## Order of topics

Teacher 1Autumn term 1 Functions- Vocabulary: domain, range, composite, inverse, 1-1, many-1, restricted domains, odd & even Graph sketching- Graph sketching with & without GDC - Modulus functions - Asymptotes - Graphical solution of equations - Transformations of graphs - Graphs of rational, inverse and reciprocal functions Polynomials- Graphs of polynomials - Factor & remainder theorem - Polynomial inequalities (up to cubics) - Quadratic Equations: - Discriminant - Quadratic simultaneous equations Binomial Theorem- Permutations and combinations - The binomial theorem. Autumn term 2Exponentials and logarithms- Index laws - Laws of logarithms - Change of base. - Graphs of exponential and logarithms - Equations involving unknown exponents - Significance of e Differentiation- Continuity and convergence - Differentiation from first principles - Finding tangents and normals to curves - Increasing and decreasing functions - Turning points - Optimisation problems - Standard derivatives (polys, sine, cosine, exp, ln) Spring term 1Differentiation - Product rule - Chain rule - Quotient rule. - Implicit differentiation - Related rates of change - Differentiating inverse trigonometric functions- Differentiating reciprocal trigonometric functions - Relationship between graphs of f(x), f'(x), f''(x). Integration- Standard integrals |
Teacher 2Autumn term 1Sequences and series- Arithmetic sequences and series - Geometric sequences and series - Sigma notation Radians- Converting from degrees to radians - Arc length and sector area - Graphs of sine, cosine and tan - Exact values for 0, pi/6, pi/4, pi/3 and pi/2 and multiples of these - SIne rule - Cosine rule - Area of a triangle - Reciprocal ratios sec, cosec and cot - Composite functions of the form f(x)=asin(b(x+c))+d - Inverse trig functions, domains, ranges and graphs Autumn term 2Micro explorationTrigonometry - Pythagorean trigonometric identities - Compound angle identity - Double angle identity - Solving trigonometric equations Spring term 1Proof by induction Complex numbers- Definition of complex numbers- The real part, imaginary part, conjugate, modulus and argument. - Cartesian form z=a+ib. - Sums, products and quotients of complex numbers - Modulus- argument form - De Moivre's theorem - nth root of complex numbers Polynomials- Conjugate roots of polynomials with real coefficients - Fundamental theorem of algebra - Properties of sums and products of roots of polynomials. |

Spring term 2IntegrationArea under & between curves- - Volume of revolutions about x and y axes - Integration by inspection and substitution - Integration by parts Summer term 1Kinematics- Applications of calculus to kinematics |
Spring term 2Vectorsum, difference, zero vector, scalar multiplication, magnitude and position vectors.- S - Scalar product - The angle between two vectors. - Vector equation of a line in two and three dimensions. - Coincident, parallel, intersecting and skew lines - Points of intersection. Summer term 1Vectors- Vector product - Geometric interpretation of the triple scalar product |

Summer term 2Statistics- Concepts of population, sample, random sample and frequency distribution of discrete and continuous data - Mean, variance, standard deviation- Grouped data: mid-interval values, width, upper and lower boundaries Probability- Concepts of trial, outcome, sample space (U) and event - Probability of an event - Complementary events A and A' - Combined events, formula for P(AUB) - Mutually exclusive events. - Conditional probability - Independent events and Bayes' theorem |
Summer term 2Introduction of exploration Vectors- Vector and cartesian equations of a plane - Intersection of: a line and a plane; two planes; three planes - Angle between: a line and a plane; two planes - Solutions of systems of linear equations. |