# Mathematics (Higher)

GCSE Course Outlines

The emphasis given to each topic will vary according to the strengths and weaknesses of the students in the groups and the syllabuses for which they have been taught. It is therefore important that students give as much detail as possible on the questionnaire about their syllabus and any specific areas of difficulty.

**Number**

Basic arithmetic; use of calculators; fractions and percentages; ratio; estimation and appropriate degree of accuracy; possible effect of errors on calculation; trial and improvement methods; standard form; evaluating formulae (including examples with negative and fractional numbers).

**Algebra**

Sequences and number patterns; symbolic notation; expressing general laws in symbolic form; manipulation of formulae; factorising; convergence and divergence of series; powers and roots; direct and inverse proportion; solving simple equations and inequalities; simultaneous equations; quadratic equations; trial and improvement for polynomial equations; growth and decay rates; mappings; graphs of functions and inequalities; y = mx + c; graphical solution of equations; sketching and comparing graphs of functions; drawing a tangent to find gradient; estimating area under a graph.

**Shape and Space**

Drawing and measurement; 2-D representation of 3-D objects; angles; symmetry; similarity; bearings; 3-dimensional coordinates; plane and solid figures; areas and volumes; arc length and sector area; congruent triangles; similar solids; vector addition and subtraction; transformations (including combined and inverse transformations and matrix representation); loci; networks; Pythagoras' theorem; sine; cosine; and tangent of any angle (including 3-D problems); graphs of trigonometrical functions; sine and cosine rules.

**Handling Data**

Design and use of an observation sheet/questionnaire; sampling; statistical diagrams including histograms; scatter diagrams and the idea of correlation; probability (estimating probabilities, independent and mutually exclusive events); mean, median and mode; frequency polygons and cumulative frequency diagrams; upper and lower quartiles; tree diagrams; flow diagrams; dispersion and standard deviation; the normal distribution; critical path analysis diagrams.