[PDF] Maths First Aid Kit 15 Oct 2011 The attached

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Engineering For Designers UWE Product Design Drew Batchelor V1 15 October 2011

Maths First Aid Kit

Preparation for Engineering for Designers / Mechanisms and Structures

For all PDT 1 and CPD 2 students,

Next semester you will be studying either Mechanisms and Structure (PDT1) or Engineering for Designers (CPD2), with me Drew Batchelor. One of key learning outcomes for these modules is to ensure that all UWE product Design Graduates have sufficient numeracy to work as professional designers. HI \RX GRQ·t feel comfortable with GCSE maths RU OMYHQ·P studied either AS-Level or A-Level maths or physics. The attached maths first aid kit will help you bring those rusty maths skills up to speed. We understand that some students are not confident with numeracy, you now have an opportunity to fix that, as it is an essential competency for the technical aspects of being a professional designer. This handout is (mostly) revision of GCSE material, It is the foundation with underpins all the analysis in the module. By the first seminar (week of 16 th January 2012) \RX·UH H[SHŃPHG PR ensure that you are comfortable with all of the material in this handout. Tutors will provide support, but for this to work, you will need to engage with your own learning, (please do*, it will save you a lot of hassle next summer).

How to use this handout

Starting this week, work through this handout, working in pairs or small groups will help. Try the exercises at the end of each topic, if you can do them, move on to the next sheet. If you find it difficult, work through the whole topic, if you still have some questions on that topic please either; visit Espressomaths or visit Drew during his clinic hours. The last 3 topics (2.10/2.11/2.12) are the most important. When you can do those, you will know that you will be comfortable with the level of maths on this module.

Topics Covered in this handout

1.1 Fractions 1.2 Powers and roots

1.3 Standard form / Scientific notation 2.1 Indices (powers)

2.2 Negative and fraction powers 2.3 Brackets 1

2.4 Brackets 2 2.5 Factorising

2.7 Simplifying fractions 2.8 Fractions

² Addition and subtraction

2.9 Fractions ² Multiplication and division 2.10 Rearranging formulas 1

2.11 Rearranging formulas 2 2.12 Solving linear equations

During the first week of tutorials we will also cover the following: SI Units, Significant figures ² Precision and accuracy, Subscripts, Pythagoras & Trigonometry, Using Scientific Calculator.

Espressomaths Support

http://www.cems.uwe.ac.uk/espressomaths/ UWE provides free 1-to-1 maths tutoring every day ² if you need it, please use it, starting this week ² take this handout along. Espressomaths is available 1200-1400, Monday-Friday in the corner of OneZone Refectory near Core24 in E-block. Espressomaths has an associated handout repository, situated in Room 2Q53, the handouts are also available online: http://www.cems.uwe.ac.uk/espressomaths/resource_centre.html The site also provide links to other online excellent learning resources:

Good luck,

Drew (*pretty please.) 1.1

Fractions

Introduction

ocu rinanlb lh ehsf gh.Tyu.lab enlc wsrglnh.vm ihlc .kqius wsrglnh.v r.y ratuisrng wsrglnh.vm nv r. uvvu.lnra vfnaa ecngc k.yusfin.v raa hlcus ratuisrng fishguvvuvd p. lcnv aurOul eu suqn.y bhk hw

che .kqius wsrglnh.v rsu vnqfianTuym ryyuym vkilsrgluym qkalnfianuy r.y ynflnyuyd1. Expressing a fraction in its simplest form

p. r.bEquation• m vrbm lcu .kqius•rl lcu lhfi nv graauy lcunslvqutoqd ocu .kqius?rl lcu ihllhq nv graauy lcuevnolinutoqd ocu .kqius?qkvl .uflus iu Lushd + wsrglnh. gr. raerbv iu u=fisuvvuy n. yn0usu.lm bulvrsixumvntwhsqvd ,hs u=rqfiaum lcu leh wsrglnh.va r.y b rsu uxknflrau.ld ocub sufisuvu.l lcu vrqu flrakud + wsrglnh. nv u=fisuvvuy n. nlvpilSmvpt Eoql ib gr.guaan.t r.b wrglhsv ) 5& I r.y vh lcusu nv r wrglhs hw 5 ecngc nv ghqqh. lh ihlc lcu .kqusrlhs r.y lcu yu.hqn.rlhsd ocnv ghqqh. wrglhs gr. iu gr.guaauy lh aurflu lcu uxknflrau.l wsrglnh.S cAulSmvba nv uxknflrau.l lh vn.gu S5 &,(- I- (7I. cAvqaipvp Sd )=fisuvv urgc hw lcu whaahen.t wsrglnh.v n. nlv vnqfiauvl whsqW rj ba mijbw mgj myj btt muj c mwj bz mtj d wnpvqp

Sd rj,

mij a mgj b myj at muj c mwj mtjb d

2. Addition and subtraction of fractions

oh ryy leh wsrglnh.v eu Tsvl su:esnlu urgc wsrglnh. vh lcrl lcub ihlc crflu lcu vrqu yu.hqn.rlhsd ocnv yu.hqn.rlhs nv gchvu. lh iu lcumovpt aollon evnolinutoqd ocu nv lcu vqraauvl SdSdS copyrightc2Pearson Education Limited, 2000 .kqius ecngc nv r qkalnfiau hw ihlc yu.hqn.rlhsvd ocu.m lcu .kqusrlhsv h.ab rsu ryyuym r.y lcu suvkal nv ynflnyuy ib lcu aheuvl ghqqh. yu.hqn.rlhsd cAulSmv

Ynqfianwb rj

c z mij c d omstion rj p. lcnv grvu lcu yu.hqn.rlhsv hw urgc wsrglnh. rsu rasuryb lcu vrqud ocu aheuvl ghqqh. yu.hqn.rlhs nv S1d 2u fiuswhsq lcu ryynlnh. ib vnqfiab ryyn.t lcu .kqusrlhsv r.y ynflnyn.t lcu suvkal ib lcu aheuvl ghqqh. yu.hqn.rlhsd Yhm c z 7 cz 7 ba d ocnv r.veus gr. iu u=fisuvvuy n. lcu vnqfiaus whsq ib gr.guaan.t lcu ghqqh. wrglhs 9d ij oh ryy lcuvu wsrglnh.v eu qkvl suesnlu lcuq vh lcrl lcub crflu lcu vrqu yu.hqn.rlhsd ocu aheuvl ghqqh. yu.hqn.rlhs nv S1 iugrkvu lcnv nv lcu vqraauvl .kqius ecngc nv r qkalnfiau hw ihlc yu.hqn.rlhsvd 4hlu lcrl nv uxknflrau.l lh x r.y vh eu esnlu c 7 c x 7 b, d cAulSmv ,n.y b a w d omstion ocu vqraauvl .kqius ecngc nv r qkalnfiau hw lcu tnflu. yu.hqn.rlhsv nv I6d 2u u=fisuvv urgc wsrglnh. enlc r yu.hqn.rlhs hw I6d S &4&*4-.().*,4&,*,4&-*,(.6*, cAvqaipvp

Sd )flrakrlu urgc hw lcu whaahen.tW

rj a z mij w b mgj z myj b b b muj a b b mwj w b d wnpvqp Sd rj a, mij. b mgj b myj b, muj. b mwj a, d

3. Multiplication and division of fractions

7kalnfiangrlnh. hw wsrglnh.v nv qhsu vlsrntclwhsersyd 2u vnqfiab qkalnfiab lcu .kqusrlhsv lh tnflu

r .ue .kqusrlhsm r.y qkalnfiab lcu yu.hqn.rlhsv lh tnflu r .ue yu.hqn.rlhsd ,hs u=rqfiau

8 I-(. I8 97S(&9

3

81I-(.8 9*(&,&)

cAvqaipvp

Sd ,n.y rj

w b, mij a 1 mgj a b myj a muj aa mwj z 1 w d wnpvqp Sd rj a mij bt mgjSmyj x muj x mwj z d SdSd5 copyrightc2Pearson Education Limited, 2000 j(:

Powers and roots

Introduction

Theabi lba tiay eoar ea elrn nh gtfnmufs l rtgwab ws mniafd baualnayfsff j( Powers poar ea emio nh gtfnmufs l rtgwab ws mniafd ea tiaVIRyx,khbvw vy,li noas lba lfih .lffayff flhb axlgufak noa Ltlrnmns 2 2 2 2 mi titlffs ebmnnar li 2V ff 1oa rtgwab c naffi ti noa rtgwab hd iaMari nh wa gtfnmufmay nhOanoabff "r nomi axlgufak noa uheabk hb mryaxk mi cff 1oa rtgwab 2 mi .lffay noa ,yff Vy =R H= = H ,=ff pa ils noln v= iLtlbay mi ,=Ik hb v= nh noa uheab U mi ,=Iff U I HU U U U U H ,Uff pa ils noln vU nh noa uheab j mi ,UIff -htb .lf.tflnhb emff wa ubaYubhOblggay nh aMlftlna uheabiff fihin .lf.tflnhbi olMa l wtnnhr glbSay?c k hb imgufsqff Fritba noln sht lba timrOshtb .lf.tflnhb .hbba.nfs ws MabmdsmrOnoln xx

H W22Wc2ff

:( Square roots poar j mi iLtlbay ea hwnlmr Ujff 1oln mi j R

H Ujff

1oa baMabia hd nomi ubh.aii mi .lffayw

vw xy xIIff 1oa iLtlba bhhn hd Uj mi jff 1omi mi ebmnnar li1 s

Uj H jk hb imgufssUjHjff

Ehna lfih noln eoaruj mi iLtlbay ea lOlmr hwnlmr Ujk noln mi 0ujR R

H Ujff 1omi galri noln Uj

oli lrhnoab iLtlba bhhnkujff "r Oarablfk l iLtlba bhhn hd l rtgwab mi l rtgwab eom.o eoar iLtlbay OmMai noa hbmOmrlf rtgwabff

1oaba lba lfelsi neh iLtlba bhhni hd lrs uhimnmMa rtgwabk hra uhimnmMa lry hra raOlnmMaff

+heaMabk raOlnmMa rtgwabi yh rhn uhiiaii lrs iLtlba bhhniff fihin .lf.tflnhbi olMa l iLtlba bhhn wtnnhrk ubhwlwfs glbSay sff 8oa.S noln sht .lr tia shtb .lf.tflnhb .hbba.nfs ws MabmdsmrOnolns23H7-777Uk nh dhtb ya.mglf ufl.aiff -htb .lf.tflnhb emff hrfs OmMa noa uhimnmMa iLtlba bhhn wtn sht iohtfy wa lelba noln noa ia.hryk raOlnmMa iLtlba bhhn miu7-777Uff )r mguhbnlrn baitfn mi noln noa iLtlba bhhn hd l ubhyt.n hd neh rtgwabi mi aLtlf nh noa ubhyt.n hd noa iLtlba bhhni hd noa neh rtgwabiff flhb axlgufa sW= Uj H sW= sUj H c jHU5

WffUffW

32
3b 2 3 2 fihba Oarablffsks Hs s +heaMab shtb lnnarnmhr mi ybler nh l .hgghr abbhb eom.o intyarni glSaff "n mi rhn nbta noln s

9Hs9sff :twinmntna ihga imgufa Mlftai dhb shtbiafd nh iaa noln nomi .lrrhn wa bmOonff

yxv,y, Wff pmnohtn timrOl .lf.tflnhb ebmna yher noa Mlfta hds

3 ,=ff

Uff flmry noa iLtlba hd noa dhffhemrO; lRs

Uk wRsWUff

,ff :ohe noln noa iLtlba hd js

U mi j5ff

w,Ryx,

Wff W7k 0lry lfihuW7Rff Uff lR Uk wR WUff

Y( Cube roots and higher roots

1oa .twa bhhn hd l rtgwabk mi noa rtgwab eom.o eoar .tway OmMai noa hbmOmrlf rtgwabff flhb

axlgufak wa.ltia c y H =c ea Srhe noln noa .twa bhhn hd =c mi ck ebmnnar 3 s =c H cff )ff rtgwabik whno uhimnmMa lry raOlnmMak uhiiaii l imrOfa .twa bhhnff +mOoab bhhni lba yaH ,Uk noa s ,UHUff yxv,y,

Wff pmnohtn timrOl .lf.tflnhb 3 s

U2k wR

3 s WUjff w,Ryx,

Wff lR ,k wR jff

-( Surds

Fxubaiimhri mrMhfMmrObhhnik dhb axlgufasU lry j

3 s

U lba lfih Srher li,x

,ff flbaLtarnfsk mr arOmraabmrO .lf.tflnmhri mn mi Ltmna l..aunlwfa nh falMa lr lrieab mr itby dhbg blnoab nolr .lf.tflnmrOmni ya.mglf luubhxmglnmhr emno l .lf.tflnhbff "n mi hdnar uhiimwfa nh ebmna itbyi mr aLtmMlfarn dhbgiff flhb axlgufaks c7 .lr wa ebmnnar lis , W=k noln mis, sW= H cs,ff yxv,y, Wff pbmna noa dhffhemrOmr noamb imgufain itby dhbg; lRs

W75k wRs=,ff

Uff =s gtfnmufsmrOrtgablnhb lry yarhgmrlnhb wss

U 9 Wk iohe noln

W s

UuWmi aLtmMlfarn nhs

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