Your journey to excellence inMathematics
By Revision Genie
Proof by deduction
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Proof by exhaustion
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Disproof by counterexample
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Proof by contradiction
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Laws of indices
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Surds and rationalising
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Quadratic functions and graphs
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Completing the square
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Quadratic equations (incl. in functions)
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Simultaneous equations (linear–quadratic)
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Linear inequalities
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Quadratic inequalities
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Inequalities on graphs
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Polynomial manipulation
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Factor theorem
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Algebraic division (linear)
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Rational expressions
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Function graphs (cubic/quartic)
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Modulus graphs
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Reciprocal graphs and asymptotes
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Graphical equation solving
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Proportion and graphs
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Composite functions
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Inverse functions and graphs
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Graph transformations
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Partial fractions
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Modelling with functions
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Straight line forms
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Parallel and perpendicular lines
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Straight line modelling
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Circle equations
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Completing the square (circles)
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Circle properties (chords, tangents)
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Parametric equations
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Parametric–Cartesian conversion
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Parametric modelling
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Binomial expansion (positive integer)
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Binomial expansion (rational)
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Binomial approximations and validity
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Recurrence relations
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Increasing/decreasing/periodic sequences
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Sigma notation
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Arithmetic sequences
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Arithmetic series (sum formula proof)
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Geometric sequences
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Geometric series (finite)
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Geometric series to infinity
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Sequence and series modelling
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Radian measure
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Arc length and sector area
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Sine rule
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Cosine rule
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Triangle area formula
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Small-angle approximations
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Sin/Cos/Tan graphs
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Symmetry and periodicity
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Exact trig values
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Sec/Cosec/Cot definitions
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Arcsin/Arccos/Arctan
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Trig identities (basic)
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Double-angle formulae
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Compound-angle formulae
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Half-angle applications
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R-form (a cosθ + b sinθ)
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Trig equations (interval)
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Trig proofs
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Trig in context problems
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Exponential functions (a^x, e^x)
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Transformations of exponentials
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Exponential differentiation idea (k e^{kx})
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Logarithms as inverses
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ln(x) graphs and inverse of e^x
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Log laws
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Solving exponential equations
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Logarithmic graphs (linearising data)
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Exponential growth and decay models
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Model limitations and refinements
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Derivative as gradient
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Derivative as rate of change
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Differentiation from first principles
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Gradient function sketches
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Second derivative and concavity
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Stationary points (f′=0)
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Second derivative test
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Points of inflection
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Power rule (rational powers)
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Derivatives of e^{kx}, a^{kx}, trig
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Derivative of ln(x)
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Tangents and normals
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Increasing/decreasing intervals
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Product rule
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Quotient rule
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Chain rule
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Connected rates of change
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Differentiation of inverse functions
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Implicit differentiation (first derivative)
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Parametric differentiation (first derivative)
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Forming differential equations
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Fundamental Theorem of Calculus
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Indefinite integrals and +C
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Power integrals (n ≠ −1)
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Integrals of e^{kx} and 1/x
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Integrals of trig functions
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Trig identity integrals
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Definite integrals
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Area under a curve
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Area between curves
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Area for parametric curves
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Integration as limit of a sum
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Substitution
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Integration by parts
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Integrals involving ln(x)
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Partial fractions integration (linear factors)
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Separable differential equations
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Particular solutions
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Solution families (sketching)
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Interpreting DE solutions in context
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Limitations of DE models
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Root locating by sign change
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Failure of sign-change methods
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Fixed-point iteration
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Cobweb diagrams
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Staircase diagrams
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Newton–Raphson method
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Failure of iterative methods
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Numerical integration (trapezium rule)
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Over/under-estimates (trapezium)
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Numerical methods in context
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2D and 3D vectors
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Unit vectors (i, j, k) and column vectors
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Magnitude and direction
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Unit vectors
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Vector addition and scaling
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Geometric interpretation (triangle/parallelogram)
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Parallel vectors
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Position vectors
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Distance between points (2D/3D)
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Vector problem solving (incl. forces contexts)
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Population vs sample
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Census vs sample (pros/cons)
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Simple random sampling
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Stratified sampling
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Systematic sampling
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Quota sampling
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Opportunity sampling
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Sampling critique and bias
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Inference variability (different samples)
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Histograms (area = frequency)
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Frequency polygons
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Box plots and outliers
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Cumulative frequency diagrams
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Scatter diagrams
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Regression lines (interpretation only)
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Explanatory vs response variables
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Interpolation
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Extrapolation risks
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Correlation strength and direction
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Correlation vs causation
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Coding in data
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Mean, median, mode
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Range and IQR
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Variance and standard deviation
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Standard deviation from summary statistics
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Percentiles (grouped data interpolation)
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Outlier rules (IQR / SD rules)
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Data cleaning (missing data, errors, outliers)
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Critiquing presentation choices
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Large Data Set familiarity
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Mutually exclusive events
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Independent events
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Venn diagrams
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Tree diagrams
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Two-way tables
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Conditional probability
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Complement rule
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Addition rule
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Multiplication rule
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Probability modelling assumptions
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Discrete uniform distribution
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Binomial distribution as a model
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Binomial probabilities (calculator)
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Normal distribution as a model
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Normal probabilities (calculator)
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Standardisation ideas
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Normal curve inflection points (µ ± σ)
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Binomial–Normal approximation
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Continuity correction
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Choosing appropriate distribution models
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Model suitability and limitations
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Null and alternative hypotheses
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Significance level
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Test statistic
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One-tailed tests
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Two-tailed tests
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Critical value and critical region
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Acceptance region
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p-values
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Binomial test for a proportion
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Interpreting test outcomes in context
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Type I error (informal)
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Normal test for a mean (known/assumed variance)
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Sampling distribution of the mean (given)
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Correlation coefficient as test statistic
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Interpreting r using p-values/critical values
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SI base units (length, time, mass)
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Derived quantities (velocity, acceleration)
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Force and weight
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Moment
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Unit conversions
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Displacement vs distance
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Velocity vs speed
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Acceleration
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Displacement–time graphs
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Velocity–time graphs
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Gradient and area interpretations
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Constant-acceleration (suvat) formulae
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Deriving suvat relationships
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2D kinematics with vectors
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Calculus in kinematics (v = dr/dt, a = dv/dt)
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Vector differentiation/integration in time
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Force types and free-body diagrams
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Newton’s first law
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Newton’s second law (scalar)
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Newton’s second law (2D vectors)
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Resolving forces (inclined planes)
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Weight under gravity (g)
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Newton’s third law
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Equilibrium of a particle
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Connected particles and pulleys
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Coplanar force equilibrium
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Resultant forces and force addition
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Dynamics in a plane
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Friction model (F ≤ μR)
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Limiting friction and statics
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