​Year 12 IB HL Analysis and Approach

Prior Knowledge

1.1- Operations with numbers in standard form
1.5- Laws of exponents with integer and rational exponents
1.6- Approximation, bounds of rounded numbers, percentage error, estimation
2.1- Different forms of the equation of a straight line, including parallel and perpendicular lines
3.1- Volume and surface area of 3D solids. 3D trigonometry.
4.2- Presentation of data: frequency tables, histograms, cumulative frequency graphs
5.3, 5.5- Differentiation and integration of integer powers of x (additional maths)

Teacher 1

Year 12 Autumn Term - First Half

2.2 Concept of a function, domain, range and graph. Function notation. The concept of a function as a mathematical model.  Informal concept that an inverse function reverses the effect of a function. Inverse function as a reflection in the line y=x and the notation f-1(x) (students should be aware that inverse functions exist for 1-1 functions and not many-1). (4.1)
2.7 Inverse function including domain restriction. Finding an inverse function. Composite functions in context. (4.3)
2.3 graph sketching with & without GDC
2.4 asymptotes, graphical solution of equations
2.5 linear, quadratic, cubic, exponential models
2.5 Direct/inverse variation
2.6 modelling skills
Test on sequences, series, functions and trigonometry

Year 12 Autumn Term - Second Half

SMC
2.8 Transformations of graphs
1.10 Simplifying expressions, both numerically and algebraically
2.9 Natural logarithm, logistic and piecewise models
2.10 Scaling numbers using logarithms, linearizing data and interpretation of log-log and semi-log graphs
3.6 Voronoi diagrams 
Test on everything so far, review test and splitting of groups as 

Year 12 Spring Term - First Half

1.12, 1.13 Definition of complex numbers; the terms real part, imaginary part, conjugate, modulus and argument.
Cartesian form z=a+ib.
Sums, products and quotients of complex numbers. Modulus-argument form and the complex plane:
z=r(cosθ+isinθ)=rcisθ=reiθ :
3.9 Geometric transformations of points using matrices
4.1 Concepts of population, sample, random sample and frequency distribution of discrete and continuous data. Reliability of data sources and bias in sampling, sampling techniques and their effectiveness. Interpretation of outliers.

Year 12 Spring Term - Second Half

4.2, 4.3 Mean, median, mode, variance, standard deviation, IQR, effect of linear changes to the data.. Grouped data: mid-interval values, width, upper and lower boundaries. Production and understanding of box and whisker diagrams.
 4.4 Bivariate data: PMCC, scatter diagrams, regression line of y on x and x on y, use of the regression line for prediction purposes.
4.10 Spearman’s rank correlation coefficient, limitations
5.1 Introduction to the concept of limit. Derivative interpreted as gradient function and as rate of change. 

Teacher 2

Year 12 Autumn Term - First Half

1.2, 1.3, 1.11 Arithmetic sequences and series. Use of the formula for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequence.  Applications. Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. (4.4)
Geometric sequences and series.  Use of the formula for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for the sums of geometric sequences.  Applications. The sum of infinite geometric series. (7.1)
1.4, 1.7 Financial applications (compound interest, annual depreciation). Amortization and annuities using technology. (7.2)
1.8 Using technology for solving polynomial equations and systems of linear equations
3.4, 3.7 Radians, arc length and sector area
3.8 Definition of cos, sin and tan in terms of unit circle, trig identities and solving trig equations using graphs.
3.2, 3.3 Reminder of cosine, sine rules and area of triangle formula
1.5 Logarithms with base 10 and e, 1.9 Laws of logarithms
2.5, 2.9 Sinusoidal models

Year 12 Autumn Term - Second Half

Micro-exploration
3.5 Equations of perpendicular bisectors
3.10 vectors
3.11 vector equation of line
3.12 vectors and kinematics
3.13 scalar product, angle between vectors, cross product

Year 12 Spring Term - First Half

1.14 Matrices: definition, algebra of, identity and zero. Determinants, inverses and solving systems of linear equations using matrices.
1.15 Eigenvalues and eigenvectors, diagonalisation
4.5 Concepts of trial, outcome, sample space (U) and event. Probability of an event. Complementary events A and A'. Expected number of occurrences.

Year 12 Spring Term - Second Half

4.6 Solving probability problems using Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes.
Combined events, formula for P(AUB), mutually exclusive events.
Conditional probability, independent events and Bayes' theorem for a maximum of three events.
4.7 Concept of discrete random variable and discrete probability distribution. Definition and use of pdf. Expected value (mean), mode, median, variance, standard deviation. Applications: to include games of chance
[4] 4.8 Binomial distribution, its mean and variance. NOT REQUIRED:  formal proof of means and variances.   
[6] 4.9 Normal distribution

Year 12 Summer Term - First Half

Internal Exams
5.2, 5.3 Increasing/decreasing functions, graphical interpretation. Derivatives of powers of x and linear combinations of.
Extended Essay Week
5.4 Tangents and normal and their equations.

Year 12 Summer Term - Second Half

4.11  Hypothesis testing
4.12  Designing data collection methods. Choosing appropriate data to analyse. Categorising data in chi-squared table. Reliability and validity tests.

Year 12 Summer Term - First Half

Internal Exams
3.14 Graph theory
Extended Essay Week
​3.15 (Weighted) adjacency matrices. Walks. Number of k-length walks between two vertices.  Transition matrices.

Year 12 Summer Term - Second Half

Introduction of exploration
3.16 Tree and cycle algorithms with undirected graphs. Walks , trails, paths, circuits, cycles. Eulerian trails and circuits. Hamiltonian paths and cycles. MST graph algorithms, Chinese postman problem and algorithm, travelling salesman problem.
​5.5, 5.6, 5.7  Integration as anti-differentiation. Local maxima and minima. Optimisation problems in context.