Course topics

\n \n \n \n function,\n \n \n \n \n \n graph,\n \n \n \n \n \n functions,\n \n \n \n \n \n line,\n \n \n \n \n \n equations,\n \n \n \n \n \n polynomial,\n \n \n \n \n \n tangent,\n \n \n \n \n \n equation,\n \n \n \n \n \n integral,\n \n \n \n \n \n sine,\n \n \n \n \n \n integration,\n \n \n \n \n \n trigonometric,\n \n \n \n \n \n rational,\n \n \n \n \n \n cosine,\n \n \n \n \n \n curve,\n \n \n \n \n \n circle,\n \n \n \n \n \n exponential,\n \n \n \n \n \n graphs,\n \n \n \n \n \n parabola,\n \n \n \n \n \n (1),\n \n \n \n \n \n differentiation,\n \n \n \n \n \n point,\n \n \n \n \n \n area,\n \n \n \n \n \n points,\n \n \n \n \n \n (2),\n \n \n \n \n \n root,\n \n \n \n \n \n linear,\n \n \n \n \n \n derivative,\n \n \n \n \n \n rule,\n \n \n \n \n \n system,\n \n \n \n \n \n solution,\n \n \n \n \n \n polynomials,\n \n \n \n \n \n angle,\n \n \n \n \n \n properties,\n \n \n \n \n \n geometry,\n \n \n \n \n \n inequality,\n \n \n \n \n \n common,\n \n \n \n \n \n derivatives,\n \n \n \n \n \n theorem,\n \n \n \n \n \n gradient,\n \n \n \n \n \n quadratic,\n \n \n \n \n \n factor,\n \n \n \n \n \n definite,\n \n \n \n \n \n transformation,\n \n \n \n \n \n difference,\n \n \n \n \n \n sum,\n \n \n \n \n \n form,\n \n \n \n \n \n triangle,\n \n \n \n \n \n intersection,\n \n \n \n \n \n inequalities,\n \n \n \n \n \n coordinate,\n \n \n \n \n \n vector,\n \n \n \n \n \n number,\n \n \n \n \n \n algebraic,\n \n \n \n \n \n series,\n \n \n \n \n \n binomial,\n \n \n \n \n \n exponent,\n \n \n \n \n \n general,\n \n \n \n \n \n degree,\n \n \n \n \n \n angles,\n \n \n \n \n \n reciprocal,\n \n \n \n \n \n basic,\n \n \n \n \n \n fraction,\n \n \n \n \n \n graphical,\n \n \n \n \n \n domain,\n \n \n \n \n \n parallel,\n \n \n \n \n \n value,\n \n \n \n \n \n local,\n \n \n \n \n \n interval,\n \n \n \n \n \n identities,\n \n \n \n \n \n translation,\n \n \n \n \n \n approximate,\n \n \n \n \n \n term,\n \n \n \n \n \n under,\n \n \n \n \n \n product,\n \n \n \n \n \n partial,\n \n \n \n \n \n substitution,\n \n \n \n \n \n plane,\n \n \n \n \n \n variable,\n \n \n \n \n \n scalar,\n \n \n \n \n \n natural,\n \n \n \n \n \n vectors,\n \n \n \n \n \n increasing,\n \n \n \n \n \n decreasing,\n \n \n \n \n \n finding,\n \n \n \n \n \n simple,\n \n \n \n \n \n curves,\n \n \n \n \n \n axis,\n \n \n \n \n \n ratio,\n \n \n \n \n \n geometric,\n \n \n \n \n \n extrema,\n \n \n \n \n \n method,\n \n \n \n \n \n secant,\n \n \n \n \n \n normal,\n \n \n \n \n \n sequence,\n \n \n \n \n \n roots,\n \n \n \n \n \n powers,\n \n \n \n \n \n inverse,\n \n \n \n \n \n cotangent,\n \n \n \n \n \n antiderivative,\n \n \n \n \n \n perpendicular,\n \n \n \n \n \n lines,\n \n \n \n \n \n approximation,\n \n \n \n \n \n Cartesian,\n \n \n \n \n \n vertex,\n \n \n \n \n \n segment,\n \n \n \n \n \n revolution,\n \n \n \n \n \n laws,\n \n \n \n \n \n factorisation,\n \n \n \n \n \n measure,\n \n \n \n \n \n general angles,\n \n \n \n \n \n formula,\n \n \n \n \n \n quotient,\n \n \n \n \n \n rules,\n \n \n \n \n \n combination,\n \n \n \n \n \n expressions,\n \n \n \n \n \n recognize,\n \n \n \n \n \n logarithm,\n \n \n \n \n \n fractions,\n \n \n \n \n \n improper,\n \n \n \n \n \n parts,\n \n \n \n \n \n methods,\n \n \n \n \n \n region,\n \n \n \n \n \n cartesian,\n \n \n \n \n \n operations,\n \n \n \n \n \n range,\n \n \n \n \n \n intercept,\n \n \n \n \n \n euler,\n \n \n \n \n \n constant,\n \n \n \n \n \n minimum,\n \n \n \n \n \n maximum,\n \n \n \n \n \n ellipse,\n \n \n \n \n \n formulas,\n \n \n \n \n \n transformations,\n \n \n \n \n \n critical,\n \n \n \n \n \n Stationary,\n \n \n \n \n \n sign,\n \n \n \n \n \n newton,\n \n \n \n \n \n composition,\n \n \n \n \n \n composite,\n \n \n \n \n \n numbers,\n \n \n \n \n \n arithmetic,\n \n \n \n \n \n progression,\n \n \n \n \n \n logarithmic,\n \n \n \n \n \n coefficient,\n \n \n \n \n \n tangents,\n \n \n \n \n \n normals,\n \n \n \n \n \n cosecant,\n \n \n \n \n \n combinations,\n \n \n \n \n \n rate,\n \n \n \n \n \n expansion,\n \n \n \n \n \n Pascal,\n \n \n \n \n \n division,\n \n \n \n \n \n generalised,\n \n \n \n \n \n arbitrary,\n \n \n \n \n \n differential,\n \n \n \n \n \n anti-derivative,\n \n \n \n \n \n parametric,\n \n \n \n \n \n remainder,\n \n \n \n \n \n radius,\n \n \n \n \n \n straight,\n \n \n \n \n \n dimension,\n \n \n \n \n \n transform,\n \n \n \n \n \n numerical,\n \n \n \n \n \n distance,\n \n \n \n \n discriminant,\n \n \n \n sridhara,\n \n \n \n quadratic equations,\n \n \n \n population,\n \n \n \n growth,\n \n \n \n radioactive,\n \n \n \n decay,\n \n \n \n logistic,\n \n \n \n exponential growth and decay,\n \n \n \n factorization,\n \n \n \n vieta,\n \n \n \n factorization of quadratic functions,\n \n \n \n sphere,\n \n \n \n cone,\n \n \n \n spherical,\n \n \n \n volumes,\n \n \n \n frustum,\n \n \n \n Volumes of revolution,\n \n \n \n law,\n \n \n \n power,\n \n \n \n index,\n \n \n \n exponents,\n \n \n \n indices,\n \n \n \n laws of indices - rational exponents,\n \n \n \n quadratic functions,\n \n \n \n perfect,\n \n \n \n squares,\n \n \n \n grouping,\n \n \n \n factorisation of polynomials,\n \n \n \n converting,\n \n \n \n measures,\n \n \n \n radian,\n \n \n \n angle measures,\n \n \n \n comparing,\n \n \n \n exponential functions,\n \n \n \n differentiation rules (1),\n \n \n \n The tangent,\n \n \n \n simplify,\n \n \n \n Rational expressions,\n \n \n \n changing,\n \n \n \n base,\n \n \n \n the logarithm,\n \n \n \n low,\n \n \n \n circumscribed,\n \n \n \n sines,\n \n \n \n ambiguous,\n \n \n \n the sine rule,\n \n \n \n decomposition,\n \n \n \n denominator,\n \n \n \n Partial fractions,\n \n \n \n Intersection points (1),\n \n \n \n integration methods (1),\n \n \n \n graphical solution of inequalities (2),\n \n \n \n simultaneous,\n \n \n \n simultaneous equations,\n \n \n \n table,\n \n \n \n relationship,\n \n \n \n notions,\n \n \n \n piecewise,\n \n \n \n functions - basic notions,\n \n \n \n absolute,\n \n \n \n graphs of trigonometric functions,\n \n \n \n shifting,\n \n \n \n work,\n \n \n \n force,\n \n \n \n The scalar product (2),\n \n \n \n the natural exponential function,\n \n \n \n multiplication,\n \n \n \n addition,\n \n \n \n unit,\n \n \n \n algebraic operations on vectors,\n \n \n \n The definite integral,\n \n \n \n monotonicity,\n \n \n \n values,\n \n \n \n finding maximum and minimum values,\n \n \n \n integration methods (2),\n \n \n \n new,\n \n \n \n solving,\n \n \n \n factorising,\n \n \n \n solving simple trigonometric equations,\n \n \n \n second,\n \n \n \n equations of curves,\n \n \n \n modulus,\n \n \n \n intervals,\n \n \n \n the modulus function,\n \n \n \n reduction,\n \n \n \n trigonometry,\n \n \n \n basic trigonometric functions,\n \n \n \n Transformations of graphs (1),\n \n \n \n carpet,\n \n \n \n finite,\n \n \n \n sierpinski,\n \n \n \n gasket,\n \n \n \n koch,\n \n \n \n snowflake,\n \n \n \n geometric series,\n \n \n \n representation,\n \n \n \n X,\n \n \n \n Y,\n \n \n \n transformation of graphs,\n \n \n \n Finding local extrema,\n \n \n \n quadratic inequalities,\n \n \n \n iterating,\n \n \n \n approximate solution of equations,\n \n \n \n Intersection points (2),\n \n \n \n The normal,\n \n \n \n rotation,\n \n \n \n argument,\n \n \n \n composition of functions,\n \n \n \n monomial,\n \n \n \n extremum,\n \n \n \n second-order,\n \n \n \n second-order derivatives,\n \n \n \n side,\n \n \n \n bearings,\n \n \n \n the cosine rule,\n \n \n \n surd,\n \n \n \n surds,\n \n \n \n arithmetic sequence,\n \n \n \n Factorisation and roots of polynomials,\n \n \n \n negative,\n \n \n \n positive,\n \n \n \n fractional,\n \n \n \n integrals,\n \n \n \n Integrals of powers with rational exponent,\n \n \n \n local extrema,\n \n \n \n stationary points,\n \n \n \n critical points,\n \n \n \n asymptote,\n \n \n \n the natural logarithmic function,\n \n \n \n area under the curve,\n \n \n \n chain,\n \n \n \n differentiation rules (2),\n \n \n \n length,\n \n \n \n measuring,\n \n \n \n sector,\n \n \n \n arc,\n \n \n \n measuring the circle,\n \n \n \n infinite,\n \n \n \n convergent,\n \n \n \n infinite convergent geometric series,\n \n \n \n terms,\n \n \n \n like,\n \n \n \n presentation,\n \n \n \n interpolation,\n \n \n \n presentation of polynomials,\n \n \n \n translations,\n \n \n \n translations and graphs,\n \n \n \n space,\n \n \n \n quantities,\n \n \n \n coordinates,\n \n \n \n magnitude,\n \n \n \n hyperbola,\n \n \n \n defined,\n \n \n \n parametrically,\n \n \n \n implicitly,\n \n \n \n Tangents and normals for implicitly or parametrically defined curves,\n \n \n \n other,\n \n \n \n Other trigonometric functions,\n \n \n \n differentiation of simple functions,\n \n \n \n derivatives of trigonometric functions,\n \n \n \n interest,\n \n \n \n compound,\n \n \n \n basic exponential equations,\n \n \n \n asymptotes,\n \n \n \n Rational functions,\n \n \n \n the binomial expansion,\n \n \n \n calculator,\n \n \n \n simple trigonometric equations,\n \n \n \n algorithm,\n \n \n \n Algebraic Division,\n \n \n \n selected,\n \n \n \n integration of selected functions,\n \n \n \n expansion of rational functions,\n \n \n \n logarithms,\n \n \n \n exponential inequalities,\n \n \n \n graphical solution of equations (1),\n \n \n \n Inverse trigonometric functions,\n \n \n \n square,\n \n \n \n integer,\n \n \n \n derivatives of powers with rational exponent,\n \n \n \n first-order differential equations,\n \n \n \n initial conditions,\n \n \n \n differential equations,\n \n \n \n transformations of graphs (2),\n \n \n \n differentiation of polynomials,\n \n \n \n indefinite,\n \n \n \n The anti-derivative,\n \n \n \n change,\n \n \n \n the derivative,\n \n \n \n separately,\n \n \n \n parametric differentiation,\n \n \n \n account,\n \n \n \n geometric sequence,\n \n \n \n long,\n \n \n \n division of polynomials,\n \n \n \n graphical solution of equations (2),\n \n \n \n binomial series,\n \n \n \n pascal,\n \n \n \n manipulation,\n \n \n \n algebraic manipulation of polynomials,\n \n \n \n arithmetic series,\n \n \n \n position,\n \n \n \n segments,\n \n \n \n midpoint,\n \n \n \n collinear,\n \n \n \n position vectors,\n \n \n \n bisector,\n \n \n \n Parallel and perpendicular lines,\n \n \n \n gradients,\n \n \n \n finding gradients,\n \n \n \n tangents and normals,\n \n \n \n integral of function,\n \n \n \n integral of power,\n \n \n \n integrating rational power,\n \n \n \n integration of rational power,\n \n \n \n integration rule,\n \n \n \n rational powers,\n \n \n \n approximation of the area under a curve,\n \n \n \n polygon,\n \n \n \n the area of a triangle,\n \n \n \n inscribed,\n \n \n \n Parametric equations of curves,\n \n \n \n using,\n \n \n \n integration using partial fractions,\n \n \n \n implicit,\n \n \n \n implicit differentiation,\n \n \n \n set,\n \n \n \n 2-d,\n \n \n \n 2,\n \n \n \n vector equations of lines in 2-D,\n \n \n \n simpson,\n \n \n \n simpson's,\n \n \n \n numerical integration - simpson's rule,\n \n \n \n disc,\n \n \n \n lattice,\n \n \n \n Coordinate geometry of a circle,\n \n \n \n construction,\n \n \n \n one,\n \n \n \n mapping,\n \n \n \n inverse function,\n \n \n \n synthetic,\n \n \n \n theorems,\n \n \n \n the factor and remainder theorems,\n \n \n \n expression,\n \n \n \n sequences,\n \n \n \n perpendicular distance from a point to a line,\n \n \n \n Trigonometric functions of the sum and difference of angles (1),\n \n \n \n variables,\n \n \n \n homogeneous,\n \n \n \n separable,\n \n \n \n equations with separable variables,\n \n \n \n integrating,\n \n \n \n derivatives of exponential and logarithmic functions,\n \n \n \n 3-d,\n \n \n \n 3,\n \n \n \n Vector equations of lines in 3-D,\n \n \n \n double,\n \n \n \n double-angle,\n \n \n \n Double-angle formulas,\n \n \n \n The scalar product (1),\n \n \n \n figures,\n \n \n \n irregular,\n \n \n \n mid-ordinate,\n \n \n \n numerical integration - mid-ordinate rule,\n \n \n \n Equation of a straight line,\n \n \n \n factorise,\n \n \n \n Trigonometric functions of the sum and difference of angles (2),\n \n \n \n Identities for trigonometric functions,\n \n \n \n graphical solution of inequalities (1),\n \n \n \n arms,\n \n \n \n sketching,\n \n \n \n zeroes,\n \n \n \n sSketching graphs,\n \n \n \n odd,\n \n \n \n zeros,\n \n \n \n continuity,\n \n \n \n zeros of a function\n \n \n