Chapter 1 Selecting and using appropriate numerical notation and units and selecting and carrying out calculations Exercise 1A Applying the four operations to whole numbers and decimal fractions 1 2250 g 2 55 kg 3 160 mm 4 £15·79 5 £6·80 6 £25·00 7 600 mm 8 a Four hundred and seventy-eight pounds b £325 9 £2·69 10 a 10·15 kg b 1·51 kg 11 £12·56 12 £10·18 13 £90·53 14 4·59 cm 15 36 000 16 4500 g 17 214 18 £57 200 19 a Nimmo b 535 c 8 476 20 £450 000 21 £234 150 22 865·4 s 23 6851·34 mph 24 £84 Exercise 1B Rounding answers 1 70 km 2 40 km 3 300 m 4 1·39 million km 5 0·1 mm 6 165–174 7 3·2 8 £45·57 9 a 3·14 b 3·1 10 13 000 km 11 3 000 000 miles 12 a 539·68 b 540 13 84·6 kg, 84·1 kg, 83·3 kg 14 65·9° 15 0·775 seconds (3 s.f.) 16 a i 2·7 ii 2·72 iii 2·718 b i 3 ii 2·7 iii 2·72 17 2·5 m 2 Exercise 1C Working with fractions and percentages 1 Shape correctly drawn and one section shaded in 2 a Shape correctly drawn and three sections shaded in b 0·75 3 £6·50 4 £144 5 £5·13 6 a £27 b £108 Answers
Transcript
Chapter 1 Selecting and using appropriate numerical notation and units and selecting and carrying out calculations
Exercise 1A Applying the four operations to whole numbers and decimal fractions
1 2250 g
2 55 kg
3 160 mm
4 £15·79
5 £6·80
6 £25·00
7 600 mm
8 a Four hundred and seventy-eight pounds
b £325
9 £2·69
10 a 10·15 kg
b 1·51 kg
11 £12·56
12 £10·18
13 £90·53
14 4·59 cm
15 36 000
16 4500 g
17 214
18 £57 200
19 a Nimmo b 535 c 8 476
20 £450 000
21 £234 150
22 865·4 s
23 6851·34 mph
24 £84
Exercise 1B Rounding answers
1 70 km
2 40 km
3 300 m
4 1·39 million km
5 0·1 mm
6 165–174
7 3·2
8 £45·57
9 a 3·14 b 3·1
10 13 000 km
11 3 000 000 miles
12 a 539·68 b 540
13 84·6 kg, 84·1 kg, 83·3 kg
14 65·9°
15 0·775 seconds (3 s.f.)
16 a i 2·7 ii 2·72 iii 2·718
b i 3 ii 2·7 iii 2·72
17 2·5 m2
Exercise 1C Working with fractions and percentages
1 Shape correctly drawn and one section shaded in
2 a Shape correctly drawn and three sections shaded in
Exercise 1E Working with perimeter, circumference, area and volume
1 a 34 m b 30 m
2 66 m2
3 1083·75 cm3
4 57·5 m2
5 870·53 mm2
6 a 26·3 m b 38·3 m2
7 810 cm3
8 339·292 cm3
9 312 cm3
10 1 337 cm3
Exercise 1F Calculating ratio
1 Frank £120, Ben £360
2 Freya 24, Eoin 18
3 4 sweets
4 Tom £14 000, Dick £21 000, Harry £49 000
5 5 : 2
6 Sharon 368, Tanya 644
7 960 mm, 560 mm, 480 mm
8 £612 000
Exercise 1G Calculating direct and indirect proportion
1 €84
2 £72
3 175 hours
4 270 g flour, 60 g ginger, 165 g butter, 45 g sugar
5 No, only enough for 19 cakes or no, she is 20 g short
6 9·6 g
7 3 h 12 m
8 2 extra
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Chapter 2 Recording measurements using a scale on an instrument
Exercise 2A Measure to the nearest marked, minor unnumbered division on a scale
1 a 8 cm b 18 cm
2 a 34 kg b 73 kg
3 a 16 °C b 24 °C
4 a 80° b 190°
5 a 2·5 kg b 4·3 kg
6 a 23 °C b 14·5 °C c 0 °C d −4·5 °C
7 a 750 ml b 200 ml c 175 ml d 925 ml
8 5·4 cm
9 a 40° b 83° c 114° d 178°
10 a 240° b 303°
11 11
16
of tank left
1116
× 420 miles = 288·75 miles
No, Sunita does not have enough fuel to
complete her journey as 288·75 < 300.
12 12·5 psi
13 Total weight is 18·5 kg + 9·2 kg = 27·7 kg No, Alison will not have to pay the extra charge as 27·7 < 30.
Chapter 3 Interpreting measurements and the results of calculations to make decisions
Exercise 3A Identifying relevant measurements and using results of calculations to make a decision
1 a 900 mm b 960 mm
2 Egg cup, coffee cup, milk carton, saucepan
3 No, as 22·1 kg > 21 kg
4 17 000 m
5 0·82 seconds
6 a 6000 cm3 b 6 l
7 410 cm
8 No; Carol needs 11·2 l of juice.
9 a 88·9 kg b 12 st c 30·1
10 a 75 mph b 48 mph (45 < answer < 50)
11 Colin should decrease the air pressure in his tyre by about 5 psi.
12 a 98 °F b 0 °C
c 32·9 °C is about 91 °F so the difference is 32 °F, or 59 °F is about 15 °C so the difference is 17·9 °C
Chapter 4 Justifying decisions by using the results of measurements and calculations
Exercise 4A Using evidence from the results of calculations to justify decisions
1 Mushrooms and onions
2 Yes, her change should be £10·18
3 No, 8 containers weigh 1024 kg, which is 24 kg too much
4 Yes, it holds 1·008 l
5 £2·50
6 Cars 4 U by £5·80
7 Yes, he will weigh 79·09 kg by the end of October (5 months)
8 No, the ramp is 0·0875 > regulations 0·0714
9 a Yes, both hold at least 20 l
b Box B uses less material; 4 526 cm2 < 4 800 cm2
10 3 h 36 m
Chapter 5 Analysing a financial position using budget information
Exercise 5A Budgeting and planning for personal use or planning an event. Balancing incomings and outgoings from a range of sources
1 £9·20
2 a £2250 b 6 months
3 a Surplus b £118·17
c Surplus reduced to £35·70
4 Surplus is reduced from £175 to £9.
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5 £6·10 per ticket
6 a £99 b Yes; £99 × 12 = £1 188 > £1 100
c £27·50
7 a i Surplus ii £8
b Now he has a deficit of £4.
Chapter 6 Analysing and interpreting factors affecting income
Exercise 6A Income and deductions for different personal circumstances and career choices
1 £122·25
2 Carpet fitter
3 Gross pay £2255·00; Deductions £452·50;
Net pay £1802·50
4 £214·50
5 £232·88
6 a £11 650 b £2330
7 a £71·16 b (H) £68·40 c (M) £0
d (B) £46·16
8 a £258·33 b £188·40 c £446·73
d £1803·27
9 Option A £215, Option B £210, so Option A is better
10 £9600
Chapter 7 Determining the best deal
Exercise 7A Comparing at least three products, given three pieces of information on each
1 £9·94
2 The 5-pack by 25p
3 300 ml bottle, which is £1 per 100 ml is better value (cheaper per ml) than the 200 ml bottle, which is £1·10 per 100 ml
4 Web TV by £15
5 420 ml bottle
6 50 ml tube = 2·8p/ml; 75 ml tube = 2·4p/ml; buy 2 × 50 ml and get third tube
half-price = 2·33p/ml So the ‘offer’ (third option) is the best deal because it is the lowest price per ml.
7 Pack of four 1 litre cartons = £1·41/litre; 1 litre carton = £1·42/litre; pack of three 330 ml cartons = £1·39/litre So the pack of 3 small cartons is the
best deal because it is the lowest price per litre.
8 Railtrack = £93·28, Cheapline = £93·60, Lowrailfare = £92·52, so Lowrailfare is the best value.
9 5 × 90 = 450 min → 1·27p per min; 10 × 8 = 800 min → 1·29p per min; 12 × 75 = 900 min → 1·28p per min So the 5-pack offers the best value.
Chapter 8 Converting between several currencies
Exercise 8A Converting between currencies
1 a 370 CHF b €310 c 2605 CNY
2 £18
3 200 CHF = 768 AED, so it is cheaper to buy the watch in Switzerland (by 82 AED, or 21 CHF).
4 15 640 CNY
5 a €930 b €530 c 604·20 CHF
d 204·20 CHF e £138·86
6 £930
7 a Switzerland b South Africa c USA
8 a €594·06 b $1293·70
c 16·47 dirham
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Chapter 9 Investigating the impact of interest rates on savings and borrowing
Exercise 9A Loans, savings, cards and credit agreements
1 a Hollifax £11 672·40; Greene Loan £12 201·60; Forthside Bank £12 931·20; C2D Finance £13 350·60
b £27·97
c £10 469
2 a £510 b £255
3 a £317·04 b £628·83
c The 12
-year plan is cheaper overall.
4 a £8 b £114·75
5 £1470
6 £6375
7 a £15·81 b £624·09
8 £4900 @ 12·1% = £592·90 interest; £5000 @ 9·4% = £470 interest. Yes, the friend is correct, they would save £22·90 (once the £100 difference in loan is accounted for).
9 £416·26
10 a Atlass Bank £220·20
b Federalle Finance £2563·20
11 £121 800
Chapter 10 Using a combination of statistics to investigate risk and its impact on life
Exercise 10A Using the link between simple probability and expected frequency
1
a 149
b 549
c 449
2
a 16
= 0·167 b 12
= 50%
3 12
4
a 230
= 115
b 13
5
a 718 b 1
2 c 4
6 12
7
a 1
30 b 16
8
a 710 b 20
9 110
10 118
11 a
Country Gold Silver Bronze Total
France 3 0 2 5
China 2 3 2 7
Total 5 3 4 12
b 27
12 Owl Club 0·031 > 0·03
Chapter 11 Using a combination of statistical information presented in different diagrams
Exercise 11A Constructing, interpreting and comparing different representations of data
1
0BBC1 BBC2 ITV1 ITV4 SKY1 Sky
SportsChannel
TV survey
Freq
uenc
y
MTV Scyfy
123456789
1011121314
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2
November
December
January
February
March
April
= 2 goals
Number of goals
3
0Apple Pear Orange Peach
Fruit
Num
ber o
f pup
ils
Banana
2
4
6
8
10
12
14
4
Monday Tuesday WednesdayDay
Thursday Friday
Num
ber o
f pup
ils a
bsen
t
0
10
20
30
40
50
5
Vegetable Tally mark Frequency
|||| |||| 10
||| 3
|||| 5
6 a £810 b £330 c £1 020
7 a 95 °F b September to October
c January d May and September
8 a
Colour Tally Frequency
Red |||| 5
Blue |||| 4
Silver |||| | 6
White |||| 4
Yellow | 1
b
Red Blue Silver White Yellow0
1
2
Freq
uenc
y
Car colour
3
4
5
6
7
9
Week 1 Week 2 Week 3Week
Week 4 Week 5 Week 60
102030
Hei
ght (
cm)
4050607080
10
30%
25%
40%
5%
Family saloonsHatchbacks4 x 4sSports
11 a
130 140 150
Height (cm)
160 170
b On average the boys are taller and their heights are more consistent.
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12 a, b
10
20
30
40
50
60
70
80
90
00 10 20 30 40 50
Maths
Phys
ics
60 70 80 90
c Yes, there is a positive correlation.
d About 77
Chapter 12 Using statistics to analyse and compare data sets
Exercise 12A Calculating different types of average, range and standard deviation
1 a 55 cm b 5·5 cm
2 a 12 °C b 38 °C
3 43 g
4 5·93 kg
5 a 106 runs b 73·67 runs
6 Yes; as mean is £6215·57, which is greater than £6000.
7 a 87·3 kg b 0·35 kg
8 Mean = 8·14 hours, median = 8 hours, mode = 6 hours, so Danny should use the mean.
9 0·05 s
10 Mean = 114·4 calories, s.d. = 10·7 calories
11 a 20 minutes b 3·16 minutes
c On average the waiting times of the second group were shorter and were more consistent.
12 a Mean = 400 ml, s.d. = 6·26 ml
b Yes, the adjustment worked as the mean was the same but a lower s.d. shows that the amounts were more consistent.
13 Mean = 20·5 °C, s.d. = 1·52 °C; it is efficient as mean is within 20 ± 0·6 °C and s.d. is less than 2 °C.
Chapter 13 Drawing a best-fitting line from given data
Exercise 13A Data presented in tabular form
1 a, b
English test
His
tory
test
100
90
70
80
60
50
40
30
20
10
00 10 20 30 40 50 60 70 80 90 100
c About 58 marks
2 a, b
Hours of sunshine
Rain
fall
(mm
)
10
9
7
8
6
5
4
3
2
1
00 1 2 3 4 5 6 7 8 9 10
c About 4·5 mm
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3 a, b
Heartbeat (bpm)
Tim
e in
gym
(hou
rs)
20
18
14
16
12
10
8
6
4
2
00 10 20 30 40 50 60 70 80 90 100
c About 67 bpm
4 a, b
Hours revising
Prel
im m
ark
100
90
70
80
60
50
40
30
20
10
00 1 2 3 4 5 6 7 8 9 10
c About 1 hour
5 a, b
Distance cycled (km)
Am
ount
rais
ed (£
)
200
180
140
160
120
100
80
60
40
20
00 5 10 15 20 25 30 35 40 45 50
c About £140
Chapter 14 Working with simple patterns and calculating a quantity
Exercise 14A Working with simple patterns
1 Tessellation of hexagons, clearly showing cuts around edge of rectangle
2 a
b
c
3 For example:
or:
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Exercise 14B Calculating a quantity based on two related pieces of information
1 20·13 m
2 0·91 kg
3 255 g
4 €14·12
5 14·3 gal
6 4·84 bar
7 0·272 therms
8 320 km
9 3·48 knots
Chapter 15 Constructing a scale drawing, including choosing a scale
Exercise 15A From written information and/or a sketch
1
2 20 m
3 a 37·1 m b 23·8 m
4 287·5 m
5 Medium table: l = 480 mm, b = 360 mm, h = 420 mm
Largest table: l = 576 mm, b = 432 m, h = 504 mm
6 Measurements on scale drawing would be: 400 m → 8 cm, 325 m → 6·5 cm, 450 m → 9 cm
7 1 : 2400 or 1 cm to 24 m
8 a
10cm
210°
50°
Port
5 cmN
N
N
b Bearing 013°, distance 110 km
9 Using a possible scale of 1 cm : 5 km
105°
75° 6cm5cm
A
B
11cm
N
C
N
N
Distance 110 km
10 a Using a possible scale of 1 cm : 10 cm
30cm
15cm20cm
35cm
b Area of sail needed 1 100 cm2
11 a, b Using a possible scale of 1 cm : 10 km
N
Alpha
N
Beta215º80º
130º
5cm
3.8cm
Gamma
c 38 km
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Chapter 16 Planning a navigation course
Exercise 16A From written information and/or a sketch
1 a
School
Houses
Train station
Station Road
School Road
Green Road
Ashby AvenueM
ain
Stre
et
Shor
t Lan
e
Bus station
Parking
Shop House
Supermarket
Entrance
b Left into Station Road, turn right into Main Street, turn left into School Road, continue and school is on right
2 a
8.2cm8cm
N
N
N7cm
Vega
Omega
Phi 140º
250º
b 41 km c 010°
3 a Using a scale of 1 cm : 1 km
8cm1
2
5cm
NN
N12.7cm
Cowes95º
110º
b 285°, 12·7 km
4
Bearing Distance (m)
Leg 1 080° 250
Leg 2 115° 175
Leg 3 230° 210
Back to start 305° 300
5 Scale of 1 : 40 000 000 is 1 cm to 400 km
FC
N
N
197°73°
255°12°
36mm
14mm
19mm
33mm
N
N
P
PH
6 a N
N
N5.6cm
3cm
Port
210°60°
b 68 km, 005°
7 a Using a scale of 1 cm : 8 km
N
L
I
N
N4cm
C
3cm
6.5cm
65°
110°
Total distance travelled 108 km
b 45% used
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8 a, c Using a scale of 1 cm : 100 kmN
N
3.8cm
4cm77°
89°
300°
FS H
TS
b 005°
d 297°, 240 km
9 a 048°, 150 km
b 060°, 145 km
c 1 hour 14 minutes
Chapter 17 Carrying out efficient container packing
Exercise 17A By assigning items to uniform containers to minimise amount of containers used
1 3 boxes
2 7 tapes
3 6 crates
4 5 rolls
5 5 planks
6 Q1: 3 boxes; decreasing first-fit algorithm is not more efficient; Q2: 6 tapes; decreasing first-fit algorithm is more efficient; Q3: 5 crates; decreasing first-fit algorithm is more efficient; Q4: 4 rolls; decreasing first-fit algorithm is more efficient; Q5: 5 planks; decreasing first-fit algorithm is not more efficient; The decreasing first-fit algorithm is usually but not always more efficient than the first-fit algorithm.
7 78 (13 × 3 on each shelf)
Chapter 18 Using precedence tables to plan tasks
Exercise 18A Constructing and using precedence tables
1 a A4
F9
G5
B6
C7
D8
E10
b Critical path is A–C–E–F–G = 35 days, so 11 January (assuming work at weekend)
2 a
A10
G5
H2
I4
B5
E5
C12
D35
F12
b Critical path is A–B–C–D–G–H–I = 73 minutes
c 7.17 pm
3 a
Task Task detail Preceded by
Time (mins)
A Buy bacon and eggs
– 15
B Warm grill A 2
C Grill bacon B 4
D Make toast A 3
E Heat oil A 1
F Fry eggs E 3
G Warm plates A 2
H Serve C, D, F, G 5
A15
D3
E1
F3
H5
B2
C4
G
b Critical path is A–B–C–H = 26 minutes, so start at 0704
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4 a
C2
B4
A4
D6
E3
F2
G8
I3
J2
H5
K1
b No; critical path is A–D–F–G–H–I–K = 29 hours
Chapter 19 Solving a problem involving time management
Exercise 19A Planning the timing of activities with complex features
1 4 h 20 min 4 h 46 min 4 h 22 min
2 0630
3 1 h 35 min
4 5 h 17 min
5 11 h 55 min
6 a 1852 b 10 h 01 min
7 0205
8 1800
9 Vladimir 1630, Emmanuel 1530
10 0655
11 a 0900 b 0115 (next day)
c 0225 (next day)
12 a 0400 b 1445 c 1200
13 a 2000 b 0100 c 0700 d 1000
14 a 11 am b 4 am c 2 am d 4 pm
15 2015
Chapter 20 Considering the effects of tolerance
Exercise 20A Calculate limits and consider implications for compatibility
1 A, B, D, E, F, I
2 a A, B, D, G, H, J b 60%
3 a 5·08 cm b 5·18 cm c 5·08–5·18 cm
4 a 6·60 cm b 6·90 cm c 6·60–6·90 cm
5 42·3 g, 41·7 g, 41·9 g
6 Yes, as only 2 (10%) were outwith tolerance.
7 Company B, because 87·5% 78( ) is within
tolerance; Company A had 2 outside tolerance (75% accurate).
8 a 48·9 cm b 5·4 cm
9 Yes; max. width of 1 book = 32·5, 20 books = 20 × 32·5 = 650 mm (65 cm)
10 Lintel is 3·58–3·62 m, space is 3·6–3·8 m, so lintel will not always fit (max. lintel length is 3·62 m but min. space is 3·6 m).
11 No; for example, max. bolt size is 7·6 mm, min. nut size is 7·4 mm, so bolt could be too big.
12 41·10 seconds
13 a 3:09·94 b 3:10·51 c No
Chapter 21 Investigating a situation involving gradient
Exercise 21A Using vertical and horizontal distances
1 14
2 16
3
Yes, as 1120
<
1100
4 425
5 a Yes, as 0·081 < 0·083. b 4·31 m
6 No, as 1·56 > 1·5.
7 No, as 0·06 is outwith limits of 0·065–0·075.
8 Advice is ‘on track’ as gradient is 0·078, which is within 0·075–0·085.
9
Yes, as 640 mm < 650 mm and gradient is
0·078, which is less than 0·083
112( )
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10 a Easy (gradient is 20%)
b Advanced (gradient is 60%)
c Intermediate (gradient is 33%)
d Easy/intermediate (gradient is 25%)
11 No; although the road is longer than 750 ft, the gradient is 7·1%, which is less than 8%.
Exercise 21B Using coordinates
1
a 34
b 43
−
c 0 d Vertical (undefined)
2 a i £3·33 ii £19·50 iii £24
b small 103
, medium 83
, large 32
c small
d They need to deliver more small packages to make money, so charge a higher rate to help, or a lower rate for larger packets may encourage greater use.
Chapter 22 Solving a problem involving a composite shape
Exercise 22A Finding the area of a composite shape
Answers obtained using � on a calculator
1 a 28 m2 b 25·6 m
2 a Area 38 m2, cost £1330
b Perimeter 36 m, cost £144
3 2800 m2
4 538 cm2
5 19·43 cm2
6 a Area 131·8175 m2
b Number of packs is 33, cost is £947·10
7 Total area = 300 m2, flower bed = 36 m2, patio = 60 m2, pond = 7·069 m2; remaining area is 196·931 ≈ 200 m2(2 s.f.)
8 No, as area is 22·93 m2, which is more than 20 m2.
Chapter 23 Solving a problem involving the volume of a composite solid
Exercise 23A Finding the volume of a composite solid
1 30 cm3
2 1 331 cm3
3 300 cm3
4 3 000 cm3
5 a 0·9 m2 b 1·98 m3
6 300 cm3
7 565·5 cm3
8 340 cm3
9 190 m3
10 11·8 cm3
11 34 000 mm3
12 425 m3
13 6·0 m3
14 1·950 m3
15 a 502·7 cm3 b 31·4 cm
Chapter 24 Using Pythagoras’ theorem
Exercise 24A Within a two-stage calculation
1 2·09 m
2 3·4 m
3 19·4 m
4 2·97 m
5 3·5 m
6 23·6 m
7 14·7 m
8 Yes, as 3·7 m < 3·81 m
9 Yes; actual diagonal is 46·6 inches
10 21 cm
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11 Yes, as 550 cm > 540 cm
12 a 5 m b 10 m2
Chapter 25 Extracting and interpreting data from different graphical forms
Exercise 25A Extracting and interpreting information in tables, charts, graphs and diagrams
1 a £310 b £527 c £325
2
0
2
4
6
Freq
uenc
y 8
10
12
Facebook Twitter InstagramSocial media site
WhatsApp Flickr
3 a 5 b Monday c 27 d Friday
4 a, b
Maths (%)
Test scores
Scie
nce
(%)
100
90
70
80
60
50
40
30
20
10
00 10 20 30 40 50 60 70 80 90 100
c 65 marks
5 a
2
3
5
4
9
1
2
2
3
4
3
5
5
3
6
4
9
6 8 9Key 4 2 : 42 mph
n = 16
b 3
6 a £60·38 b £20 c £141·75 d £11·50
7 a
10
11
13
14
15
12
5
0
0
1
3
5
0
3
4
0
9
0
5
7
1
5
4
5
8
6
8
7
8
99
Women
100m
Men
1
1
3
1 1 2 2 3 5 7 8
6
1
7 8 9
Key 11 1 : 11.1 seconds
n = 20
Key 4 14 : 14.4 seconds
n = 20
b Men 11·25 s, women 12·95 s
c Men 1·15 s, women 1·3 s
d Various, e.g. women’s times are less consistent, or on average men are faster
8 a
1
2
6
0
Absences
0 0 1 1 1 2 2 31
8 8 9 9 9 9 9 97 7 8
Key 1 6 : 16 people
n = 21
b 19
c 1·5
d 621
27=
9 a
Number of calls 0 200 400 1000 1500
On the Move (£) 20 26 32 50 65
Under Cut (£) 0 14 28 70 105
b
Time (minutes)
Mobile phone costs
Cos
t (£)
120Under Cut
On the Move
110100
80604020
0
020
040
060
080
010
0012
0014
0016
0018
00
c 500 minutes
d On the Move
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Chapter 26 Making and justifying decisions using evidence from the interpretation of data
Exercise 26A Making and justifying decisions based on patterns, trends or relationships in data
1 Zainab 62·25, Torvil 61·25, so Zainab gets the prize.
2 Toolkit £161, Spark Plug £158·67, so Ben should go to Spark Plug.
3 Type of car Emissions (kg/km)
For 300 km
Small petrol (up to 1·4 l)
0·18 54
Medium petrol (1·5–2·0 l)
0·22 66
Large petrol (> 2 l)
0·30 90
Small diesel (up to 1·7 l)
0·15 45
Medium diesel (1·8–2·0 l)
0·19 57
Large diesel (> 2 l)
0·26 78
Small diesel, small petrol, medium diesel, medium petrol, large diesel, large petrol.
4
Year
Tim
e
4min
3min 50 s
3min 40 s
3min 30 s1950 1960 1970 1980 1990 2000 2010 2020
Between 2010 and 2020, if physically possible!
Exercise 26B Understanding the effects of bias and sample size
1 a January has a lower mean, indicating on average a better service.
b Different number of days in each month
c No; even if three ‘0’s were taken off and the total divided by 28, January would still have a lower mean.
2 a i 3 ii 15
b Managers 3, clerical 9, floor staff 45
3 a 18 b 6
Chapter 27 Making and justifying decisions based on probability
Exercise 27A Recognising and using patterns and trends to state the probability of an event happening
1 0·5
2 a 530
or 16
b 20%
3 a One-fifth, or one in five
b 0
15 1
25
35
45
4 6 bulbs
5 8·8 × 10−6
6 150
7 0·059
Exercise 27B Interpret and use probability to make and justify decisions
1 146 656
2 1
48
3 140
4 6
5 38100 = 19
50 [ P(RR) + P(BB) + P(YY)]
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Chapter 28 Preparation for assessment
Exercise 28A
1 175 runners
2 8·4 km
3 25 pupils
4 60 cars
5 3428 cm2
6 a i St Cyrus mean is 54·8 cm, Inverbervie mean is 54 cm
ii St Cyrus median is 53 cm, Inverbervie median is 53 cm
b They have compared their median rainfall to the mean rainfall of Inverbervie to make it seem that St Cyrus has better weather.
7 a 72 km/h b 12
hour more
8 distance = 5 4 6 3 84 1 962 2− = =. . . m
The ladder placement satisfies the regulations because 1·96 m > 1 m.
9 For first-fit algorithm, boxes are put in the first available space:
7kg
2kg
8kg3kg
So 7 kg into first container, then 8 kg into second. 2 kg fits into first container as that is first available, meaning 3 kg cannot fit into second container and so goes into third container.
10 a s.d. = 4·15 g
b No, as the s.d. is greater than previously, therefore weights are less consistent.
11 Option 1: £1300 + £294 = £1594 Option 2: £975 + £756 = £1731 So option 2 is better.
12 a Min. 146 ft, max. 150 ft
b A = π(22 – 0·52) = 11·78 ft2
c Blue ring = 62·8 ft2, white ring = 37·7 ft2; so, no, blue ring is not twice the area of the white ring.
13 a
4
6
7
5
8
5
1
0
1
2
8
0
5
9
2
5
5
Male Female
9
5
5
8 9
Key 0 7 = 70kg
n = 9
Key 7 0 = 70kg
n = 9
b 70 kg
c Q1 = 50 kg, Q3 = 68·5 kg
d Male
e
L = 48 Q1 = 50 Q2 = 65 H = 70Q3 = 68.5
14 a Volume = 2 811 cm3
b 4 gift boxes in 1 carton
c 48 @ £4·23 = £203·04 12 @ £1·15 = £13·80 (12 cartons needed) 12 @ £0·68 = £8·16 (transport of 12 cartons) TOTAL = £225·00
d 30% mark-up; invoice shop for £292·50
e Shop profit of 20% gives a total of £351; divided by 48 gift boxes = £7·3125; so shop should charge £7·32
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15 a Using a scale of 1 : 100
6.5cm
4.5cm
8cm
CP1
25º
240º
150º
CP2
S
N
N
N
b Total distance = 450 + 800 + 650 = 1900 m
t = ds
= 19005100
0 373= . hour
This is 22 minutes 21 seconds, so no record is not beaten as time is greater than 21 minutes 20 seconds.
16 a €240·80 = £215 3618·25 ZAR = £205 So Peter should buy from South Africa.
b €8·96 = £8 so total from France = £223 353 ZAR = £20 so total from
South Africa = £225 So the car is now cheaper from France.
c Value = 320 × 1·0823 = 405·351 So value = £405 to nearest pound.
