCTIONS AND EQUATIONS 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Domain and range; Composite Functions f(g(x)). Inverse function Graphing functions; vertical and horizontal asymptotes; roots Transformation of graphs: translation, stretch, reflection in axes. Trig graphs. The inverse function; reflection in y = x Reciprocal function and y = 1/x The quadratic: axis of symmetry x = b/a; completing the square The quadratic: roots; discriminant x y = a and its inverse: y = logax x y = e and y = lnx 2D 2D 2D 2D
SL TOPIC 3: CIRCULAR FUNCTIONS AND TRIGONOMETRY 3.1 3.2 3.3 3.4 3.5 3.6 Radians sin and cos and the unit circle; tan = sin/cos; cos + sin = 1 Double angle formulae Graphs of sinx, cosx, tanx; f(x) = asin(b(x + c)) + d Solving trig equations Sine and cosine rules 2D Extras: Trig 2D
SL TOPIC 4: MATRICES 4.1 4.2 4.3 4.4 Matrix : element, row, column, order Matrix algebra 2D and 3D Determinants; 2D inverse Solving linear equations (2D and 3D)
2D
SL TOPIC 5: VECTORS 5.1 2D and 3D vectors; distance between two points. Sum, difference; zero vector, negative vector; Scalar multiplication, magnitude, unit vector. Scalar product; perpendicular vectors; angle between two vectors Vector equation of a line; angle between two lines Intersection of two lines 2D 3D
SL TOPIC 6: STATISTICS AND PROBABILITY 6.1 6.2 Population and sample statistics; discrete and continuous Box and whisker plots; grouped data; histogram (equal class intervals) 6.3 Mean, median, mode, quartiles; standard deviation 6.4 Cumulative frequency graph; percentiles. 6.5 Probability 6.6 Probability: combined events 6.7 Conditional probability 6.8 Venn diagrams] 6.9 Discrete probability distribution, eg: P(X=x) = 5/18, 6/18, 7/18 Expected value for discrete data 6.10 Binomial distribution; its mean 6.11 Normal Distribution; Standardisation; inverse calculations
STATISTICS STATISTICS
STATISTICS STATISTICS
SL TOPIC 7: CALCULUS 7.1 Ideas of limit and convergence n x Basic principles; Derivative of x , sinx, cosx, tanx, e , lnx Gradient; rate of change; Equations of tangents and normals Chain rule, product and quotient rules; Second derivative Local max and min; points of inflexion n x Integration: x , sinx, cosx, 1/x and e Area under a curve; between two curves; Volume of revolution about x-axis Displacement, velocity, acceleration, and time Area under v-t represents distance. Horizontal and vertical asymptotes Second derivative: points of inflexion with non-zero gradient
2D 2D 3D
2D
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HL TOPIC 2 - CORE: FUNCTIONS AND EQUATIONS Domain and range; Composite Functions f(g(x)). Inverse function. 2.2 Graphing functions; vertical and horizontal asymptotes; roots 2.3 Transformation of graphs: translation, stretch, reflection in axes. Trig graphs. The inverse function; reflection in y = x y = 1/f(x); graphs with absolute value, eg y = |f(x)|, y f(|x|) 2.4 Reciprocal function and y = 1/x 2.5 The quadratic: axis of symmetry x = b/a; completing the square 2.6 The quadratic: roots; discriminant x 2.7 y = a and its inverse: y = logax x 2.8 y = e and y = lnx 2.9 Inequalities: in one variable; g(x) f(x), one linear and one quadratic 2.10 Roots of polynomial equations; repeated roots 2.1
2D 2D 2D 2D 2D
HL TOPIC 3 CORE: CIRCULAR FUNCTIONS AND TRIGONOMETRY 3.1 3.2 3.3 3.4 3.5 3.6 Radians sin and cos and the unit circle; tan = sin/cos; cos + sin = 1; 1 + tan = sec ; 1 + cot = scs; sec, csc, cos. Double angle formulae; Compound angle Identities Graphs: sinx, cosx, tanx, asin(b(x + c)) + d Inverse trig: arcsinx, arccosx, arctanx Solving trig equations Sine and cosine rules 2D Extras: Trig 2D 2D
HL TOPIC 4 CORE: MATRICES 4.1 4.2 4.3 4.4 Matrix : element, row, column, order Matrix algebra 2D and 3D Determinants; 2D inverse Solving linear equations (2D and 3D)
2D,
3D
HL TOPIC 5 CORE: VECTORS 5.1 2D and 3D vectors; distance between two points. Sum, difference; zero vector, negative vector; Scalar multiplication, magnitude, unit vector. Scalar product; perpendicular vectors; angle between two vectors Vector equation of a line; angle between two lines Parametric form: x = xo + l, y = yo + m, z = zo + n Intersecting and skew lines; Intersection of two lines Vector product (cross product) Vector equation of a plane; Equation of plane: ax + by + cz = d Intersections: line and plane, two planes, three planes. Angle between: line and plane, two planes
3D 3D 3D 3D
HL TOPIC 6 - CORE: STATISTICS AND PROBABILITY 6.1 6.2 Population and sample statistics; discrete and continuous Box and whisker plots; grouped data; histogram (equal class intervals) 6.3 Mean, median, mode, quartiles; standard deviation 6.4 Cumulative frequency graph; percentiles. 6.5 Probability 6.6 Probability: combined events 6.7 Conditional probability 6.8 Venn diagrams 6.9 Discrete probability distribution, eg: P(X=x) = 5/18, 6/18, 7/18 Continuous probability density functions Expected value and Variance for discrete data 6.10 Binomial distribution; its mean and variance Poisson distribution: its mean and variance 6.11 Normal Distribution; Standardisation; inverse calculations STATISTICS STATISTICS
STATISTICS STATISTICS
HL TOPIC 7 CORE: CALCULUS Ideas of limit and convergence, eg sin/ n x Basic principles; Derivative of x , sinx, cosx, tanx, e , lnx Gradient; rate of change; Equations of tangents and normals 7.2 Chain rule, product and quotient rules; Second derivative 7.3 Local max and min; points of inflexion n x 7.4 Integration: x , sinx, cosx, 1/x and e 7.5 Area under a curve; between two curves; Volume of revolution about x-axis 7.6 Displacement, velocity, acceleration, and time Area under v-t represents distance. 7.7 Horizontal and vertical asymptotes Second derivative: points of inflexion with non-zero gradient 7.8 Implicit differentiation 7.9 Further Integration (substitution; parts) 7.10 First Order Differential Equations (variable separable) 7.1
2D 2D 2D 2D 2D
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HL TOPIC 8 OPTION: STATISTICS AND PROBABILITY (CONTINUED) 8.1 8.2 Expectation algebra Cumulative distribution functions Discrete distributions: uniform, Bernoulli, binomial, negative binomial, Poisson, geometric, hypergeometric Continuous distributions: uniform, exponential, normal Central limit theorem Confidence intervals for the mean of a population Confidence intervals for the proportion of successes in a population Null and alternative hypotheses: Type I and type II errors One-tailed and two-tailed test Goodness of fit test
STATISTICS STATISTICS
STATISTICS
HL TOPIC 9 OPTION: SETS, RELATIONS AND GROUPS 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 Sets; De Morgans Laws Ordered pairs Functions and inverse functions Binary operations Associative, distributive, commutative Identity element; inverse Axioms of a group Groups Finite and infinite groups Cyclic groups Subgroups, Lagrange theorems Isomophism of groups
HL TOPIC 10 OPTION: SERIES AND DIFFERENTIAL EQUATIONS Infinite sequences Convergence Convergent series Power series Taylor polynomials x p Maclaurin series: e , sinx, cosx, arctanx, ln(1+x), (1+x) Limits of the form f(x)/g(x) LHpitals Rule and/or the Taylor series 10.6 First order differential equations - slope fields y' = f(x,y): Numerical solution, Eulers Method Homogeneous DEs, y = f(y/x) y + P(x)y = Q(x) using Integrating factor 10.1 10.2 10.3 10.4 10.5
2D
2D
HL TOPIC 11 OPTION: DISCRETE MATHEMATICS 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 Division and Euclidean algorithms Integers in different bases Linear diophantine equations Modular arithmetic Fermats little theorem Graphs Trails and circuits Adjacency matrix Graph algorithms Travelling Salesman
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1.3
2D
1.4
DOUGLAS BUTLER iCT Training Centre, Oundle, UK debutler@argonet.co.uk www.tsm-resources.com www.autograph-maths.com Oundle May 2009