Maths IGCSE.pdf

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Information Systems Management
ISMM1-UC 726

Mathematics IGCSE notesIndex1 Decimals and standard form 2 Accuracy and Error 3 Powers and roots click on a topic to 4 Ratioproportion visit the notes 5 Fractions ratios 6 Percentages 7 Rational and irrational numbers 8 Algebra simplifying and factorising 9 Equations linear quadratic simultaneous 10 Rearranging formulae 11 Inequalities 12 Parallel lines bearings polygons 13 Areas and volumes similarity 14 Trigonometry 15 Circles 16 Similar triangles congruent triangles 17 Transformations 18 Loci and ruler and compass constructions 19 Vectors 20 Straight line graphs 21 More graphs 22 Distance velocity graphs 23 Sequences trial and improvement 24 Graphical transformations 25 Probability 26 Statistical calculations diagrams data collection 27 Functions 28 Calculus 29 Setsalso use the intranet revision course of question papers and answers by topic 1 Decimals and standard form top a multiplying and dividing25136iMove the decimal points to the right until each is a whole number noting the total number of moves perform the multiplication then move the decimal point back by the previous total so the answer is 34 251363400Note in the previous example that transferring a factor of 2 or even better 4 from the 136 to the 25 makes it easier2513625434254341003434000001750042ii Move both decimal points together to the right until the divisor is a whole number perform the calculation and that is the answer 17542 but simplify the calculation by cancelling down any factors first 0256In this case both numbers share a 7 so divide this outand004166025 so the answer is00416iii decimal places To round a number to n dp count n digits to the right of the decimal point If thth5the digit following the n isthen the n digit is raised by 1 eg round 3012678 to 3 dpso 3013 to 3 dp 30126783012678iv significant figures To round a number to n sf count digits from the left starting with the first nonzero digit then proceed as for decimal places eg round 310985 to 3 sf so 3110 to 3 sf 310985310985eg round 00030162 to 3 sfso 000302 to 3 sf 0003016200030162 b standard formiii Convert the following to standard form a 25 000 b 00000123 110xMove the decimal point until you have a number x whereand the number of places you moved the point will indicate the numerical value of the 45250002510 and 0000012312310 power of 10 So56 As all the ivmultiplying in standard form 44103510elements are multiplied rearrange them thus 561112 443510101541015410 2 123210vdividing in standard formAgain rearrange the calculation to 3251012393225101012810 67The 251037510vi addingsubtracting in standard form hardest of the calculations Convert both numbers into the same denomination 67ie in this case 10 or 10 then add 7770251037510410 Questions25415a 2550015 bc Convert into standard form and multiply2500000000000000002432 2610210d34 e 155102510 Answers25415381 soa 254153810 bNotice a factor of 5 so lets cancel it first 25500152550155103170710325102410610 c32526210101310 d33315510025101310 e3
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