Unit Title Estimated hours 8 Differentiation a Differentiating sin and cos from first principles 2 x x b Differentiating exponentials and logarithms 3 c Differentiating products, quotients, implicit and parametric functions. 6 d Second derivatives (rates of change of gradient, inflections) 2 e Rates of change problems* (including growth and kinematics) 3 *see Integration (part 2) Differential equations – 9 Numerical methods* a Location of roots 1 b Solving by iterative methods (knowledge of and cobweb’ ‘staircase 3 diagrams) c Newton-Raphson method 2 d Problem solving 2 *See Integration (part 2) for the trapezium rule 10 Integration (part 1) a Integrating (including when = exponentials and trigonometric xn n –1), 4 functions. Integrating functions defined parametrically. b the reverse of differentiation, and using trigonometric identities to 5 manipulate integrals 11 Integration (part 2) a Integration by substitution 4 b Integration by parts 3 c Use of partial fractions 2 d Areas under graphs or between two curves, including understanding the area is the limit of a sum (using sigma notation). 4 Areas under curves expressed parametrically e The trapezium rule 2 f Differential equations (including knowledge of the family of solution 4 curves) Vectors (3D): Use of vectors in dimensions; knowledge of column 5 vectors and i, j and k unit vectors 120 Remaining A Mathematics applied content
Unit Title Estimated hours 8 Differentiation a Differentiating sin x and cos x from first principles 2 b Differentiating exponentials and logarithms 3 c Differentiating products, quotients, implicit and parametric functions. 6 d Second derivatives (rates of change of gradient, inflections) 2 e Rates of change problems* (including growth and kinematics) 3 *see Integration (part 2) – Differential equations 9 Numerical methods* a Location of roots 1 b Solving by iterative methods (knowledge of ‘staircase and cobweb’ diagrams) 3 c Newton-Raphson method 2 d Problem solving 2 *See Integration (part 2) for the trapezium rule 10 Integration (part 1) a Integrating xn (including when n = –1), exponentials and trigonometric functions. Integrating functions defined parametrically. 4 b the reverse of differentiation, and using trigonometric identities to manipulate integrals 5 11 Integration (part 2) a Integration by substitution 4 b Integration by parts 3 c Use of partial fractions 2 d Areas under graphs or between two curves, including understanding the area is the limit of a sum (using sigma notation). Areas under curves expressed parametrically 4 e The trapezium rule 2 f Differential equations (including knowledge of the family of solution curves) 4 Vectors (3D): Use of vectors in dimensions; knowledge of column vectors and i, j and k unit vectors 5 120 Remaining A Mathematics applied content