AQA A Level Mathematics Year 1 (AS).

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Cover; Book title; Copyright; Contents; Getting the most from this book; Prior knowledge; 1 Problem solving; 1.1 Solving problems; 1.2 Writing mathematics; 1.3 Proof; Problem solving: Mountain modelling; 2 Surds and indices; 2.1 Using and manipulating surds; 2.2 Working with indices; 3 Quadratic functions; 3.1 Quadratic graphs and equations; 3.2 The completed square form; 3.3 The quadratic formula; 4 Equations and inequalities; 4.1 Simultaneous equations; 4.2 Inequalities; 5 Coordinate geometry; 5.1 Working with coordinates; 5.2 The equation of a straight line.

5.3 The intersection of two lines5.4 The circle; 5.5 The intersection of a line and a curve; Problem solving: Integer point circles; Practice questions: Pure mathematics 1; 6 Trigonometry; 6.1 Trigonometric functions; 6.2 Trigonometric functions for angles of any size; 6.3 Solving equations using graphs of trigonometric functions; 6.4 Triangles without right angles; 6.5 The area of a triangle; 7 Polynomials; 7.1 Polynomial expressions; 7.2 Dividing polynomials; 7.3 Polynomial equations; 8 Graphs and transformations; 8.1 The shapes of curves; 8.2 Using transformations to sketch curves.

8.3 Using transformations8.4 Transformations and graphs of trigonometric functions; 9 The binomial expansion; 9.1 Binomial expansions; 9.2 Selections; Practice questions: Pure mathematics 2; 10 Differentiation; 10.1 The gradient of the tangent as a limit; 10.2 Differentiation using standard results; 10.3 Tangents and normals; 10.4 Increasing and decreasing functions, and turning points; 10.5 Sketching the graphs of gradient functions; 10.6 Extending the rule; 10.7 Higher order derivatives; 10.8 Practical problems; 10.9 Finding the gradient from first principles; Problem solving: Proofs.

11 Integration11.1 Integration as the reverse of differentiation; 11.2 Finding areas; 11.3 Areas below the x axis; 11.4 Further integration; 12 Vectors; 12.1 Vectors; 12.2 Working with vectors; 12.3 Vector geometry; 13 Exponentials and logarithms; 13.1 Exponential functions; 13.2 Logarithms; 13.3 The exponential function; 13.4 The natural logarithm function; 13.5 Modelling curves; Practice questions: Pure mathematics 3; 14 Data collection; 14.1 Using statistics to solve problems; 14.2 Sampling; 15 Data processing, presentation and interpretation; 15.1 Presenting different types of data.

15.2 Ranked data15.3 Discrete numerical data; 15.4 Continuous numerical data; 15.5 Bivariate data; 15.6 Standard deviation; 16 Probability; 16.1 Working with probability; Problem solving: Alphabet puzzle; Problem solving: Estimating minnows; 17 The binomial distribution; 17.1 Introduction to binomial distribution; 17.2 Using the binomial distribution; 18 Statistical hypothesis testing using the binomial distribution; 18.1 The principles and language of hypothesis testing; 18.2 Extending the language of hypothesis testing; Practice questions: Statistics; 19 Kinematics.

Give students the confidence to identify connections between topics and apply their reasoning to mathematical problems, so as to develop a deeper understanding of mathematical concepts and their applications, with resources developed with subject specialists and MEI (Mathematics in Education and Industry).- Prepare students for assessment with plenty of practice questions, worked examples and skill-focused exercises. - Help build connections between topics with points of interest and things to notice such as links to real world examples and noticing patterns in the mathematics.- Enhance under.

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