MathsQ&A by dot point

Newton's three laws of motion, weight and the relationship between mass and force, resolving forces, friction and the coefficient of friction, and connected particles.

Displacement, velocity and acceleration, motion graphs, the constant acceleration formulae, and using calculus to relate displacement, velocity and acceleration that vary with time.

The moment of a force about a point, the principle of moments, equilibrium of a rigid body, and problems involving rods, beams and reactions at supports.

Projectile motion resolved into horizontal and vertical components, the independence of the two motions, and finding range, maximum height, time of flight and the path.

Fundamental and derived quantities and their SI units, scalar and vector quantities, and the modelling assumptions used to simplify mechanics problems.

Algebra and functions including indices and surds, quadratics, simultaneous equations, inequalities, polynomials, graphs, functions and transformations, the binomial expansion and partial fractions.

Coordinate geometry in the x and y plane including straight lines, the equation of a circle, tangents, chords and parametric equations of curves.

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

The exponential function and the number e, the natural logarithm, the laws of logarithms, solving exponential equations, and using logarithms to linearise and model real data.

Indefinite and definite integrals, areas under curves, integrals of standard functions, integration by substitution and by parts, integration using partial fractions, and differential equations.

Locating roots by change of sign, iterative methods including the Newton-Raphson method, the trapezium rule for numerical integration, and the conditions under which these methods fail.

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

Sequences and series including arithmetic and geometric sequences, sigma notation, sums to infinity, recurrence relations, and the binomial expansion for any rational power.

Radian measure, arc length and sector area, exact values, the Pythagorean and addition identities, reciprocal and inverse functions, and solving trigonometric equations.

Vectors in two and three dimensions, magnitude and direction, addition and scalar multiplication, position vectors, unit vectors, and geometric applications.

Measures of location and spread, diagrams for single and bivariate data, outliers and cleaning, correlation and the equation of a regression line, and interpolation versus extrapolation.

Null and alternative hypotheses, one- and two-tailed tests, significance levels and critical regions, hypothesis tests for a binomial proportion, and for a correlation coefficient and a normal mean.

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

Discrete random variables and probability distributions, the binomial distribution, its conditions, and calculating binomial probabilities with technology.

Populations and samples, census and sampling, random and non-random sampling methods, and the advantages and limitations of each in context.

The normal distribution as a model for continuous data, finding probabilities, the standard normal distribution, using the inverse normal, and approximating the binomial.