1.01c c) Be able to show disproof by counter example. Section 5: The 7890 specification explicitly states that: candidates ‘…, Specification are expected to understand the nature of a mathematical Learners should understand that this means that, Content proof. In A2 units, questions that require proof by contradiction or disproof by counter-example may be given a statement of the form is true then P(x) Q(x) set.’ “if is a single for which is true but x P(x) true”, finding Q(x) is false is to offer a disproof by counter example. Questions requiring proof will be set on content with which the learner is expected to be familiar e.g. Appendix B: The notation for the terms and ‘integer’, ‘real’ ‘rational’ can through study of GCSE (9-1) or AS Level Mathematical be found in Appendix B of the 7890 specification under Set Mathematics. Notation Notation. The term is implicitly covered in C1 in ‘irrational’ dealing with Indices and Surds. Learners are expected to understand and be able to C1 Indices and – use the terms and “integer”, “real”, “rational” Surds (b) & (c) “irrational”. 1.02 Algebra and Functions 1.02a a) Understand and be able to use the laws of indices C1 Indices and (a) understand rational indices (positive, negative and zero), – for all rational exponents. Surds (a) & (b) and use laws of indices in the course of algebraic applications Includes negative and zero indices. (b) recognise the equivalence of surd and index notation Problems may involve the application of more than (e.g. ) one of the following laws: .
1.01c c) Be able to show disproof by counter example. Learners should understand that this means that, given a statement of the form “if P(x) is true then Q(x) is true”, finding a single x for which P(x) is true but Q(x) is false is to offer a disproof by counter example. Questions requiring proof will be set on content with which the learner is expected to be familiar e.g. through study of GCSE (9-1) or AS Level Mathematics. Learners are expected to understand and be able to use the terms “integer”, “real”, “rational” and “irrational”. Section 5: Specification Content Appendix B: Mathematical Notation C1 – Indices and Surds (b) & (c) The 7890 specification explicitly states that: ‘…, candidates are expected to understand the nature of a mathematical proof. In A2 units, questions that require proof by contradiction or disproof by counter-example may be set.’ The notation for the terms ‘integer’, ‘real’ and ‘rational’ can be found in Appendix B of the 7890 specification under Set Notation. The term ‘irrational’ is implicitly covered in C1 in dealing with Indices and Surds. 1.02 Algebra and Functions 1.02a a) Understand and be able to use the laws of indices for all rational exponents. Includes negative and zero indices. Problems may involve the application of more than one of the following laws: . C1 – Indices and Surds (a) & (b) (a) understand rational indices (positive, negative and zero), and use laws of indices in the course of algebraic applications (b) recognise the equivalence of surd and index notation (e.g. )
360173-mapping-guide-legacy-as-and-a2-units-7890-to-h240.docx