Modelling in Mechanics
Modelling assumptions, scalar & vector quantities, SI base units & derived units, weight, and representing forces on free body diagrams.
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Notes
A-Level Maths
- 3 min
Acceleration, Projectiles & Kinematics
Velocity is the rate of change of an object's position, and therefore has direction. This makes it a vector quantity, unlike speed which...
A-Level Maths
- 3 min
Forces, Friction & Motion
Newton's Laws, F=ma, forces in two dimensions, moments, equilibrium, tilting, friction, static rigid bodies, connected particles and pulleys
A-Level Maths
- 5 min
Data
To start off with, there is some terminology you need to be familiar with. A population is the whole set of items that are of interest A...
A-Level Maths
- 2 min
Probability
Sample space diagrams, conditional probability, Venn diagrams, set notation, independent and mutually exclusive events and tree diagrams.
A-Level Maths
- 2 min
Correlation & Regression
Bivariate data, correlation & causation, product moment coefficient, regression, line of best fit, dependent and independent variables.
A-Level Maths
- 6 min
Statistical Distributions
Probability mass functions, discrete uniform distributions, the binomial distribution, the normal distribution and inverse & standard normal
A-Level Maths
- 5 min
Hypothesis Testing
Null & Alternative hypotheses, critical regions & values, one & two tailed tests and binomial, normal & zero correlation hypothesis tests.
A-Level Maths
- 4 min
Indices & Algebraic Methods
Indices laws, surds, algebraic fractions, long division of polynomials, partial fractions, and mathematical proof.
A-Level Maths
- 3 min
Sequences & Series
Arithmetic sequences & series, geometric sequences & series, sum to infinity, sigma notation and recurrence relations.
A-Level Maths
- 2 min
Quadratic & Simultaneous Equations and Inequalities
Solving quadratic equations, linear and quadratic simultaneous equations, graphing simultaneous equations, linear and quadratic inequalities
A-Level Maths
- 4 min
Graphs, Functions & Transformations
Linear, Quadratic, Cubic, Quartic and Reciprocal graphs, functions, modulus and transformations.
A-Level Maths
- 1 min
Circles
Finding midpoints of lines and the centre of a circle, the equation of a circle, intersecting lines and circle theorems.
A-Level Maths
- 1 min
The Binomial Expansion
Pascal's triangle, factorial notation, the choose function, expanding (a+b)ⁿ, Expanding (1+x)ⁿ, dealing with coefficients and general terms.
A-Level Maths
- 5 min
Trigonometry
Trig graphs, the sine and cosine rules, area of a tirangle, CAST diagrams, radians, trig ratios, trigonometric identities, sec, cosec & cot.
A-Level Maths
- 2 min
Parametric Equations
Parametric equations, converting between parametric and Cartesian form, domain and range, parametric trigonometry and sketching parametrics.
A-Level Maths
- 6 min
Differentiation
Increasing/decreasing functions, stationary points, chain, product and quotient rules, implicit, trigonometric & parametric differentiation.
A-Level Maths
- 6 min
Integration
Definite & indefinite integrals, areas under graphs, reverse chain rule, integration by parts & substitution, the trapezium rule & modelling
A-Level Maths
- 2 min
Vectors
Representing vectors, multiplying by a scalar, vector addition, magnitude & direction, position vectors, vector geometry and vectors in 3D.
A-Level Maths
- 2 min
Exponentials and Logarithms
Exponential functions, exponential graphs, e, e^x, logarithms, laws of logarithms, log rules, natural logarithm, ln, non-linear data.
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