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A-LEVEL IB
PRE-UNI

This section deals with strategic methods required in solving tricky advanced level questions required to pass your exams for successful entry  into  your desired university. 

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MATHEMATICS

M1
M2
P1
P2
P3
S1
S2

MECHANICS 1

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types of number rots and poer
types of number rots and poe1
types of number rots and poe 2
Acceleration
Using areas to find distances and displacements
2 Momentum and newton`s laws
Setting up a mathematical model
The content acceleration formulae
3 Force and Newton`s laws of motion
Force diagrams
Force and motion
4 Applying Newton`s second law along a line
Newton`s second law
Newton`s second law applied to connected objects
Reviewing a mathematical model: air resistance
5 Vectors
Adding vectors
Components of vector
The magnitude and direction of vectors written in Component Form
Resolving vectors
Velocity triangles
6 Projectiles
Modelling assumptions for projectile motion
The path of a projectile
General equations
7 Forces and motion in two dimensions
Finding resultant forces
Force in equilibrium
Newton`s second law in two dimensions
8 General motion
Motion in one dimension
Motion in two and three dimensions

MECHANICS 2

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PURE MATHEMATICS 1

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1 Co-ordination geometry
Co-ordination geometry 1: Co-ordinates, Plotting , sketching and drawing
Co-ordination geometry 2: Co-ordinates, Plotting , sketching and drawing
Plotting , sketching and drawing
The gradient of a line
Distance between two points
Mid-point of a line joining two points
The equation of a straight line
Intersection of two lines
Curves
The circle
Intersection of a line and a curve
Intersection of two curves
2 Trigonometry
Trigonometrical functions
Trigonometrical functions for angles of any size
The sine and cosine graphs
The tangent graph
Solution of equations using graphs of trigonometrical functions
Reciprocal trigonometrical functions
Triangles without right angles
The area of a triangle
Circular measure
The length of an arc of a circle
The area of a sector of a circle
3 Polynomials
Operations with Polynomials
Polynomial curves
The graphs of quadratic functions
Binomial expansions
4 Uncertainty
Errors and inequalities
The algebra of inequalities
5 Differentiation
The gradient of a curve
Finding the gradient of curve
Finding the gradient from first principles
Differentiating by using standard results
Tangents and normals
Maximum and minimum points
Points of inflection
Applications
6 Integration
Reversing differentiation
Finding the area under a curve
Area as the limit of sum
Areas below the x axis
The area between two curves
Area between curves and the y axis
Finding volumes by integration
Numerical integration
7 The language of mathematics
Problem solving
Types of number
Writing mathematics
The converse of a theorem
Proof

PURE MATHEMATICS 2

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1 Indices
Working with square roots
Negative and fractional indices
Logarithms
Exponential functions
Modelling curves
2 Sequences and series
Definitions and notation
Patterns in sequences
Arithmetic sequences
Geometric sequences
Periodic sequences
Oscillating sequences
Sequences with other pattern
Arithmetic sequences and series
Geometric sequences
3 Functions
Mathematical mappings
Using transformations to sketch the curves of the functions
Composite functions
Inverse functions
Inverse trigonometrical functions
Even, odd and periodic functions
Curve sketching
4 Calculus techniques
Higher derivatives
The chain rule
The product rule
Differentiating an inverse function
Integration
Integration by substitution
5 Natural logarithms and exponentials
A new function
The natural logarithm function
The Exponential function
Differentiating natural logarithms and exponentials
Integrals involving the exponential function
Integrals involving the natural logarithm function
Extending the domain for logarithm integrals
6 Numerical solutions of equations
Interval estimation – change of sign methods
Fixed point estimation

PURE MATHEMATICS 3

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STATISTICS 1

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1 Exploring data
Looking at the data
Categorical or qualitative data
Numerical or quantitative data
Measures of central tendency
Frequency distributions
Grouped data
Working with grouped data
Measures of spread
Linear coding
2 Data presentation and related measures of central and spread
Bar charts and vertical line charts
Pie charts
Histograms
Measures of central tendency and spread using quartiles
Cumulative frequency curves
3 Probability
Measuring Probability
Estimating probability
The complement of an event
The probability of events from two trials
Expectation
Conditional probability
4 Sampling
Terms and natation
Sampling
Sampling techniques
Case study
5 Further probability
Factorials
Permutations
Combinations
The binomial coefficients, ``C,
Calculating probabilities in less simple cases
6 The binomial distribution
The binomial distribution
The expectation of B(n,p)
Using the binomial distribution
Does the binomial distribution really works
7 Hypothesis testing using the binomial distribution
Defining terms
Hypothesis testing checklist
Choosing the significance level
Critical values and critical regions
1-tail and 2-tail tests
Asymmetrical cases

STATISTICS 2

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1 Discrete random variables
Statistical models
Discrete random variables
The conditions for a discrete random variable
Expectation of a function X, E(g[X])
Expectation algebra
Variance
Some standard discrete probability distributions
2 The Poisson distribution
Approximating the binomial terms
The Poisson distribution
The sum of two or more Poisson distribution
3 The normal distribution
Using normal distribution tables
The normal curve
Modeling discrete situations
Approximating the binomial distribution
Approximating the Poisson distribution
The central limit theorem
Normal probability graph paper
4 Bivariate data
Interpreting scatter diagrams
Line of best fit
Product moment correlation
Rank correlation
The last square regression line
Appendix?????
1. Mean and variance of the binomial distribution
2. Mean and variance of the Poisson distribution
3. The sum of two independent Poisson distributions
4. Equivalence of spearman`s rank correlation coefficient and Pearson’s rank correlation coefficient
5. The least squares regression line
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PHYSICS

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Momentum

This section covers:

 the idea of momentum * modelling and collision* defining liner collision * understanding collusion exploring crash landing

momentum 1
momentum 2
momentum 3
momentum 4
2 Momentum and newton`s laws
Understanding motion
Impulse of force
Newton`s laws and conservation of momentum
3 Circular motion
Describing circular motion
Angles in radians
Steady speed, changing velocity
Centripetal forces
Calculating force and acceleration
The origins of centripetal forces
4 Gravitational fields
Gravitational forces and fields
Gravitational field strength g
Orbiting under gravity
The orbital period
Orbiting the earth
5 Oscillations
Free and forced oscillations
Observing oscillations
Describing oscillations
Simple harmonic motion
Graphical representations of s.h.m
Frequency and angular frequency
Equations of s.h.m
Energy changes in s.h.m
Damped oscillations
Resonance
6 Thermal physics
The kinetic model
Explaining pressure
Changes of state
Internal energy
The meaning of temperature
Calculating energy changes
7 idea gases
Measuring gases
Boyle`s law
Changing temperature
Three variables, one question
Real and ideal gases
Ideal gas equation
Temperature and molecular kinetic energy
8 Electric fields
Attraction and repulsion
Investigating electric fields
Representing electric fields
Electric fields strength
Force on a change
Coulomb`s law
Electric field strength for a radial field
Comparing gravitational and electric fields
9 Magnetic fields
Magnets and currents
Magnetic force
Magnetic flux density
Currents crossing fields
Moving particles
Orbiting charges
Electric and magnetic fields
10 Electromagnetic induction
Generating electricity
Explaining electromagnetic induction
Faraday`s law of electromagnetic induction
Lenz`s law
Using induction: a.c. generator
Using induction: transformations
11 Capacitors
Using capacitors
Energy stored in a capacitor
Capacitors in parallel
Capacitors in series
Comparing capacitors and resistors
Capacitor networks
Capacitor discharge
Discharge equations
12 Atomic structure
Alpha-particle scattering and the nucleus
A simple atom model
Nucleons and electrons
Forces in the nucleus
Families of particles
Evidence for quarks
13 Nuclear physics
Nuclear fission
Nuclear fusion
Explaining fission and fusion
Binding energy and stability
Nuclear power
14 Radioactivity
Radiation from radioactive substances
Balanced equations
Energy released in radioactive decay
Properties of ionizing radiation
Randomness and decay
Decay graphs and equations
15 X-rays
The nature and production of x-rays
X-ray attenuation
Improving x-ray images
Computerized axial tomography
16 Diagnostic methods in medicine
Choosing a radionuclide
The gamma camera
Positron emission tomography
Magnetic resonance imaging
17 Using ultrasound in medicine
Working with ultrasound
Echo sounding
Ultrasound scanning
18 The Nature of the universe
The life of stars
Measuring the universe
The expanding universe
The birth of the universe
19 The evolution of the universe
Back to the beginning
The future of the universe
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CHEMISTRY

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BIOLOGY

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A-LEVEL I.B PRE-UNI

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