MathsQ&A by dot point

Force as a vector, the resultant of forces, Newton's three laws of motion, weight and the relationship between mass and weight, connected particles, and resolving forces in two dimensions.

The nature of friction, the coefficient of friction, the limiting friction model with the inequality between friction and the normal reaction, and applying friction to objects on horizontal and inclined surfaces.

Displacement, velocity and acceleration, motion graphs and the meaning of their gradients and areas, the constant acceleration equations, motion under gravity, and using calculus to relate displacement, velocity and acceleration.

The moment of a force about a point, the principle of moments, equilibrium of a rigid body under coplanar forces, reactions at supports, and modelling uniform and non-uniform rods.

Modelling projectile motion by resolving into independent horizontal and vertical components, using the constant acceleration equations, and finding range, maximum height, time of flight and the equation of the path.

The base and derived SI units used in mechanics, the distinction between scalar and vector quantities, modelling assumptions such as particles and smooth surfaces, and the conventions for representing forces and motion.

Indices, surds, quadratics, simultaneous equations, inequalities, polynomials, the factor theorem, partial fractions, graphs of functions, composite and inverse functions, the modulus function and graph transformations.

Equations of straight lines, gradients, parallel and perpendicular lines, the equation of a circle, tangents and chords, and parametric equations of curves.

Differentiation from first principles, the rules for powers, the chain, product and quotient rules, derivatives of standard functions, stationary points and their nature, and connected rates of change.

The exponential function and its derivative, the natural logarithm, the laws of logarithms, solving exponential and logarithmic equations, and using logarithms to linearise data and model exponential growth and decay.

Integration as the reverse of differentiation, indefinite and definite integrals, the area under a curve, integration of standard functions, integration by substitution and by parts, and using partial fractions to integrate rational functions.

Locating roots by sign change, iterative methods including fixed point iteration and the Newton-Raphson method, the conditions under which they succeed or fail, and the trapezium rule for approximating definite integrals.

Methods of proof including proof by deduction, proof by exhaustion, disproof by counter-example and proof by contradiction, applied to statements about numbers and inequalities.

Arithmetic and geometric sequences and series, sigma notation, the conditions for convergence of a geometric series, the binomial expansion for positive integer and rational powers, and recurrence relations.

Radian measure, arc length and sector area, the trigonometric ratios and their graphs, exact values, identities, the reciprocal and inverse functions, the addition and double angle formulae, and solving trigonometric equations.

Vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, unit vectors and components, position vectors, and using vectors to solve geometric problems.

Measures of location and spread, histograms, box plots and cumulative frequency, identifying outliers, scatter diagrams, correlation and the use of regression lines.

Setting up null and alternative hypotheses, the significance level, one-tailed and two-tailed tests, hypothesis tests for a binomial proportion and for a normal mean, critical regions, and interpreting the conclusion in context.

Probability of events, mutually exclusive and independent events, the addition and multiplication rules, Venn diagrams and tree diagrams, and conditional probability.

Discrete random variables and their probability distributions, the requirement that probabilities sum to one, the use of statistical distributions to model real situations, and an introduction to the binomial and normal models.

Populations and samples, the advantages and limitations of sampling, simple random sampling, systematic, stratified, quota and opportunity sampling, and the importance of the large data set.

The conditions for a binomial model, the binomial probability formula, calculating individual and cumulative probabilities, the mean of a binomial distribution, and using the model in context.

The normal distribution as a model for continuous data, its mean and standard deviation, calculating probabilities, the standard normal distribution and standardising, finding values from probabilities, and using the normal approximation to the binomial.