MathsQ&A by dot point

Newton's three laws of motion, weight, resolving forces, equilibrium of a particle, friction and the coefficient of friction, motion on an inclined plane, and connected particles.

Displacement, velocity and acceleration, the constant-acceleration (suvat) equations, motion under gravity, displacement-time and velocity-time graphs, and using calculus when acceleration varies.

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

Motion of a projectile under gravity, resolving the initial velocity into horizontal and vertical components, the independence of horizontal and vertical motion, and finding range, maximum height and time of flight.

The SI base and derived units used in mechanics, the distinction between scalar and vector quantities, and the standard modelling assumptions such as particles, light strings and smooth surfaces.

Exponential functions and their graphs, the number e and the natural logarithm, the laws of logarithms, solving exponential and logarithmic equations, and using logarithms to estimate parameters in exponential and power-law models.

The language of functions (domain, range, composite and inverse functions), the modulus function and its graph, and solving modulus equations and inequalities.

Decomposing a proper algebraic fraction into partial fractions, including denominators with distinct linear factors and a repeated linear factor, and using partial fractions in integration and binomial expansion.

Radian measure, the relationship between radians and degrees, arc length and the area of a sector and segment, and the small-angle approximations for sine, cosine and tangent.

The Pythagorean and quotient identities, the reciprocal functions, the compound and double angle formulae, the R form for a sin theta plus b cos theta, and solving trigonometric equations over an interval.

The sine, cosine and tangent functions and their graphs, the sine and cosine rules, the area of a triangle, and exact values of trigonometric ratios for standard angles.

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

Tangents and normals, increasing and decreasing functions, stationary points and their nature using the second derivative, points of inflection, optimisation, and connected rates of change.

Forming first-order differential equations from a context, solving them by separation of variables, finding particular solutions from initial conditions, and interpreting the solution in modelling.

Differentiation from first principles, the power rule, the chain, product and quotient rules, derivatives of standard functions including exponentials, logarithms and trigonometric functions, and implicit and parametric differentiation.

Integration by substitution, integration by parts, integration using partial fractions, and integrating expressions of the form f prime over f and products reducible by a trigonometric identity.

Indefinite and definite integrals as the reverse of differentiation, the integrals of standard functions, the area under a curve and between two curves, and the trapezium rule for numerical integration.

Locating roots by change of sign, iterative methods of the form x equals g of x, the Newton-Raphson method, and the conditions under which these numerical methods fail.

Quadratic functions, completing the square, the quadratic formula and the discriminant, simultaneous equations (linear and quadratic), and linear and quadratic inequalities.

Straight lines, gradients, parallel and perpendicular conditions, the equation of a circle, the relationship between a tangent and the radius, and parametric equations of curves.

Sketching curves including polynomials, the reciprocal function and its variations, intersections of graphs, and the transformations y equals f(x) plus a, f(x plus a), f(ax) and af(x).

Laws of indices for all rational exponents, surd manipulation and rationalising denominators, and the meaning of negative and fractional indices.

Polynomial manipulation, the factor theorem and algebraic division, and the binomial expansion of (a plus b) to the power n for positive integer n using binomial coefficients.

Methods of proof: proof by deduction, proof by exhaustion, disproof by counter-example, and proof by contradiction, including the irrationality of root 2 and the infinitude of primes.

Arithmetic and geometric sequences and series, sigma notation, sum formulae, recurrence relations, increasing, decreasing and periodic sequences, and the sum to infinity of a convergent geometric series.

Measures of central tendency and spread, histograms, box plots and cumulative frequency, identifying outliers, comparing distributions, and correlation and the regression line.

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

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

Discrete random variables and probability distributions, the binomial distribution as a model and its probabilities, the Normal distribution, standardising, the inverse Normal, and the Normal approximation to the binomial.

Populations and samples, the census, sampling methods (simple random, systematic, stratified, quota and opportunity), their advantages and disadvantages, and the role of the large data set.