A student named Elena makes the claim that there is a finite set of prime numbers P={p1,p2,p3,…,pk}P = \{p_1, p_2, p_3, \dots, p_k\}P={p1,p2,p3,…,pk} where pk p_k\,pk is the largest prime. Use the method of proof by contradiction to show that Elena's claim is incorrect, and thus prove that there are infinitely many prime numbers.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.