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Challenge Workbook Answers
All sample answers to the Cambridge Secondary 1 Checkpoint-style questions have been written by the authors of this work. 1
Integers 1.1 Negative numbers 1
a –6
b –4
c –10
d 12
2
a 14
b 4
c –14
d –10
3
a –2
b –5
c 16
d –25
4
19 and –18
5
13, –2 or –17
6
a i 03*00
ii –04*00
iii –02*30
b i
1745
ii 0615
iii 0145
c 1625 1.2 Tests for divisibility 1
1 or 4
2
The digits add up to a multiple of 3 AND the last digit is 0 or 5
3
The number is even AND the digits add up to a multiple of 9
4
a 60
b It is a multiple of 60
1.3 Prime numbers 1
25
2
There are 12. We can show this by listing them systematically: 2 × 3, 5, 7, 11, 13, 17 or 19; 3 × 5, 7, 11 or 13; 5 × 7
3
There are five. They are 2 × 3 × 5, 2 × 3 × 7, 2 × 3 × 11, 2 × 3 × 13 and 2 × 5 × 7.
Mixed questions 1
a 7, 11 and 13
2
a 53, 61, 71
b 1, 7, 11, 13, 77, 91, 143 and 1001
b Mia is not correct. If she chooses 41, then 41 is a factor of the answer. It does work for all the whole numbers up to 41. 3
a 1 + 3 = 4, 1 + 3 + 5 = 9, and so on. b e.g. 1 + 3 + 5 + 7 + 9 = 25, 1 + 3 + 5 + 7 + 9 + 11 = 36 c 2500, the sum of the first 50 odd numbers is 502 which is 2500.
1
Challenge Workbook Answers
2
Sequences, expressions and formulae 2.1 Generating sequences (1) 1
a 4.7, 5.0
b 7.9, 7.5
c –8, –14
d –10.5, –9
2
×3 –2
3
a Student’s answer, e.g. ×5, 25, 125 or ×2 +3, 13, 29
e
1 1 , 16 32
f
4 5 , 9 11
b Student’s answer, e.g. +5, 12, 17 or ×4 –1, 27, 107 2.2 Generating sequences (2) 1
a 16
b Square numbers
c i 1 ii 1
d i 24 ii 99
2.3 Representing simple functions 1
Student’s answer, e.g. +1 +12, ×2 +10, ÷3 +15
2
a input = 5 and unknown; subtract 3; multiply by 5; output = unknown b No. Student’s answer, e.g. 1 and –10, 2 and –5, 3 and 0…
2.4 Constructing expressions 1
a y+x
b y–x
c 2n + m
d 3b – a
2
a 2x + 3
b 5x – 6
c 4(x + 7)
d
x +9 2
e h2 e
f w z
x–8 4
2.5 Deriving and using formulae 1 2
a i 750 Newtons
ii 103 440 Newtons
b i 120 Newtons
ii 16 550.4 Newtons
a i 10ºC
ii –55ºC
b –40 ºF = –40 ºC Mixed questions 1
No, Shen is not correct – an input of a half gives an odd output of 5
2
a Student’s answer, e.g. 1 and 1, 2 and 2, 3 and 3 b The inputs and their outputs are identical. The ×2 and the ÷2 cancel each other out, as does the +5 and the –5 c Student’s answer e.g. ×5, –2, +2, ÷5
3
a 2
b Yes
c Student’s answer, e.g. ‘Think of a number, then add three and double the result.’ Gives 2(n + 3) or 2n + 6. ‘Then subtract the number you first thought of’ leaves us with n + 6. ‘then subtract 4’ leaves us with n + 2. ‘Then finally subtract the number you first thought of again’ leaves us with 2. So whatever number we choose for n we will always finish with a total of 2. Or 2(n + 3) – n – 4 – n = 2 4 2
p = 2 and q = –4
Challenge Workbook Answers
3
Place value, ordering and rounding 3.1 Understanding decimals 1
ARE DECIMALS EASY?
3.2 Multiplying by 10, 100 and 1000 1
150
2
423 BWP
3.3 Ordering decimals 1
2000 ÷ 1000; 0.0208 × 100; 0.23 × 10; 2320 ÷ 1000; 1.9 × 10; 2110 ÷ 100
3.4 Rounding 1
a 235
b 244
2
a 8.650
b 8.749
3
a
Full calculator display
Rounded to 1 decimal place
√7
2.645751311
2.6
√8
2.828427125
2.8
√10
3.16227766
3.2
√11
3.31662479
3.3
b Because √9 = 3 4
a 85 267 000
b 85 270 000
c 850 000 000
d 90 000 000
3.5 Adding and subtracting decimals 1
720.76, 653.26, 518.98, 584.28, 54.99
3.6 Multiplying decimals 1
a 120.4
b 120.4
c 120.4
d 1.204
3.7 Dividing decimals 1
Cost of his meal = $13.60, cost of sharing = $13.72. Shaun is better off by $0.12 if he pays for his own food rather than an equal share of the bill.
2
a 90
b 90
c 9
d 900
3.8 Estimating and approximating
3
1
a $110
b $110 – 5 = 105, 105 ÷ 15 = 7. 7 days in a week
2
a Student’s answer, e.g. 24 or 25
b 24.1
c Student’s answer
Challenge Workbook Answers
Mixed questions 1
a E = 2A, C = E – 5.22, F = 10C, G = F ÷ C, D = F ÷ 4, H = (D + F) ÷ G so H = 3.975 b B = 3E – A c Student’s answer
4
Length mass and capacity 4.1 Knowing metric units 1 a 2.9 m or 229cm 1.67 m or 167 cm 0.62 m or 62 cm 1.4 m
27 cm
b
3100 kg 1t
2.1 t or 2100 kg
0.15 t or 150 kg 2
350 mm
850 kg
1.25 t or 1250 kg
a From the large container fill the small and medium containers 5 l – 1.25 l – 750 ml = 3 litres. b From the large container fill the small container 3 times 5 litres – 3 × 750 ml = 2750 ml. c From the large container fill the medium containers 5 l – 1.25 l = 3.75 litres. From the medium container fill the small container, then empty the small container back into the large one 3.75 litres + 750 ml = 4.5 litres.
3
$322.40
4.2 Choosing suitable units 1 T H I 1 litre T
S
C
190 kg 250 ml 80 litres R
I
1 litre 40075 km 250 ml
C 340 g
A
N
340 g 420 g 590 kg K
Y
!
46 g 6853 km !
4.3 Reading scales
4
1
6 ºC
2
a 1.23 l
3
1.452 m
b Four more full cups (so five cups altogether)
B
E
1200 kg 42 km
Challenge Workbook Answers
Mixed questions
5
1
a 189 g
b 168.57 ml (accept 168 ml or 169 ml or 168.6 ml)
2
a 80 kilometres per hour
b 32 km
c 48 kilometres per hour
Angles 5.1 Drawing and measuring angles 1
a Possible, e.g. 30° and 40°
b Possible, e.g. 150° and 60°
c Not possible, total over 180° 2
Three whole turns are 360° × 3 = 1080°; the triangle angles add up to 180°; 1080° – 180° = 900°
5.2 Calculating angles 1
a 35° and 35°
b 65° and 65° or 50° and 80°
c If the angle given is less than 90° there are two possible answers 2
a False; the sum < 4 × 90° = 360°
b True; for example, 100°, 120°, 70° and 70°
c False; the sum > 4 × 90° = 360° Mixed questions 1
72°, 54° and 54°
2
a Student’s own sketch
3
30°, 60° and 90°
4
120°
5
a They add up to 720° = 2 quadrilaterals × 360°
b 45°, 67.5° and 67.5°
b Yes, you can always divide it into two quadrilaterals
6
Planning and collecting data 6.1 Planning to collect data 1
a He is only asking the members of the maths club so they will probably choose maths as their favourite subject. b He should ask an equal number of students from each year group and each form class. Also, if it is a mixed school he should ask an equal number of boys and girls.
2
5
For example, ‘Collect primary data by asking a random selection of people in the town where I live.’ or ‘Find secondary data on the internet, giving the number of users of Facebook and Twitter worldwide.’
Challenge Workbook Answers
6.2 Collecting data 1
For example:
Questionnaire on school uniform 1
Are you: ❒ male
❒
2
What year group are you in?
3
Do you think that having a school uniform is a good idea?
female
❒ 7 ❒ 8 ❒ 9 ❒ 10 ❒ 11
❒ Yes ❒ No
Give a reason for your answer: .......................................................................................... ..............................................................................................................................................
❒ No 5 Would you rather not wear school uniform? ❒ Yes ❒ No 4
Are you happy to wear school uniform? ❒ Yes
Give a reason for your answer: .......................................................................................... .............................................................................................................................................. 6.3 Using frequency tables 1 a i Score Tally 1–18 llll llll llll 19–25
llll
Frequency 17
ll
lll
8 Total
25
ii Emyr is correct. The groups are not equal in size and there are only two groups so it does not show the difference in data very well. b For example: Score Tally Frequency 1–5
lll
6–10
llll
3 l
6
11–15 llll
4
16–20 llll
5
21–25 llll
ll
7 Total
2
Time (t seconds)
Tally
10 ≤ t < 15
ll
2
15 ≤ t < 20
llll
5
20 ≤ t < 25
llll
5
25 ≤ t < 30
llll llll l
11
30 ≤ t < 35
llll ll
7 Total
Mixed questions 1 6
Frequency
Student’ owns answers.
30
25
Challenge Workbook Answers
7
Fractions 7.1 Simplifying fractions 8 1 = b 2 1 a 16 2 11 1 1 1 7 2 a b c d e 12 4 5 3 10 48 3 3 is the odd one out; the others are all in their simplest form 80 7 7.2 Recognising equivalent fractions, decimals and percentages 14 7 = ii 70% b 30% (100% – 70% = 30%) 1 a i 20 10 2
a i
3 10
ii 30%
b i
1 4
ii 25%
7.3 Comparing fractions 1
a
2 12 4 8 5 15 = , = , = 3 18 9 18 6 18
b
4 2 5 , , 9 3 6
c
7 3 5 , , 12 4 6
7.4 Improper fractions and mixed numbers 1 1 1 b 3 c 2 1 a 1 3 6 4 2 a 3.2 b 2.75 c 2.25 11 18 5 3 a b c 2 5 4 7.5 Adding and subtracting fractions 7 1 1 a 5 b 3 c 81 8 8 24 13 2 a 9 b 1 c 24 28 12 5 5 3 a b 27 c 1 8 6 10 7.6 Finding fractions of a quantity 1
110 litres
2
Lynn has $200 left and Sal has $150 left, so Lynn has the most left
7.7 Finding remainders 1
100 → ÷ 7 → R2 137 → ÷ 8 → R1 213 → ÷ 6 → R3 179 → ÷ 9 → R8
7
Challenge Workbook Answers
Mixed questions
8
1
8 1 3 3 6 2 and , and , and 12 2 6 4 8 3
2
3 17 13 85 52 33 13 1 – = – = =1 Yes: 4 – 2 = 5 20 20 20 20 5 4 4
Symmetry 8.1 Recognising and describing 2D shapes and solids 1
a D
b F
c E
d B
8.2 Recognising line symmetry 1
2
8.3 Recognising rotational symmetry 1
For example: a
c
2
d
Order 3
For example:
a
8
b
Order 1
b
c
Order 2
Order 6
e A
f C
Challenge Workbook Answers
8.4 Symmetry properties of triangles, special quadrilaterals and polygons 1
For example: a
b
Mixed questions 1
a For example: y 10 9 8
A
7 6 5 4
B
3 2 1 0
0
1
2
3
4
5
6
7
8
9
10
x
7
8
9
10
x
b For example: y 10 9 8 A
7 6 5
B
4 3 2 1 0
2
9
0
1
2
3
4
5
6
Student’s own flow diagram
Challenge Workbook Answers
9
Expressions and equations 9.1 Collecting like terms 1
2
a
5x – 3x
2x
x×x
x2
3 × 3x
9x
5x × x
5x2
8x 2
4x
3x × 2x
6x2
7x – 4x
3x
8
1
6
3
5
7
4
9
2
b a+b
b–a–c
b+c
b+c–a
b
a+b–c
b–c
a+b+c
b–a
9.2 Expanding brackets 1
a 7x + 6
b 12 + 4x c 11x + 7
d 10x – 20
e 16x + 23
2
LHS = 4(2x + 7) + 3(6x – 5) = 8x + 28 + 18x – 15 = 26x + 13
f 22 + 19x
RHS = 13(2x + 1) = 26x + 13 3
a 9(3x + 2) = 3(9x + 6)
b 5(8 – 6z) = 10(4 – 3z)
9.3 Constructing and solving equations 1
a i x + x + 70° = 180° ii x = 55° iii 55° and 125° iv 55° + 125° = 180° b i 2x + 3x + 15° = 180° ii x = 33° c i x + 4x + 85° = 180° ii x = 19°
iii 66° and 114° iv 66° + 114° = 180° iii 19°, 76° and 85° iv 19° + 76° + 85° = 180°
d i 2x + 5x + 15° + x + 5° = 180° ii x = 20° iv 40° + 115° + 25° = 180°
iii 40°, 115° and 25°
Mixed questions 1
a i 3x + 10 + 3x + 5 + x + 5 = 360° ii x = 50° iv 160° + 155° + 45° = 360°
iii 160°, 155° and 45°
b i 2x + 30 + 3x + 25 + 2x – 5 + x + 30 = 360° ii x = 35° iv 100° + 130° + 65° + 65° = 360° c i 2x + 13 + x + 18 = 136 ii x = 35° 10
iii 100°, 130°, 65° and 65°
iii 83° and 53° iv 19° + 76° + 85° = 180°
Challenge Workbook Answers
10
2
a x=7
b x=4
3
a 5(x + 6) = 70, x = 8
c x = 25 d x = 10.5 x – 8 = 12, x = 44 b 3
Averages 10.1 Median, mode and range 1
24
2
a Many possible answers, e.g. 18, 19, 21, 26 b Many possible answers, e.g. 14, 15, 22, 22 c 14, 18, 22, 22
3
18
4
Three children are 120 cm; the fourth child is any height between 120 and 145 cm
5
a 22, 23, 34 and 40 b Either 23, 25, 28 and 34 or 22 and 40 and any two of the other four
6
a 20
b 38
10.2 The mean 1
a i 10
ii 20
iii 80
iv 14
b 2140
2
a 14
b 6
3
a 31
b The 11th person would be 75 years old
4
10.86 km
5
1.375
C 3
Mixed questions 1
6
2
Must be true The mean wage has increased
11
Must be false
Could be true or false
√
The median wage has increased
√
The range has increased
√
The range has decreased
√
Challenge Workbook Answers
3
a 6
b 5
c 10
d 0
e 6
f 9
4
a There are lots of possible answers, e.g. 3, 3, 4, 7, 8 b There are lots of possible answers, e.g. 1, 1, 5, 6, 7 c Not possible d There are lots of possible answers, e.g. 3, 4, 9, 10, 10
5
11
a Cannot say
b Cannot say
c It has increased
c 12.5% or 12½ %
d 6¼ % or 6.25%
Percentages 11.1 Simple percentages 1
a 50%
2
a 12.5% b 37.5% c 62.5% d 87.5%
3
a 3/20
b 1/40
c 9/20
d 3/40
4
a 125%
b 175%
c 250%
d 130%
5
a 11 10
b 14 5
c 23 10
d 11 20
6
7
b 25%
Percentage
20%
40%
65%
Fraction
1 5
2 5
13 20
Decimal
0.2
0.4
0.65
a Possible
b Impossible
130%
175%
190%
3 10
13 4
19 10
1.3
1.75
1.9
1
c Impossible
d Possible
11.2 Calculating percentages 1
a $14
b $11.20
c $78.75
d $6.30
2
a $420
b $21
c $147
d $2079
3
a 9 kg
b 27 kg
c 45 kg
d 63 kg
4
50% – 5% = 1200 – 120 = 1080
5
a 18 kg
6
a&b $5.30
7
Answers for each pair are the same. A% of B is the same as B% of A
8
a $645
b $64.50
c $6450
9
a $12.96
b $7.56
c $20.52
b $669.30
c $1290.30
10 a $60.03
b 78 kg c&d 13.5 kg
c 138 kg e&f 6 km
Mixed questions
12
1
They are $457.50 and $462 so the second is larger.
2
50%, $144, 200%, 20%, $45, 150%
Challenge Workbook Answers
12
3
20%, $1700, $2550
4
a 12 cm
b 40%
5
a 72 000
b 20% of 72 000 is 14 400, so the population is 57 600
c 140%
Constructions 12.1 Measuring and drawing lines 1
487 mm or 48.7 cm; 112 mm × 4 + 13 mm × 3
2
Student’s own answer
12.2 Drawing perpendicular and parallel lines 1
a Accurate drawing
b AD = 3.2 cm
c CH = 6.3 cm
12.3 Constructing triangles 1
Accurate drawing
12.4 Constructing squares, rectangles and polygons 1
a Accurate drawing 113°
b 126° 98°
93°
110°
Total = 540°, which is correct as it is the sum of the interior angles of a pentagon. Mixed questions 1
a x = 34°, y = 25° b AB = 4.2 m, BC = 5.7 m
13
Graphs 13.1 Plotting coordinates
13
1
a (5, 8)
b (–4, 3) c (3, –1)
d (–2, –1)
2
a (2, 3)
b (–2, 5) c (2.5, –2)
d (–1.5, –2.5)
3
a (2.5, 1.5)
b (–2, 3) c (–4, –3)
d (7, 0)
Challenge Workbook Answers y
4 5 4 3 2 1 –4
–3
–2
0
–1
1
2
3
4
5
6
7
x
–1 –2 –3
5
(–2, 8) and (4, 8) or (–2, –4) and (4, –4) or (1, 5) and (1, –1)
13.2 Other straight lines 1
(8, 9), (12, 13), (–3, –2), (–10, –9)
2
(0, 6), (5, 1), (–4, 10), (9, –3)
3
a YES
b NO
c NO
d YES
4
a NO
b YES
c NO
d YES
5 6
a YES a
b YES
c YES
d YES
6
x
4
2
0
–2
–4
1 x+2 2
3
2.5
2
1.5
1
b and 7
5 4 3 2
6b –6
–5
–4
1 –3
–2
–1 0 –1 –2
7 8
a (3, 0) and (0, –6) b (–3, 0) and (0, 6) c (–12, 0) and (0, 6) d (12, 0) and (0,–6)
14
–3 –4
1
2
3
4
5
6
Challenge Workbook Answers
Mixed questions 1
(2, –1) and (–3, 4)
2
a
y 6 5 4 3 2 1 –5
–4
–3
–2
0
–1
1
2
3
4
5
6
7
x
–1 –2 –3 –4
b (–3, 1) and (–1, –3) 3
a y = x + 2 is M; y = 2x – 2 is L; y = x – 2 is N; y = 1 x + 2 is P 2 b 7y 6 5 4 3 2 1 –5 –4 –3 –2 –1 0 –1
1 2
3
4
5
6
7
8
9 10 11
x
–2 –3
14
4
A y = 2x + 1
B y = 2x – 2
5
A y = 4x + 2
B y=x+2
C y = 2x – 8 C y= 1 x+2 2
D y = 2x + 12 D y=2
E y = –x + 2
Ratio and proportion 14.1 Simplifying ratios 1
a 25 : 1
2
8:5:7
3
8 : 5 : 30
4
9 : 13 : 6
b 8:1
c 24 : 1
d 16 : 3
14.2 Sharing in a ratio
15
1
a 25 5-cent coins, 15 10-cent coins and 10 25-cent coins
2
Mia $270, Ewan $135 and Dai £27
3
$9.60
4
562.5 ml
b $5.25
Challenge Workbook Answers
14.3 Using direct proportion 1
Offer 2, because it is the cheapest per bag: Offer 1 is 28.33 c per bag, Offer 2 is 25 c per bag, Offer 3 is 26.6 c per bag
2
$1.39
Mixed questions 1
a 10 : 7 : 2 : 1
b 280 g
2
a 135 cm or 1.35 m
b 24 cm or 0.24 m
c i 191.25 cm (accept 191 cm or 192 cm or equivalent in metres) ii Student’s own answers e.g. Yes, assuming the hat fitted him. No, as it might not be his hat. No, as he may have dropped a different sized hat to fool the police, etc.
15
Time 15.1 The 24-hour clock 1
a 11 hours 15 minutes
b 10 hours 35 minutes
c 27 hours 35 minutes
d 34 hours 40 minutes
2
a 14 35
b 11 55
3
a 05 30 Monday
4
11 35 Wednesday
5
Chicago is seven hours behind Amsterdam
b 08 00 Monday
c 22 30 Sunday
15.2 Timetables 1
a 4 hours 44 minutes
b 3 hours 23 minutes
2
a 6 hours 25 minutes
b 2 hours
c 1 hour 58 minutes
c The missing entries are: 6 h 50 m; 23 55; 6 h 45 m; 06 15 + 1 day; 06 50 + 1 day 3
a 3h
b 4 h 30 m
c 30 minutes
d 07 20
15.3 Real-life graphs
16
1
a 150 ÷ 2 = 75 b 100 ÷ 2 = 50 c 25 km/h
2
a 15 km/h
b 10 km/h
c 10 km/h
3
a 50 km/h
b 33.3 km/h
c 40 km/h
d 6 hours
e 50 km/h
Challenge Workbook Answers
Mixed questions 1 Jakarta 22.22
16
Karachi
London
Mexico City
Moscow
20.22
16.22
10.22
18.22
2
08 50 on Tuesday 5 March
3
6 km/h
4
a 6 hours 51 minutes
b 2 hours 40 minutes
c 14 10, 15 27, 16 50, 20 06
Probability 16.1 Equally likely outcomes 1
a 0.5
b 0.1
c 0.9
2
a 0.01
b 0.81
c 0.18
3
a 0.001
b 0.027
c 0.729
4
There are six 2s, three 4s, two 6s and one face is any other number
d 0.243
16.2 Estimating probabilities 1
a i 0.3
2
a
ii 0.7
b i 0.26 ii 0.74
Total throws
10
20
30
Probability
0.2
0.1
0.1
b
c 48 times. This is 0.26 × 186
40
50
60
70
0.075 0.08 0.1 0.129
80
90
100
0.15
0.156
0.16
Experimental probability
0.3
0.2
0.1
0
0
10
20
30
40
50 60 Throws
70
80
90
100
c The probabilities will get closer to the theoretical probability of 1/6 or 0.167 3
17
a i 0.15
ii 0.25
iii 0.2
c i 0.3
ii 0.19
iii 0.18
b i 0.4
ii 0.15
iii 0.17
Challenge Workbook Answers
Mixed questions
17
1
a 15
b 30
c 1/10
2
a No
b 0.8
c Ahmed 8; Beth 14
3
a 0.15
b 0.3
4
a i 0.5
ii 0.3 iii 0.6
iv 0.7
b i
YES
ii NO iii YES iv YES
Position and movement 17.1 Reflecting shapes y 1 8 7 6
C
5 A
4
D
3 B
2 1 0
d 4 2
0
1
2
3
4
5
6
7
x
8
e 4 y
a i and c i Q2ai and ci
6 5 B1 4 3 A 1 2 1
–6 –5 –4 –3 –2 –1 0 B3 A3 –1 Answer to ci –2 C3 –3 –4 –5 –6
a ii
18
C1 C2 Answer to ai A2
B2
1 2 3 4 5 6
x
Object A1 B1 C1
A1
(1, 3)
B1
(1, 4)
C1
(3, 4)
Image A2 B2 C2
A2
(3, 1)
B2
(4, 1)
C2
(4, 3)
Challenge Workbook Answers
b The x and y numbers are swapped over c ii Object A B C A1 (1, 3) 1 1 1 Image A3 B3 C3
A2
(–3, –1)
B1
(1, 4)
C1
(3, 4)
B2
(–4, –1)
C2
(–4, –3)
iii The x and y numbers are swapped over and become negative. d Student’s own answers 17.2 Rotating shapes 1
y
a–c 8 7 6 5
B
4
C
3 2
A
1 0
D
0
1
2
3
4
5
6
7
d Rotation 180° centre (6, 2)
8
9 10 11 12 13
x
e Reflection in line x = 6
2 a
b
c
B
A
A
B Rotation 180°
A
B
rotation clockwise 60° or rotation anticlockwise 300° rotation anticlockwise 120° or rotation clockwise 240°
17.3 Translating shapes 1
a Translation 5 squares right and 1 square up b Translation 8 squares right and 3 squares up
2
a i e.g. translation 1 square right and 2 squares down followed by 1 square right and 2 squares up ii 2 b i e.g. translation 1 square right and 2 squares up followed by 1 square right and 2 squares down, followed by 1 square right and 2 squares up ii 3
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Challenge Workbook Answers
Mixed questions 1 a y 6 5
B
4 3 2
A
1 0
0
1
2
3
4
5
x
6
b Transformation 1: rotation of 180° about centre (3, 3); Transformation 2: reflection in the line y = 3 2
a–c
y 6 5
F
4 3 2 1
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
x
–1 –2 –3
C
–4
x = -1
E D
–5
d Reflection in the line y = 0.5 e Rotation 180° centre (–1, 0.5)
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Area, perimeter and volume 18.1 Converting between units for area
20
1
For example, 8 cm2 = 800 mm2 because there are 100 mm2 in 1 cm2
2
a i 950 mm2
ii 9.5 cm2
b i 275 mm2
ii 2.75 cm2
Challenge Workbook Answers
3 4
a i 14 500 cm2
ii 1.45 m2
b i 4 72 000 cm2
ii 47.2 m2
a 0.32 m2
b 3200 cm2
18.2 Calculating the area and perimeter of rectangles 1
48 m
2
4705.96 m2
3
a 17.4 cm2 or 1740 mm2
b 6.45 m2 or 64500 cm2
18.3 Calculating the area and perimeter of compound shapes 1
a 110 cm2
2
15 cm
b 116 cm2
18.4 Calculating the volume of cuboids 1
6 cm
2
a 120 cm3 b For example, 3 cm × 8 cm × 5 cm, 12 cm × 2 cm × 5 cm, 6 cm × 2 cm × 10 cm, 3 cm × 4 cm ×10 cm
3
7 mm
18.5 Calculating the surface area of cubes and cuboids 1
384 cm2
2
684 cm2
3
Surface area = 24 400 cm2, yes because 30 000 cm2 > 24 400 cm2
Mixed questions 1
Length = 17 cm and width = 3 cm
2
a 250 cm3
3
a B = 4 cm, C = 2 cm
b 240 cm3 b A = 92 cm2, B = 80 cm2, C = 88 cm2
c B, because the surface area is the smallest so the box would cost less to produce d Student’s own answers D = 4 cm × 4 cm × 4 cm has SA = 96 cm2 E = 2 cm × 8 cm × 4 cm has SA = 112 cm2 F = 1 cm × 4 cm × 16 cm has SA = 168 cm2
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Challenge Workbook Answers
19
Interpreting and discussing results 19.1 Interpreting and drawing pictograms, bar charts, bar-line graphs and frequency diagrams 1
a
Flavour
Tally
Frequency
Vanilla
llll lll
8
Strawberry
llll llll llll l
16
Chocolate
llll l
6 Total
30
b Example of pictogram: Key:
represents 2 milkshakes
Vanilla Strawberry Chocolate 2
a 60 b
Time (seconds)
Tally
Frequency
10–19
llll ll
7
20–29
llll llll ll
12
30–39
llll llll llll llll llll
24
40–49
llll llll llll ll
17 Total:
60
c For example: Time taken for students to complete a puzzle 25
Frequency
20
15
10 5 0
10-19
20-29
Time in seconds
22
30-39
40-49
Challenge Workbook Answers
19.2 Interpreting and drawing pie charts 1
Example of pie chart Proportion of different colour T-shirts sold
Red Blue Yellow Green
19.3 Drawing conclusions 1
a For example: There were twice as many students in class 7P that had no brothers compared to class 7T. Class 7P had more students with 2 and 3 brothers than class 7T. b i 28
ii 35
c i 42
ii 49
d i 1.5
ii 1.4
e For example: Class 7T had a higher mean number of brothers per student than class 7P
Mixed questions 1
a i $57.50
ii $55
b i $25
ii $75
c For example: John raised the most money in April, compared with Raul who raised the most money in March. John raised more on average than Raul as he had a higher mean. Raul had a higher range, which shows that the amount he raised each month was more varied than John.
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