MathsNotes - Mathematics IGCSE notes Index 1 Decimals and...

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Mathematics IGCSE notes Index 1. Decimals and standard form 2. Accuracy and Error 3. Powers and roots click on a topic to visit the notes 4. Ratio & proportion 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. Sets {also use the intranet revision course of question papers and answers by topic }
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1. Decimals and standard form top (a) multiplying and dividing (i) Move 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: 2.5 1.36 × , so the answer is 25 136 3400 →× = 3.4 {Note in the previous example, that transferring a factor of 2, or even better, 4, from the 136 to the 25 makes it easier: } 25 136 25 (4 34) (25 4) 34 100 34 3400 ×=× × =× ×= ×= (ii) Move both decimal points together to the right until the 0.00175 0.042 ÷ divisor is a whole number, perform the calculation, and that is the answer. 1.75 42 →÷ , but simplify the calculation by cancelling down any factors first. In this case, both numbers share a 7, so divide this out: , and 0.25 6 0.0416 60 . 2 5 ± , so the answer is 0.0416 (iii) decimal places To round a number to n d.p., count n digits to the right of the decimal point. If the digit following the n th is , then the n 5 th digit is raised by 1. e.g. round 3.012678 to 3 d.p. so 3.012678 3.012|678 3.013 to 3 d.p. (iv) significant figures To round a number to n s.f., count digits from the left starting with the first non-zero digit, then proceed as for decimal places. e.g. round 3109.85 to 3 s.f., 3109.85 so 310|9.85 3110 to 3 s.f. e.g. round 0.0030162 to 3 s.f., 0.0030162 , so 0.00301|62 0.00302 to 3 s.f. (b) standard form (iii) Convert the following to standard form: (a) 25 000 (b) 0.0000123 Move the decimal point until you have a number x where 11 0 x < , and the number of places you moved the point will indicate the numerical value of the power of 10. So 4 25000 2.5 10 , and 5 0.0000123 1.23 10 (iv) multiplying in standard form: ( ) 5 (4.4 10 ) 3.5 10 ××× 6 As all the elements are multiplied, rearrange them thus: () 5 6 11 12 (4.4 3.5) 10 10 15.4 10 1.54 10 =×× × = × = × 2
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(v) dividing in standard form: 12 3 3.2 10 2.5 10 × × Again, rearrange the calculation to 12 3 9 (3.2 2.5) (10 10 ) 1.28 10 ÷× ÷ = × (vi) adding/subtracting in standard form: The hardest of the calculations. Convert both numbers into the same denomination, i.e. in this case 10 67 (2.5 10 ) (3.75 10 ) ×+ × 6 or 10 7 , then add.
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MathsNotes - Mathematics IGCSE notes Index 1 Decimals and...

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