Intermediate 1

This resource from Nelson Thornes was for students following the Intermediate 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 - Place value • Multiples, factors and primes • Decimals • Rounding • Fractions • Fractions and decimals • Percentages, decimals and fractions • Standard form.

2. Geometrical patterns - Angles round a point • Symmetry • Angles and lines • Triangles • Quadrilaterals • Polygons • Angles in polygons.

3. Functions and formulae - Using rules with numbers • Calculating with negative numbers • Using algebra for functions • Using algebra to solve problems • Simplifying algebraic expressions • Order of operations • Substitution.

4. Working with data - Statistics and why we need them • Types of data • Answering questions using data • Representing data • Analysing data • Means of frequency distributions • Means of grouped frequency distributions.

5. Area and Pythagoras' theorem - Areas of triangles and parallelograms • Coordinates and area • Areas of tilted squares • Proving area formula for tilted squares • Pythagoras' theorem • Isosceles right-angled triangle.

6. Percentages - Percentages, fractions and decimals • Percentages of quantities • Percentage change • Finding one number as a percentage of another * Using percentages to compare amounts • Repeated percentage changes • Reverse percentages.

7. Cubes and sequences - Cube models • Linear sequences • Extended difference tables • Quadratic sequences. Explaining your results.

8. Rate and ratio - Ratio • Proportional division • Map scales • Scale drawing • Speed.

9. Trigonometry - Naming sides of triangles • Sketching and drawing right-angled triangles • Sine, cosine and tangent as multipliers • Length of a side • Length of the hypotenuse • The trigonometric graphs • Finding angles • Using trigonometry to solve problems.

10. Probability - Using equally likely outcomes • Drawing conclusions from experiments • Experimental probabilities • Adding, subtracting and multiplying fractions • Probabilities of more than one event • Tree diagrams

11. Graphs - Making straight lines • Exploring rules for straight Iines • Gradient of a line and intercept • Practical uses of straight line graphs • Non-linear graphs.

12. Measures - Metric and Imperial measures • Circumference and area of a circle • Volume • Surface area of prisms.

13. Equations - Solving equations by doing and undoing • Solving equations by balancing. Working with brackets • Thinking with letters • Forming and solving linear equations • Quadratic equations by trial and improvement.

14. Geometry -Accurate drawing • Solid shapes and nets • Triangles, including the exterior angle theorem • Congruence • Loci • Ruler and compass constructions Revision Exercises

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