Cambridge Single tier Additional Maths Maths Practice

Calculus

• Connected rates of change and small increments
• Definite integrals and plane areas
• The derivative: concept and notation
• Classifying stationary points
• Gradients, tangents, and normals
• Integrating powers of x and reciprocals
• Integrating standard forms (ax+b)
• Integration as the reverse of differentiation
• Kinematics via differentiation and integration
• Kinematics graphs
• Practical maximum and minimum problems
• The product and quotient rules
• Standard derivatives and the chain rule
• Stationary points

Circular Measure

• Arc length and sector area in radians

Coordinate Geometry of the Circle

• Equation of a circle: centre and radius
• Intersection of a circle and a line
• Tangents to a circle
• Intersection of two circles

Equations, Inequalities and Graphs

• Features of a cubic graph and its modulus
• Solving cubic inequalities
• Solving modulus equations
• Solving modulus inequalities
• Substitution to quadratic form

Factors of Polynomials

• Finding factors of a polynomial
• The remainder and factor theorems
• Solving cubic equations

Functions

• Composite functions
• Finding the inverse of a function
• The graphical relationship between f and its inverse
• The modulus of a function
• Explaining why a function has no inverse
• Function notation
• What makes a mapping a function

Logarithmic and exponential functions

• Solving exponential equations
• Laws of logarithms and change of base
• Properties, graphs and asymptotes

Permutations and Combinations

• Arrangement and selection problems
• Factorial, nPr, and nCr notation
• Recognising permutations vs combinations

Quadratic Functions

• Discriminant conditions
• Quadratic inequalities
• Maximum and minimum value by completing the square or differentiation
• Range of a quadratic for a restricted domain
• Solving quadratic equations for real roots

Series

• nth term and sum of an AP or GP
• Recognising arithmetic and geometric progressions
• The general term of a binomial expansion
• Binomial theorem expansion
• GP convergence and sum to infinity

Simultaneous Equations

• Simultaneous equations, linear and nonlinear

Straight-line graphs

• Straight-line equation forms
• Linear law: transforming relationships
• Midpoint, length, and perpendicular bisector
• Parallel and perpendicular lines

Trigonometry

• Amplitude, period, and related graphs
• Proving trigonometric identities
• The six trig functions for any magnitude
• Solving trigonometric equations
• Drawing and using trig graphs
• The Pythagorean trig identities

Vectors in Two Dimensions

• Magnitude and arithmetic of vectors
• Vector notation
• Position vectors and unit vectors
• Velocity vectors and kinematics