Mathematics Pure Mathematics 1 - "Goldie, Sophie" (Hodder Education London, 2018)
; 1 Problem solving1 b; 1.1 Solving problems; 1.2 Writing mathematics; 1.3 Proof; 2 Algebra; 2.1 Using and manipulating surds; 2.2 Quadratic equations; 2.3 Solving quadratic equations; 2.4 Equations that cannot be factorised; 2.5 The graphs of quadratic functions; 2.6 The quadratic formula; 2.7 Simultaneous equations; 2.8 Inequalities; 3 Coordinate geometry; 3.1 Coordinates; 3.2 Plotting, sketching and drawing; 3.3 The gradient of a line. 3.4 The distance between two points3.5 The midpoint of a line joining two points; 3.6 The equation of a straight line; 3.7 Finding the equation of a line; 3.8 The intersection of two lines; 3.9 Drawing curves; 3.10 The circle; 3.11 The intersection of a line and a curve; 4 Sequences and series; 4.1 Definition sand notation; 4.2 Arithmetic progressions; 4.3 Geometric progressions; 4.4 Binomial expansions; 5 Functions and transformations; 5.1 The language of functions; 5.2 Composite functions; 5.3 Inverse functions; 5.4 Using transformations to sketch curves. 5.5 The equation of a transformation of a curve5.6 Combining transformations; 6 Differentiation; 6.1 The gradient of a curve; 6.2 Finding the gradient of a curve; 6.3 Finding the gradient from first principles; 6.4 Differentiating by using standard results; 6.5 Using differentiation; 6.6 Tangents and normals; 6.7 Maximum and minimum points; 6.8 Increasing and decreasing functions; 6.9 Points of inflexion; 6.10 The second derivative; 6.11 Applications; 6.12 The chain rule; 7 Integration; 7.1 Reversing differentiation; 7.2 Finding the area under a curve; 7.3 Area as the limit of a sum. 7.4 Areas below the x-axis7.5 The area between two curves; 7.6 The area between a curve and the y-axis; 7.7 The reverse chain rule; 7.8 Improper integrals; 7.9 Finding volumes by integration; 8 Trigonometry; 8.1 Trigonometry background; 8.2 Trigonometrical functions; 8.3 Trigonometrical functions for angles of any size; 8.4 The sine and cosine graphs; 8.5 The tangent graph; 8.6 Solving equations using graphs of trigonometrical functions; 8.7 Circular measure; 8.8 The length of an arc of a circle; 8.9 The area of a sector of a circle. 8.10 Transformations and graphs of trigonometrical functionsAnswers