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Number and Algebra
SL 1.1—Using standard form
SL 1.2—Sequences and Sigma Notation
SL 1.3—Geometric Sequences
SL 1.4—Financial apps – compound interest, annual depreciation
SL 1.5—Exponents and Logarithms
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—Complex numbers continued
AHL 1.14—Introduction to matrices
AHL 1.15—Eigenvalues and eigenvectors
Functions
SL 2.1—Equations of a line
SL 2.2—Functions, domains, range, graphs
SL 2.3—Graph of a function
SL 2.4—Features of a graph
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
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
Statistics and Probability
SL 4.1—Introduction to Statistics
SL 4.2—Presentation of data
SL 4.3—Mean, median, and mode
SL 4.4—Correlation of Data
SL 4.5—Trial and outcome
SL 4.6—Venn diagrams
SL 4.7—Discrete random variables
SL 4.8—Binomial distribution
SL 4.9—Normal distribution
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
Calculus
SL 5.1—Introduction to Limits
SL 5.2—Increasing and decreasing functions
SL 5.3—Introduction to derivatives
SL 5.4—Tangents and normals
SL 5.5—Introduction to integration
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
For the moving points P1(t)=214+t591 and P2(t)=101+t872, find the time t at which the points are closest to each other.
For the points P1(t)=(0,0,0)+t(1,2,3) and P2(t)=(3,1,0)+t(4,−1,2), determine the time t at which the distance between them is minimal.
Determine whether the lines r1=123+t257 and r2=345+s431 intersect.
Find the time t at which P1(t)=111+t201 and P2(t)=023+t13−1 are closest.
Find the value of m for which the lines r1=521+tm34 and r2=253+s4−12 intersect.
Find the minimum distance between the points P1(t)=(0,0,0)+t(1,2,3) and P2(t)=(3,1,0)+t(4,−1,2).
Find the value of m such that the lines r1=230+t11m and r2=041+s312 intersect.
Determine whether the lines with equations r1=214+t591 and r2=101+s872 intersect.
Consider two points, P1 and P2, such that the displacement vector from P1 to P2 at time t is given by d(t)=1−3t1+2t3−t where t∈R.
Determine the minimum distance between P1 and P2.
Determine whether the lines r1=0−12+t341 and r2=213+s652 intersect.
Determine the value of m such that the lines r1=102+t3m5 and r2=241+s613 intersect.
Question Type 2: Determining with an object given a trajectory passes a specific point
Question Type 4: Finding the time at which two objects are closest each other given some trajectory