CGP GSCE Maths/Mathematics AQA Revision Guide Higher 17/06/2018

140 Pages·2017·29.02 MB·English

by  CGP

CGP

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The Revision Guide
Higher Level
= CGP

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This lifesaving CGP bcok is totaly up te-date for she caw GCSE course
Its packed with -o-ninsense exz)anations, pls worked examples,
grade irfo and exam-sty e practize questirs for every topic.

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Contents

Section One —Numher
“joes of Nunber and 3COMAS ae
Muliles, Factors and Prine Factors
LOM ane HCE

Fractions

Fractions, Dee male and Peivontages
Fractions and Recut Decimal nom

Rounding Numbers.

itaneecTin> Gaphs
lortyTinw Gach

Gradhents of Rea
Revision Questions for Setion Three

Ife Graph omen

Lina =——

come ———

el ee Section Four — Ratio,

ek eee ser a Samir sere
Seine :

Section Two — Algebra ede Pron

Aga Baie :

mypaurd Groweh ard Decay...
nie Carversions

Speed, Censity and Pressure
“ruiisn Questions 9" Sarton“

Powers and Rost.
Multilying Out Bra
Factoring
‘Manipulating Sucde
Slaing Equations
Reatranging Formulas nna

Factonsing Quadtatie ca Section Five —
The Quastatic Forma aa Geometry and Measures
Completing the Square son Geomety. liao

‘Nesbrais FracLons..
Sequences... ai
Insquaities

Graphical Inezuaiites...
Iterative Method yon. snne so
Simultancous Equations.
Preof.

Parallel Lite cece
Geometry Prob em ann
Falygans

“Taangles nd Quacrlte

ngruert Shae
Similar Shapes nanan

Functions. See : Ta The Four Irsnstormatons.
Revision CQustions fr Seton Too 22 Reon Trarales and Quad seri
fora — Gide =
Section Three — Graphs 3D Stapes — Sure Ares,
Straight Lines ard Grades. 43 3D apes — Wilt seennannno
reece 44 Move Enlugere't an Projo
Drawing Staight Line Grapks.- 245 Tangle Construction =
Goordinaes al Ratio 46 a
Paral! ani Perpendicular Lives “7 d Corstcion — Worked Examp e.—-31
Quadra Graphs Ces Bearings. mi
Harder Graphs. SEETEEES4p Revlon Quastiens > Soctio z

bauteieent tn OOO®

But rememaer — to ce a tp grade you have te Know everything, “ot ut tre vardest topics
Section Six — Pythagoras and
Trigonometry
Pythagoras’ Tarot
Tignometry — Sin, C25, Tan
es.
Tigooomet“y — Common Vales
“The Sine and Cesine Rul
3D Pythagoras ana
3D Trgonematy..
Veto seme
Revision Questions for Sei

Tiigonomely —

magna

abtshed by CP

‘Writer by Richard Pacnons

Section Seven —

Probability and Statistics

Peaealily Vases 106
iunticg Ouenanes 1

ee A

The AND / OR Ral
Tree Diagrars..

‘ond onal Probab: y. a2
Sets and Ven Diegrars... ats
Sampling and Data Co lec: on aa

"Maan, Madan, Mode and Rage. on nnn 6
Frequency Tables — Ending Averages an ann—cll7
Grouped Frequensy “Able

hots - alt
Curative Fresueney... cs EO.
Histograms and Frecurney ons y m1
Seatter Graphs ad

ther Cnaphe and Charts rad
ramping Dara Sets 4
Revisicn Questions for Section Seven, 126
Answer a 17

Lpbtea by: kab Hazen, shaun Haroue, Allon Palle, Dev Ryan, Calby Sime, Ruth Wiens

[Wit thanks. Altair Duncombe and Sir Kite forthe prosteaing

‘ipo fom core"

ext dss, lot ax rina astra
Allright ererved

© tte

sre 2018

6800 IIE 71 + worweapbookseo.
a Section One — Number

Types of Number and BODMAS

socks af fis, but lean # you mast
"about whal order fo do things i,

Ah, the glorious word of BOSE Matis. OK maybe i's mre ee
Here ate some bendy defiilions of different Iypas of ruriber. and a

Integers: (3)
‘You need fo make eure yout know the meaning of ths word — i'l oome up al the Hine in GCSE Maths.
An Integer fe another name for a whole number — either # postive or negative number, or zero.

Examales —Infegers: G65. 0. 1. 17, 989, 1204667 890

hotmisene: 05, 2, v7, #28, 10008, 68.68, =

All Numbers are Either Rational or Irrational (3)

nan be written we fructons, Muvt numbere you deel with ure ratonal

Raiunal number
Rational umbers came in dilfeent forma:

1) Intogore og. 4 Ph 12-2)

2) Exactons ply, where p und « are (non-zero) inlegers, wa 3-2.
9) lerminsting ot acuming acme ef, 0.126 (= 4), 0.98880098.
‘cational ourbers are messy. They cent be written as fractions — they're never-ending,

non-repeating
decimal. quote cools of +e intagere ato ether mfegere ot imatonal (ef. . 2 and » & ore trakonal, but
54 = Zier}, Suds (eco p.20) are numbors oF exproscions containing rational raote. ie azo i

BODMAG fells ou the ORDER in whieh theze operatiors should be dane:
Work out Brackets frst, hen Oller “hinge fie squsring, Mey Divide / Many
_groupe of eursbers hefore Adding or Subicacting thee

‘You oan wee BODMAG whon ite not elozt what to do next,

‘rif thare'e more than one thing you oouid do.

VAP RII2~2) Brackets firet.

—— Finally, take the reciprocal (the reciprocal

‘of a nurmbor ie juot 1 + tho numba).

What's your BODMAS? About 50 kg, dude...
105 really important to check your working on BODMAS ques:ions, You might be certain you did it
right, but its surprisingly easy to make 2 sia, Try tris Exam Practice Question and see how you do,

Qt Withour sing = exlulator fine the valve a? 3-223 14 (2 marks (3

Section One — Number
Multiples, Factors and Prime Factors

I you think ‘factor’ Ie hort For al acto

Multiples and Factors | (3))

The MULTIPLES of a number Pexnnnrse: | Find the firet 8 mulkiples of 13
are just its times table You ust rece to ind the Feet 8

B26 39 52 65

‘you should give this page a ead. toa thinking sbout fat actors

‘The FACTORS of a under are al
‘the numbers thst divide into it.

‘Thoto's ¢ mothod shat guarantece youl Find thom al:

1) Start off with 1% the nunsher ital, ther hy 2, —

‘then & % ond 20 en ting he para in row. fe
2) Try cach eves turn. Cross out the raw ii! doesn't — B42] ace
ide exci. —
3) Evantualy, when you get a number ropsctd,ctop. aus
48) The numbers inthe rows you haven’ crossed aut geapeen teers
turk up the Bat of factors. 42,346 812,26

Prime Numbers: (3)
299 °5 7 N18 719 23 29 31 a7
‘prime ow cb which dart i bg anti pert mn

Tue ile only Factors are sell ad 1. (The only exception is |. eich i NOT a prt tuber.)

Finding Prime Factors — The Factor Tree | (4)

Any nurcar an he broken dawn int mango pri fates all lipid gator —
this ic oolled ‘prime faotnr denorposition’ oF ‘prime factoriaaton’
To urea number ao product of ts
PexannPce: | Express 420 as a product of prime factors. prime factors, use the Factor Tree method:
1) tn withthe number athe Fp,
and spt tit fora 98 shown.

2) Every the you get a pime, ring
8) Keepy glug ll you oa" go further
(oe. you're just left with primes),

then wits the primes cut in ors.
_— = IF thore's more than ono of tho cae

footos, you oan write thom ac poware,
@®@ “
So #2042 424345 47

oRege5e7

Takes me back, scrumping prime factors from the orchard.
Make sure you know the Factor Tree method inside out, then g.ve this Exam Practice Questo
QI Express as products of their prime factors: a} 990 [2 marks] b) 160 (2 marks) (4)

Section One —Number
| LCM and HCF

the previous peye wesr't env excitement, here's wume mure factors andl multiples fun,

[ LCM — ‘Least Common Multiple’ (8)

‘The SMALLEST number thet will DIVIDE BY ALL the numbers in quest

I you're givan fuss nutnbers and ack fo Find ther LCM, just LIST the MULTIPLES of BOTH numbers
and find the SMALLEST ony PhaPe iy BOTH sks
So, to nd the LOM.

and rips of 15 = 15,

75,1 ans Gd Ue sna eb ae ba i

However, you deady lmcw the ptm: fants of the numbers, you can woe this method iat
0 Saale FRMETACIORO et) pees atid anaes
‘appeer in EITHER number. Fd the LOM of 18 and 30.
2) Ia factor appoare MORE THAN ONCE Geass Uae
in one nf he numbers, Et
‘THALMANY TIMES. Sune wis iecore Hat ares eae
5 in ether number are 2.3,5, 5-1 2
8) MULTIPLY. these ‘ogether Be ee ee ee
4 give Hw LOM,

HCF — ‘Highest Common Factor’ | (5)

IF you're given two numbers and asked to frd their HCE,
eG she EAGIORS of AOIH numiers
fand find tho BIGGEST one that's in BOTH Late
Sto find te HCF of 36 ane 5, ot the
(reo 54212, 3 69,10, 27 and BA) ae

re factors oF 36
the i

5)6,9,'2,18 and 36 ane
1 one thas Led Lalo — s0 ECE = 18

Aes te lst read yuan se yo hn te pre ls the nara
i) oe Pa aos e228 smd = B37
Sipe me, Us sid et eo nt

21 MAMIE eestor to o-COGis v- OOO?

2,2 and 3 are prime foetors of both numbers, so
HoF=28243=12

LCM and HGF live together — it’s a House of Commons...
Method 1 is much simpler in hoth eases, but mae ae yor ‘er: Method 2 a8 well jas in ease
the exam question specifically tli you to we the prime factors othe murs are realy big.
QI a) Find the lowest comson tntple (LCM of 8 and (2
1) Given tha 28 = 2° 7 and 8 = 2, i the LOM of 28 and 4 marks '3)
Q2 a) Find the highest common factor (HCF) of 36 and 84 bs)
’) Given that 150-2 3 «5% and €0 ~ 2! + 3 $, find the HICF 07150 and 60, [3 marks}{3)

Section One — Number
Fractions

‘These pages show yu how #9 enne vith faction calcula w thon

1) Cancelling down | (=)
To cancel dows or amplify a frection, dvds top ond bottom by the care numb til they won't go further:

2
Ce .,,., © ed

dows aa senes henge steps — ste9 gong “ll 8
esd tstn eating 2

2) Mixed numbers | (3)
Mise P
wher hp bei ger an a om mbar

COIS) a.

eobers nen things Ble 1 th ning patron park. peep anton: are ones
rol tobe abn to convert hehunen the 0

f Wiededaleienminss | | Eadie o acim
Baad 1) The nse gives che hcl wanber past
hae Dene eenyacg

2) Tum the inzage~ par: into frac: or pagan ee eee aes

ey a1 -4=7 aman we Per
be bedemge pa

3) Multiplying (3)
‘Multiply top and bottom seperately. If usuell helps 10 cencel down frst if you ean.

fexaurcc BE

sce des hy dsng tp end bottom hy any
smn factors yeu fi noth Faction:

5 ord 2 oath

Now multi the tap and bottom curbs epaae,

4) Dividing (3)

Tur the 2rd fraction UPSIDE DOWN end then mull My

4.

ere iene?
Ten J opi dow: and uli $5
Siu yyernesiig ers -$xb-2

Section One —Number
Fractions

§) Common denominators | (4)

This comes in handy for onder g raslions by size, and for adding o- sublracling Peotone
You eed to fad a vunube thal all the devotions ui ol — hic wil be your gotten denomiealen

The simplest woy i fo nd the ees: comma mulible of

The LOM 3,4 aid 58 6
tamale (Othe conmor dmvmmatar

rer rrrcrsimrer sie tas

6) Adding, subtracting — sort the denominators first (4)
1) Make sure the denominators a-e the same (see abave). “
2) Add (or cubtroot) tho top lincs (numerators) only.

1 yout ag or satin ane ler, aly has a anal than fo pi actin est
[exhuiPLt: Rng
eter ere ee

Find a commoa de-onira:ze

Corton the top ines

2) Fractions of something 8) Expressing as a Fraction

= What is of 3602 oma Craton ere:

ah mers oo mali te ie ane Meher ranceea ene
Piva tele theta or Te eel
sack hws
wo.e (3)
2B otro = (co +90) <9=" tS 2)
Berea

No fractions were harmed in the making of these pages.

although ons was slightly frightened for aw: and several were ticked.
When you think you've learata'l this, 0y a! of

Baa Practiow Questions without a ale

Ql Cateutate:

a dx [3 mors] bey [S marks} 7
1 , nl 3)
oy [3 mars] asp - 94 [3 marks’

ea hs made 3

{othe sarewiches he has mae ere wepetariar
and 3 of the vegetarians sandwiches are che
low many checac sandwiches has he mde

se sedwichss

(omnis) (BY

Section One — Number