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# Mathematics 1 11 May, 2015M L1 MH. your maths teacher for Maths 1 Dr Michael Hughes (Mike) The required textbook A2 Pure Mathematics.

## Presentation on theme: "Mathematics 1 11 May, 2015M L1 MH. your maths teacher for Maths 1 Dr Michael Hughes (Mike) The required textbook A2 Pure Mathematics."— Presentation transcript:

Mathematics 1 11 May, 2015M L1 MH

your maths teacher for Maths 1 Dr Michael Hughes (Mike) m.s.hughes@exeter.ac.uk The required textbook A2 Pure Mathematics C3/C4 11 May, 2015M L1 MH

Lesson 1- Basics 11 May, 2015M L1 MH Objectives : - Scientific Notation - Error estimation - Surds recap - Algebraic expression recap

Standard Form 11 May, 2015M L1 MH A short-hand way of writing large or small numbers without writing all of the zeros Example : The Distance From the Sun to the Earth 93,000,000

Step 1 Move decimal left Leave only one number in front of decimal 11 May, 2015M L1 MH Step 2 Write number without zeros

Step 3 Count how many places you moved decimal Make that your power of ten 11 May, 2015M L1 MH

Standard Form 11 May, 2015M L1 MH Example: Partial pressure of CO 2 in atmosphere  0.000356 atm. This number has 3 sig. figs, but leading zeros are only place-keepers and can cause some confusion. So expressed in standard form this is 3.56 x 10 -4 atm This is much less ambiguous, as the 3 s.f. are clearly shown.

Engineering Notation 11 May, 2015M L1 MH This is the same as scientific notation except the POWER is replaced by the letter E Examples NumberScientific Notation/ Standard Form Engineering Notation 1001.x10 2 1.E2 1000 (1 sig fig)1. x 10 3 1.E3 1000 (2 dec pl)1.00x 10 3 1.00E3 -0.00123-1.23x 10 -3 -1.23E-3 10071.007x10 3 1.007E3

Rational/Irrational Numbers Rational numbers can be expressed as a fraction with no common factors Irrational numbers can not be expressed as a fraction in its lowest terms Surds are irrational numbers like π, √2 They have a non repeating infinite pattern of decimal places. 11 May, 2015M L1 MH

Rules for Surds Try not to be lazy and therefore express them in their lowest form Example 11 May, 2015M L1 MH Surd Rules

Rationalise the denominator If you have the following Rationalise it by multiplying by 1 11 May, 2015M L1 MH Example Exercise 5a page 130

Errors Suppose a cars petrol tank holds 50 litres of petrol and you think the car does 12km for each litre of petrol. Is it safe to travel 600 km on a full tank of Petrol? Solution In practice the car may travel as little as 10km / ltr or as much as 12.5 km/ltr Therefore one might be able to drive anywhere between 500 ≤ distance ≤ 650 11 May, 2015M L1 MH

Example If we say a piece of wood is 5.0 m long We are implying that it is 4.95 ≤ length ≤ 5.05 if we say a piece of wood is 5.23 m long We are implying that it is 5.225 ≤ length ≤ 5.235 11 May, 2015M L1 MH

Relative and absolute error A lawn is said to be 12m x 22m (a) Between what bounds does the area lie The true Area is 272.55m 2 and the householder measured the area as 264m 2 (b) What is the absolute error (c) What is the relative (Percentage) error 11 May, 2015M L1 MH

Solution Max Area is 12.5 x 22.5 = 281.25 Min area is 11.5 x 21.5 = 247.25 247.25 ≤ Area ≤ 247.25 Absolute error is |272.55-264| = 8.5m2 Relative error is |272.55-264| = absolute error = 3.1% 272.55 true value 11 May, 2015M L1 MH

Question Exercise Find the percentage error when π is given the following approximate values: (i) 3(ii) (iii) 3.14(iv) √10 Take the true value of π to be the number stored on your calculator. 11 May, 2015M L1 MH

Solution 11 May, 2015M L1 MH

Algebraic expressions Adding 11 May, 2015M L1 MH

Subtracting 11 May, 2015M L1 MH

Multiplying and Dividing Remember our index rules here 11 May, 2015M L1 MH

Summary We have recapped on the following topics - Scientific Notation - Rational Numbers and Surds - Absolute and Relative error - Algebraic Expressions 11 May, 2015M L1 MH

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