Course outline

The revision courses are for Higher Tier students and will consist of 14 hours of tuition over 2 days. The emphasis will be mainly on Higher Tier topics depending on the strengths /weaknesses of the group. (It may not be possible to cover every topic of the syllabus.)

Aim

• to build confidence and understanding of key mathematical ideas
• to enable the student to interpret and to solve a range of mathematical problems
• to improve problem solving techniques both with and without a calculator
• to strengthen revision techniques and strategies.

Key Topics Covered

Ma2: Number and Algebra

• Basic Operations – BIDMAS; directed number; rounding; upper and lower bounds (appropriate degrees of accuracy)
• Factors and Multiples – factors/divisors and multiples; prime factor decomposition; HCF& LCM
• Indices – index notation; laws of indices for multiplication and division of integer powers; squares, cubes, square roots and cube root; fractional and negative indices to solve equations; standard form; dividing and multiplying by powers of 10
• Fractions, Decimals and Percentages (FDP) – equivalent fractions; simplifying fractions; ordering fractions; basic operations with FDP; reciprocals; finding a fraction of an amount; terminating and recurring decimals; repeated proportional change (compound interest); finding a given percentage; percentage increase and decrease; reverse percentages; interchanging between FDP; simplifying ratios and how they relate to fractions; dividing a quantity in a given ratio
• Algebraic expressions – general manipulation: expanding brackets, simplifying, factorising, substituting numerical values, changing the subject of a formula (including where the subject appears twice or a function of the subject appears)
• Language of Algebra – expressions, formulae, equations, identities, factors etc...; f(x) notation
• Equations – forming and solving linear equations; solving simple non-linear equations; solving simple linear inequalities; factoring quadratics; solving quadratics by all three methods; simultaneous equations (up to one linear and one quadratic) and their graphical representation; systems of linear inequalities with two unknowns and representing them in the x-y plane; systematic trial and improvement
• Sequences – find terms from both nth term and recurrence relation formulae, generating terms from these formulae.
• Graphs – plotting and sketching y=mx+c; understanding gradient (parallel and perpendicular) and intercepts; finding the equation of a straight lin; plotting quadratics, cubics, basic reciprocals, trig and exponentials; graphical methods for solving equations; drawing and interpreting graphs from a scientific context; transformations (inc. transformations of functions); equations of circles
• Proportion – inverse and direct proportion (including squared proportion etc...)
• Surds – calculating with exact irrationals (surds and pi); rationalising
• Arithmetic ‘tricks’ – scaling when multiplying and dividing two numbers (e.g when dividing by a decimal)

Ma3: Shape, Space and Measure

• Angles - properties of angles at a point and on a straight line; perpendicular lines; alternate, opposite and corresponding angles; angles in a triangle; sums of interior and exterior angles; bearings
• Polygons – properties of equilateral, isosceles and right angle triangles; SSS, SAS, ASA and RHS congruence; similar triangles (extended to general polygons); angle properties of quadrilaterals; properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus; formulae for areas and perimeters; properties of regular polygons
• Area and Volume – calculate the area and volume of simple and compound 2D and 3D shapes; arc length and sector area; changing units; the link between length, area and volume scale factors
• Transformations – performing and describing rotations, reflections, translations and enlargements (including fractional and negative scale factors); combining transformations; vector notation and graphical representation; vector arithmetic; resultant vector; reflectional and rotational symmetry (congruence in this context and similarity in the context of enlargement)
• Co-ordinates – midpoint and distance of a line segment
• Constructions – ruler and compass constructions: midpoint and perpendicular bisector of a line segment, perpendicular from a point to a line, perpendicular from a point on a line, bisector of an angle, triangle given all three sides; constructing a triangle using a ruler and protractor;loci
• Pythagoras’ Theorem – solving 2D and 3D problems
• Trigonometry – using sin, cos and tan; angle between a plane and a line; 0.5absinC; sine rule and cosine rule in 2D and 3D
• Circle theorems – construct geometrical proofs using the following: tangent and radius, perpendicular bisector of a chord, tangents from a point being of equal length, same/alternate segment theorem, angle in a semi-circle, angle at the centre vs angle at circumference (all cases), cyclic quadrilaterals; links to regular polygons
• Solids – nets; plans; isometric drawing

Ma4: Handling Data

• Representing Data – create and interpret pie charts, line graphs (time series), scatter graphs, correlation, frequency diagrams, stem-and-leaf diagrams, two-way tables, bar charts, pictograms, frequency polygons, frequency diagrams, cumulative frequency tables and diagrams, box plots, histograms (frequency density) and tree diagrams for categorical, discrete and/or continuous data as appropriate; adding and using lines of best fit
• Location / Spread – calculating the mean, median, mode range and IQR from small data sets; finding median, modal class and IQR for large data sets; moving averages; calculating an estimate of the mean from grouped data
• Probability – systematic listing; probability from relative frequency; recognising events that are mutually exclusive, independent or neither; calculations with two or more probabilities
• Collecting Data – random and stratified sampling; awareness of bias; designing surveys
• Correlation – identifying the strength and sign of any correlation and relating it to the context of the data; appreciating the linearity of correlation

Other Information

The revision courses do not cover the coursework component of GCSE Mathematics.

Students will be required to bring a scientific calculator.