IB Questionbank

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Syllabus

Section name
Topic 1—Number and algebra
SL 1.1—Using standard form
SL 1.2—Arithmetic sequences and series
SL 1.3—Geometric sequences and series
SL 1.4—Financial apps – compound interest, annual depreciation
SL 1.5—Intro to logs
SL 1.6—Approximating and estimating
SL 1.7—Loan repayments and amortization
SL 1.8—Use of technology to solve systems of linear equations and polynomial equations
AHL 1.9—Log laws
AHL 1.10—Expressions with non-integer exponents
AHL 1.11—Sum of infinite geometric sequences
AHL 1.12—Complex numbers introduction
AHL 1.13—Polar and Euler form
AHL 1.14—Introduction to matrices
AHL 1.15—Eigenvalues and eigenvectors
Topic 2—Functions
SL 2.1—Equations of straight lines, parallel and perpendicular
SL 2.2—Functions, notation domain, range and inverse as reflection
SL 2.3—Graphing
SL 2.4—Key features of graphs, intersections using technology
SL 2.5—Modelling functions
SL 2.6—Modelling skills
AHL 2.7—Composite functions, finding inverse function incl domain restriction
AHL 2.8—Transformations of graphs, composite transformations
AHL 2.9—HL modelling functions
AHL 2.10—Scaling large numbers, log-log graphs
Topic 3—Geometry and trigonometry
SL 3.1—3d space, volume, angles, midpoints
SL 3.2—2d and 3d trig
SL 3.3—Angles of elevation and depression
SL 3.4—The circle, arc and area of sector, degrees only
SL 3.5—Intersection of lines, equations of perpendicular bisectors
SL 3.6—Voronoi diagrams
AHL 3.7—Radians
AHL 3.8—Unit circle, Pythag identity, solving trig equations graphically
AHL 3.9—Matrix transformations
AHL 3.10—Vector definitions
AHL 3.11—Vector equation of a line in 2d and 3d
AHL 3.12—Vector applications to kinematics
AHL 3.13—Scalar and vector products
AHL 3.14—Graph theory
AHL 3.15—Adjacency matrices and tables
AHL 3.16—Tree and cycle algorithms, Chinese postman, travelling salesman
Topic 4—Statistics and probability
SL 4.1—Concepts, reliability and sampling techniques
SL 4.2—Histograms, CF graphs, box plots
SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
SL 4.4—Pearsons, scatter diagrams, eqn of y on x
SL 4.5—Probability concepts, expected numbers
SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
SL 4.7—Discrete random variables
SL 4.8—Binomial distribution
SL 4.9—Normal distribution and calculations
SL 4.10—Spearman’s rank correlation coefficient
SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
AHL 4.12—Data collection, reliability and validity tests
AHL 4.13—Non-linear regression
AHL 4.14—Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators
AHL 4.15—Central limit theorem
AHL 4.16—Confidence intervals
AHL 4.17—Poisson distribution
AHL 4.18—T and Z test, type I and II errors
AHL 4.19—Transition matrices – Markov chains
Topic 5—Calculus
SL 5.1—Introduction of differential calculus
SL 5.2—Increasing and decreasing functions
SL 5.3—Differentiating polynomials, n E Z
SL 5.4—Tangents and normal
SL 5.5—Integration introduction, areas between curve and x axis
SL 5.6—Stationary points, local max and min
SL 5.7—Optimisation
SL 5.8—Trapezoid rule
AHL 5.9—Differentiating standard functions and derivative rules
AHL 5.10—Second derivatives, testing for max and min
AHL 5.11—Indefinite integration, reverse chain, by substitution
AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y
AHL 5.13—Kinematic problems
AHL 5.14—Setting up a DE, solve by separating variables
AHL 5.15—Slope fields
AHL 5.16—Eulers method for 1st order DEs
AHL 5.17—Phase portrait
AHL 5.18—Eulers method for 2nd order DEs
Prior learning

DP Mathematics: Applications and Interpretation Questionbank