Download harrow school easter revision courses

EASTER REVISION COURSES 2017
COURSE OUTLINE FOR
GCSE (9-1) MATHEMATICS
SUITABLE FOR EXAM BOARDS: ALL, COURSE CODE: GCMATALL
The emphasis of this revision course 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). Students will require a scientific calculator.
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
1. Number
• 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/decrease; reverse percentages.
• Surds – calculating with exact irrationals (surds and pi); simplifying and rationalising
• Upper & Lower Bounds – calculating and interpreting limits of accuracy
2. Algebra
• 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 linear and quadratic 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; •
Sequences – find terms from both nth term and recurrence relation formulae, generating terms from these formulae. Find
expressions for the nth term for both linear and quadratic sequences.
• 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 and finding equation of a tangent to circle at a given point. Turning points of quadratics by completing the
square.
• Algebraic Fractions– simplifying by factorising and expressing a sum as a single fraction.
• Simple Proof – using algebra for consecutive integers and odd & even numbers.
• Functions – use of notation, inverse and composite functions
3. Ratio, proportion and rates of change
• Ratio simplifying ratios and how they relate to fractions; dividing a quantity in a given ratio
• Proportion – inverse and direct proportion (including squared proportion etc...)
• Rates of Change estimate gradients of curves
Harrow School Enterprises Ltd.
5 High Street, Harrow on the Hill, Middlesex, HA1 3HP
Tel: 020 8426 4638 Fax: 020 8864 7180 E-mail: [email protected]
EASTER REVISION COURSES 2017
COURSE OUTLINE FOR
GCSE (9-1) MATHEMATICS
SUITABLE FOR EXAM BOARDS: ALL, COURSE CODE: CMATALL
• Numerical methods Solving equations using systematic trial and improvement and iterative equations.
• Scale factors the link between length, area and volume scale factors
4. Geometry and Measures
• 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; congruence; similar triangles; 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; use the basic congruence criteria for
triangles (SSS, SAS, ASA, RHS)
• Area and Volume – calculate the area and volume of simple and compound 2D and 3D shapes; arc length and sector area;
changing units
•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
• Trigonometry – Pythagoras’ theorem ; using sin, cos and tan; angle between a plane and a line; ½absinC; sine rule and
cosine rule in 2D/3D. the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90° and tan θ for θ = 0°, 30°, 45° and 60°
• 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
• Vectors – to include ratios and problems involving parallel vectors & collinear points.
5. Probability
• Probability systematic listing; probability from relative frequency; recognising events that are mutually exclusive, independent
or neither; calculations with two or more probabilities. Two way tables, tree diagrams including non-replacement; Venn
diagrams including set notation. Conditional probability.
6. Statistics
• Representing Data – create and interpret pie charts, line graphs (time series), scatter graphs, correlation & lines of best fit,
danger of extrapolation, 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).
• 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
• Collecting Data – random and stratified sampling; awareness of bias; designing surveys
Please note that the emphasis given to particular topics will be weighted to the needs and requirements of the candidates in the group.
GCSE courses include 14 hours of tuition (excluding breaks but including some testing) taken over 2 consecutive days.
For more information and availability, please look at our Fees and Dates.
Harrow School Enterprises Ltd.
5 High Street, Harrow on the Hill, Middlesex, HA1 3HP
Tel: 020 8426 4638 Fax: 020 8864 7180 E-mail: [email protected]