Higher 1

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.

Contents

1.Numbers and algebra - Multiples, factors and primes •Decimals •Estimation •Fractions • Equivalence of decimals, fractions and percentages •Powers and indices •Trial and improvement •Standard form.

2. Geometrical patterns - Tessellation •Quadrilaterals •Regular polygons •Sum of angles in a polygon •Symmetry •Transformations.

3. Algebraic manipulation - Brackets •Algebra to solve problems •Manipulating formulae and factorising •Mental strategies for long multiplication.

4. Working with data - Using statistics • Histograms with unequal class intervals •Analysing small sets of data •Standard deviation •Using cumulative frequency diagrams •Estimating the mean of a grouped frequency distribution.

5. Pythagoras' theorem and similar shapes - Proving and Applying Pythagoras' theorem •Manipulating square roots•Pythagoras' theorem without a calculator•Similarity • Areas of similar shapes.

6. Percentages - Using percentage •Percentage scale factors •Reversing a percentage change •Repeated percentage change.

7. Cubes and sequences - Linear sequences • Difference patterns •Find the nth term of a quadratic, cubic and other sequences •Sequences of cube models •Sequences of similar cube models •Proving theorems about the surface areas of cube models •Exploring volumes, surface areas and lengths in cuboids.

8. Rate, ratio and proportion - Using ratios •Rates: speed and density •Direct and Inverse proportion.

9. Trigonometry - Sine, cosine and tangent •Solving right-angled triangles •Using trigonometry to solve problems •Trigonometry and polygons •Angles greater than 90°, graphs of trigonometric functions.

10. Probability - Drawing conclusions from experiments •Relative frequency •Two-way tables •Identifying all possible outcomes •Combining probabilities •Conditional probability •Further problems.

11. Graphs - Equations of straight lines •Practical uses of straight-line graphs •Non-linear graphs • Interpreting graphs of real-life situations.

12. Measures - Metric and Imperial measures •Areas of plane shapes, including sectors and segments of circles •Upper and lower bounds •Volume and surface area of prisms •Pyramids, cones and spheres •Similar solids •Distinguishing formulae

13. Equations - Linear equations •Using graphs to solve linear and simultaneous equations •Solving simultaneous equations algebraically •Using simultaneous equations to solve problems •Using factorisation to solve quadratic equations •Quadratic equations and graphs•Solving equations by trial and improvement.

14. Geometry - Solid shapes and nets •Triangles •Congruence • Loci •Ruler and compass constructions •Circle theorems.

Revision Exercises

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