Higher 2

This resource from Nelson Thornes was for students following the Higher tier in mathematics and part of a series of books which delivered the three tier structure of GCSE. Each chapter begins with learning outcomes and contains reference boxes which explain techniques or concepts to be mastered, as well as discussion points and key facts. The second part of the book is a comprehensive revision guide which provides notes and relevant questions for the whole syllabus.

Contents

1. Extending number systems - Powers, roots and indices • Standard form with and without a calculator • Writing rational numbers as terminating or recurring decimals • Converting recurring decimals to fractions • Irrational numbers • Surds • The real numbers.

2. Transformations and vectors - Revisiting transformations • Combining reflections and rotations • Negative enlargement • Combining enlargements • Properties of transformations • Congruent triangles • Similarity • Combining vectors • Velocity vectors • Force vectors

3. Quadratic equations - Factorising quadratic expressions • Completing the square • Using completing the square • Solving quadratic equations by factorising • Solving quadratic equations by completing the square • The formula for solving quadratic equations • The number of solutions of a quadratic equation • Problems involving quadratic equations.

4. Statistics and probability - Counting systematically • Counting populations • Sampling techniques. Designing questionnaires • Correlation and lines of best fit • Standard deviation • Analysing and comparing sets of data • Using probability to analyse random events.

5. Algebraic manipulation - Algebraic fractions • Solving equations involving algebraic fractions • Changing the subject of a formula • Inequalities • Graphs of inequalities • Using inequalities for modelling.

6. Further trigonometry - Pythagoras' theorem and trigonometry in three dimensions • The sine and cosine rules • The formula 1/2 ab sinC • Applications of the sine and cosine rules • Sines, cosines and tangents for angles of any size • Trigonometric equations • Rationals and irrationals.

7. Using graphs to solve problems - Revisiting quadratic graphs • Transforming graphs • Graphs of trigonometric functions • Graphs of various functions • Solving equations from intersecting graphs • Using graphs to solve inequalities • The area under a curve • Tangents to graphs.

8. Circles and vectors - Chords and tangents and circles • Revisiting some circle theorems • The alternate segment theorem and other theorems • Vector geometry • Ruler and compass constructions and loci • Rational and irrational ratios in polygons and circles • Gradients of perpendicular lines and equations of circles and their tangents. Revision Exercises

Please note, some pages and images have been removed from the resource file.