Mathematics Revision Guide: IGCSE

by Martin Law

• ISBN13: 9780521539029
• ISBN10: 0521539021
• Format: Paperback
• Copyright: 2004-05-17
• Publisher: Cambridge University Press

Summary

Written by an experienced mathematics teacher Karen Morrison, the text is enquiry-based, designed for face-to-face learning and has an interactive approach to the subject. Case studies and questions are used to help students understand the implications of the topic.

Table of Contents

Curriclum outline	vi
Number, set notation and language	1	(7)
Know natural numbers, integers, prime numbers, common factors and multiples, rational and irrational numbers; describe sequences, patterns using words and nth term
Set definition and elements, universal set and complement of set, empty sets, subsets, intersection and union of sets, Venn diagrams
Squares, square roots and cubes	8	(1)
Perform calculations with squares, square roots and cubes, with and without calculator
Directed numbers	9	(1)
Directed numbers in practical situations; arithmetic with directed numbers
Vulgar and decimal fractions and percentages	10	(3)
Fraction and percentage calculations and conversions; equivalence
Ordering	13	(1)
Order numbers by magnitude using =, ≠, >, <, ≥, ≤ signs
Standard form	14	(2)
Change numbers into standard form and vice versa
The four rules	16	(4)
Calculations with whole numbers, decimals, BODMAS
Estimation	20	(3)
Estimate numbers using rounding, decimal places, significant figures
Limits of accuracy	23	(2)
Limits of accuracy, upper and lower bounds of numbers
Upper and lower bounds of problems, such as areas and perimeters
Ratio, proportion, rate	25	(6)
Ratio, direct and inverse proportion, rates, scales, average speed
Direct and inverse variation in algebraic terms; increase and decrease by a given ratio
Percentages	31	(3)
Percentages of quantities, one quantity as a percentage of another, percentage increase and decrease
Reverse percentages
Using an electronic calculator	34	(2)
Efficient use of a calculator, appropriate checks of accuracy
Measures	36	(3)
Know and convert units of mass, length, capacity, area and volume
Time	39	(4)
12- and 24-hour clock conversions, time calculations, timetables, dials
Money	43	(4)
Currency conversions, calculations involving money
Graphs in practical situations	47	(4)
Interpret and construct coordinate graphs, e.g. travel and conversion graphs
Speed-time graphs, acceleration/deceleration, distance travelled
Graphs of functions	51	(8)
Construct tables of values; draw linear, quadratic, reciprocal graphs; find gradients, solve equations using graphs
Harder functions involving powers; estimate gradients of curves, solve equations
Straight line graphs	59	(3)
Calculate gradient and length of line from coordinates, obtain the equation of a straight line graph (v = mx + c)
Algebraic representation and formulae	62	(5)
Algebraic representation, substitution, simplification, transformation
Construct equations, transform harder formulae
Algebraic manipulation	67	(6)
Expand brackets, factorise
Harder algebraic expressions, algebraic fractions, factorisation using difference of two squares, quadratic, grouping methods
Functions	73	(2)
Find input and output of a function, inverse and composite functions
Indices	75	(3)
Rules for positive, negative, zero indices
Fractional indices
Solution of equations and inequalities	78	(6)
Solve linear and simultaneous equations
Solve quadratic equations by factorisation and formula, solve linear inequalities
Linear programming	84	(2)
Graphical inequalities, use of broken lines and shaded regions, solve for x and y
Geometric terms and relationships	86	(6)
Angle calculation; use of point, line, parallel and bearing; right, acute, obtuse and reflex angles; perpendiculars, similarity, congruence, types of triangles, quadrilaterals, circles, polygons and solid figures, nets
Areas and volumes of similar triangles, figures and solids
Geometrical constructions	92	(3)
Construct lines, angles, bisectors and simple shapes using ruler, protractor and compasses; scale drawings
Symmetry	95	(4)
Line and rotation symmetry, symmetrical properties of shapes
Solid shape symmetries, equal chords, perpendicular/tangent symmetry
Angle properties	99	(7)
Angles at a point and in parallel lines, shapes, circles
Irregular polygons, circle theorems
Locus	106	(8)
Constructions using compasses and ruler from fixed point, straight line, two points, two straight lines of a parallelogram and trapezium, volume of a cuboid, prism and cylinder, surface area of a cuboid and cylinder
Arc length and sector area of a circle; surface area and volume of a sphere, pyramid and cone
Trigonometry	114	(9)
Use bearings, find missing sides, angles in right-angled triangles, Pythagoras' theorem
Angles of elevation and depression, sine and cosine rules, sine and cosine functions between 90 and 360, area of triangles, three-dimensional trigonometry
Statistics	123	(11)
Interpret, tabulate and draw bar charts, pictograms, pie charts, histograms (equal intervals) from data; mean, mode and median calculations and uses; scatter diagrams, positive, negative and zero correlation
Histograms (unequal intervals), cumulative frequency diagrams, median, upper/lower quartiles, interquartile range, estimate of mean, modal class and median
Probability	134	(6)
Probability calculations of single events as fractions or decimals; probability scale from 0 to 1; probability of events not occurring, relative frequency
Combined probabilities using trees and possibility diagrams
Vectors in two dimensions	140	(5)
Describe translation using vectors; addition, multiplication by scalar quantities
Magnitude of vectors, represent vectors by line segments; sum and difference of vectors, position vectors
Matrices	145	(4)
Notation, addition, subtraction, multiplication of matrices; equations involving matrices; determinants and inverses
Transformations	149	(34)
Describe and perform reflections, rotations (multiples of 90°), translations, enlargements
Transformations and combinations including shears and stretches, matrix transformation
Practice exams
Core exams 1-5	157	(8)
Answers to practice Core exams	165	(2)
Extended exams 1-8	167	(12)
Answers to practice Extended exams	179	(4)
Formulae	183	(1)
Grade descriptions	184	(1)
Index	185