Functional Skills Maths Level 2 Answer Book v1.1
Contents Understand and use positive and negative numbers of any size in practical contexts... 4 Place Value... 5 Positive and Negative Numbers... 6 Apply the Skill... 7 Carry out calculations with numbers of any size in practical contexts, to a given number of decimal places... 8 Rounding... 9 Multiples... 10 Estimating and Checking... 11 Levels of Accuracy... 11 Apply the Skill... 12 Understand, use and calculate ratio and proportion, including problems involving scale... 13 Ratio... 14 Scale Diagrams... 14 Apply the Skill... 15 Understand and use equivalences between fractions, decimals and percentages... 16 Equivalent Fractions and Simplest Form... 17 Finding a Fraction of an Amount... 17 Evaluate One Number as a Fraction of Another... 18 Adding and Subtracting Fractions... 18 Rounding Decimals... 19 Add, Subtract, Multiply and Divide Decimals... 20 Percentages... 21 Percentage Increase and Decrease... 22 Converting between Fractions, Decimals and Percentages... 23 Apply the Skill... 24 Understand and use simple formulae and equations involving one- or two-step operations... 25 Bidmas... 26 Formulae... 26 Substitution... 27 Apply the Skill... 28 Recognise and use 2D representations of 3D objects... 29 3D Shapes... 30 Nets... 31 Plans... 31 Parallel Lines... 31 Apply the Skill... 32 Find area and perimeter of common shapes... 33 Perimeter... 34 Circumference... 34 Area... 35 www.bksb.co.uk 2
Find volume of common shapes... 36 Volume... 37 Apply the Skill... 38 Use, convert and calculate using metric and, where appropriate, imperial measures... 39 Convert Currencies... 40 Dates... 41 Time... 41 Temperature... 42 Length... 42 Weight... 43 Capacity... 44 Apply the Skill... 45 Collect and represent discrete and continuous data, using ICT where appropriate... 46 Types of Data... 47 Gathering Discrete Data with Tally Charts... 47 Gathering Continuous Data... 48 Representing Data in a Bar Chart... 49 Representing Data in a Pie Chart... 49 Representing Data in a Line Graph... 50 Representing Data in a Scatter Graph... 51 Using ICT... 51 Apply the Skill... 51 Use and interpret discrete and continuous data... 52 Reading and Extracting Data from Tables... 53 Reading and Extracting Data from Bar Charts... 53 Reading and Extracting Data from Pie Charts... 53 Reading and Extracting Data from Line Graphs... 53 Reading and Extracting Data from Scatter Graphs... 54 Reading Continuous Data... 54 Apply the Skill... 55 Use statistical methods to investigate situations... 56 Mean, Median and Mode... 57 Range... 57 Apply the Skill... 58 Use probability to assess the likelihood of an outcome... 59 Probability... 60 Tree Diagrams & Tables... 61 Apply the Skill... 61 www.bksb.co.uk 3
Functional Skills Maths Level 2 Understand and use positive and negative numbers of any size in practical contexts v1.0 www.bksb.co.uk 4
Place Value 1) 30 000 2) Yes 3) Five thousand and twenty 1 000 510 000 One million five hundred and one thousand 52 Fifty one thousand and ten 1 501 000 One billion five hundred and ten thousand 51 010 Fifty two 5020 4) 200 miles 5) 2 320 502 6) 400 000 7) 7 Billion 8) 20 001 030 001 9) 6000 www.bksb.co.uk 5
Positive and Negative Numbers 1) No 2) Tom 3) Coldest 25 C 16 C 11 C 2 C -6 C -25 C -33 C 4) 22.98 5) -1 C 6) Stockholm 7) - 39.67 8) 9 C www.bksb.co.uk 6
Apply the Skill 1) a) Eve s account b) 34.34 2) 156.56 + 75 3) - 73.88 4) Yes 5) 17 C 6) - 64.49 7) 1400 8) 417.00 www.bksb.co.uk 7
Functional Skills Maths Level 2 Carry out calculations with numbers of any size in practical contexts, to a given number of decimal places v1.0 www.bksb.co.uk 8
Rounding 1) 895 472 = 900 000 5 352 369 = 5 400 000 651 2 004 = 651 700 000 2) 1 986 159 = 2 000 000 78 520 405 = 79 000 000 981 559 951 = 982 000 000 3) 2 045 000 4) 455 500 5) 400 000 6) 254 000 000 7) $ 2 billion 8) 454 billion 9) 64.5 million 10) 12.5 million www.bksb.co.uk 9
Multiples 1) a) 8, 16, 24, 32, 40 b) 9, 18, 27 2) 12 3) 1, 2, 4, 5, 10, 20 4) 1, 2, 3, 6, 9, 18 5) 2 x 3 2 6) 48 2 x 24 2 x 12 2 x 6 2 x 3 7) 2 2 x 3 x 5 8) 7, 14, 21, 28, 35 9) 1, 2, 3, 5, 6, 10, 15, 30 10) 6 11) 8, 16, 24, 32 12) 8 www.bksb.co.uk 10
Estimating and Checking 1) 56 = 60 270 = 300 1836 = 2000 63 500 = 60 000 8.6 = 9 2) 1749.60 Inverse calculation: 1749.60/ 12 = 145.80 3) 17.50 Inverse calculation: 17.50 x 14= 245 4) 200 ~ 250 miles 5) $200 Levels of Accuracy 1) 45.77 2) 259.74 3) 11 glasses 4) 7 5) 333 mm www.bksb.co.uk 11
Apply the Skill 1) 177 600 000 2) 4 million 3) 600 000 4) 1, 2, 4, 8, 16, 32 5) 2 2 x 3 x 5 6) 3 billion 7) 6000 minutes 8) 757 jackets Inverse calculation: 757 X 25 = 18925 9) 15 miles Inverse calculation: 1460 x 15 = 21 900 10) 560 km 11) 43.23 www.bksb.co.uk 12
Functional Skills Maths Level 2 Understand, use and calculate ratio and proportion, including problems involving scale v1.0 www.bksb.co.uk 13
Ratio 1) 90 kg 2) 240g 3) 1.75 litres 4) 3 lengths 5) 9 litres of blues paint 3 litres of white paint 6) 300 7) 15 cm 8) 3000 birds Scale Diagrams 1) 60 cm 2) 21.75 m 3) 2.5 km 4) 14 cm 5) 8.5 cm 6) 1 cm : 2 m www.bksb.co.uk 14
Apply the Skill 1) 300 2) 1.5 kg 3) 300 4) 80 g 5) 19 : 15 6) 1.85 7) 520 loaves 8) 180 9) 320 miles 10) 87.5 km 11) 300 12) 34 cm 13) 1 : 20 www.bksb.co.uk 15
Functional Skills Maths Level 2 Understand and use equivalences between fractions, decimals and percentages v1.0 www.bksb.co.uk 16
Equivalent Fractions and Simplest Form 1) 5 12 = 15 36 3 14 = 9 42 8 24 = 1 3 16 40 = 2 5 14 21 = 2 3 3 5 = 30 50 2) 15 20 = 3 4 11 66 = 1 6 6 24 = 1 4 28 32 = 7 8 9 27 = 1 3 48 64 = 3 4 Finding a Fraction of an Amount 1) 1 8 of 72 = 9 1 6 1 7 of 1050 = 150 2 5 of 1272 = 212 of 275 = 110 5 9 of 135 = 75 11 12 of 576 = 528 2) 152 bricks 3) 42 4) 8 828 000 people 5) 1140.00 www.bksb.co.uk 17
Evaluate One Number as a Fraction of Another 1) 2) 3) 4) 5) 6) 7 10 1 10 2 3 7 25 11 20 2 25 Adding and Subtracting Fractions 1) 3 4 + 1 8 = 7 8 2 1 2 + 3 5 = 3 1 10 4 3 8 + 1 2 3 = 6 1 24 2) 3 1 2 + 5 6 = 2 2 3 3) 6 7 12 4 3 4-1 3 8 = 3 1 8 3 3 5-1 9 10 = 1 7 10 4) 5 24 5) 1 20 www.bksb.co.uk 18
Rounding Decimals 1) 21.65 = 21.7 4.27 = 4.3 109.883 = 109.9 8.6749 = 8.7 2) 34.356 = 34.36 2.874 = 2.87 124.459 = 124.46 15.9857 = 15.99 3) 3.9856 = 3.986 69.1287 = 69.129 1.0408 = 1.041 456.9518 = 456.952 4) 1.5 cm 5) 30.85 6) 7.866 m www.bksb.co.uk 19
Add, Subtract, Multiply and Divide Decimals 1) 20.72 + 2.027 = 22.747 101.01 + 10.11 + 1.001 = 112.121 2) 3.8 1.09 = 2.71 21.7 4.106 = 17.594 3) 20.1 x 0.23 = 4.623 0.067 x 2.5 = 0.1675 4) 6.5 0.2 = 32.5 0.475 0.25 = 1.9 5) 7.775 m 6) 1.78 7) 17.85 8) 312.50 9) 98.00 10) 170.80 www.bksb.co.uk 20
Percentages 1) 405 2) 8 3) 21 4) 30% 5) 20% 6) 2% 7) 192.50 8) 305.25 9) 75% 10) 70% 11) 32% www.bksb.co.uk 21
Percentage Increase and Decrease 1) 455 2) 228 3) 53.76 4) 655.20 5) 29.75 6) 10 500 7) 129.50 8) 320 9) 6% 10) 20% www.bksb.co.uk 22
Converting between Fractions, Decimals and Percentages 1) 0.875 FS MATHS LEVEL 2 - ANSWERS 2) 33 40 3) 0.075 4) 57.8% 5) 16 25 6) 15% 7) 0.125 8) 37.5% 9) 4 25 www.bksb.co.uk 23
Apply the Skill 1) a) 20% b) 3 20 2) a) 295.75 b) 4% 3) 252.48 4) 24.50 5) 202.10 6) 3.03 7) 6% www.bksb.co.uk 24
Functional Skills Maths Level 2 Understand and use simple formulae and equations involving one- or two-step operations www.bksb.co.uk 25
Bidmas 1) 7 + 8 x 3 = 31 3 x 6 9 = 9 18 5 x 2 + 3 = 11 4 x 7-45 5 = 19 (12 3) 3 + 5 = 8 15 x 2 (8 + 4) = 18 (14 6) x (6 + 2) = 64 3 x 2² x 5 = 60 3 + (4² - 2³) = 11 8 x 5 (5² - 9) = 24 Formulae 1) 40y 2) T = 25 + 50h 3) C = 4 + 1.25m 4) T = 35 + 0.04e 5) T = 50y + 270 www.bksb.co.uk 26
Substitution 1) 3a + b = 18 4a + 2b = 26 5a + 3b c = 25 6(a + b) = 48 5(b + c) = 12 a 2) 160 cm 3 3) 2500 p 4) 61.00 5) C = 30 www.bksb.co.uk 27
Apply the Skill 1) 550.00 2) 19.00 3) 20 C 4) 44 m 2 5) 70 6) 1.5 hours 7) 39 www.bksb.co.uk 28
Functional Skills Maths Level 2 Recognise and use 2D representations of 3D objects v1.0 www.bksb.co.uk 29
3D Shapes 1) Shape Name Faces Edges Vertices Cube 6 12 8 Cuboid 6 12 8 Cylinder 3 2 0 Pyramid 5 8 5 Triangular Prism 5 9 6 www.bksb.co.uk 30
Nets 1). 2) Pyramid 3) Triangular Prism Plans 1) Parallel Lines 1) 2) Bookcase, Carpet Tile, Door 3) 60 4) No www.bksb.co.uk 31
Apply the Skill 1) A = 3 B = 7 C = 6 D = 1 E = 8 F = 4 G = 2 H = 5 2) a) Plan b) 0.9 m by 3.5 m 3) a) A b) 0.65 m 4) Tutor mark 5) Tutor Mark www.bksb.co.uk 32
Functional Skills Maths Level 2 Find area and perimeter of common shapes v1.0 www.bksb.co.uk 33
Perimeter 1) 72 m 2) 129 m 3) 13.1 m 4) 38.2 m 5) 127 m 6) 75 m 7) 8.3 m Circumference 1) 62.8 cm 2) 345.4 cm 3) 423.9 m 4) 238.64 5) 13.4 m 6) 398.02 m www.bksb.co.uk 34
Area 1) 703 m 2 2) 8.58 m 2 3) 10.6 m 2 4) 10 344.47 m 2 5) 17 m 6) 4 tins 7) 36 tiles www.bksb.co.uk 35
Functional Skills Maths Level 2 Find volume of common shapes v1.0 www.bksb.co.uk 36
Volume 1) 105 cm 3 2) 1.5 cm 3) 12 cm 4) 502.4 cm 3 5) 12.9 m 3 6) 288 cm 3 7) 2.772 m 3 8) 47 cm 9) 50 cm 10) 21.28 m 3 11) 461.58 cm 3 12) 20 cm 13) 18 840 cm 3 www.bksb.co.uk 37
Apply the Skill 1) 5132 m 2) 75.42 m 2 3) 1.35 m 3 4) a) 706.5 cm 2 b) 28 260 cm 3 5) 61.3 m 6) 163.28 m 3 7) 5 8) Length = 15 cm Width = 15 cm Height = 16 cm www.bksb.co.uk 38
Functional Skills Maths Level 2 Use, convert and calculate using metric and, where appropriate, imperial measures v1.0 www.bksb.co.uk 39
Convert Currencies 1) 400 = 528 350 = 462 780 = 1029.60 2) 250 = $377.50 475 = $717.25 3) $165 = 96.49 $770 = 450.29 4) a) $855 b) 168.98 5) 28 500 Indian Rupees 6) 121.05 www.bksb.co.uk 40
Dates 1) 25 / 12 / 2017 01 / 04 / 1999 29 / 07 / 2010 2) Dear Rob, We are looking forward to you meeting you on 07 / 10 / 2015 at 14 : 00 at your office in Liverpool. Please confirm this is still convenient. Thanks, Tom The meeting time in Birmingham will be 16:30. 3) a) 02 / 12 / 2015 b) Thursday Time 1) 05:17 2) 6 minutes 33 seconds 3) 5 years 6 months 4) 16:52 5) 08:06 www.bksb.co.uk 41
Temperature 1) 90 F 2) 50 C 3) 8 C 4) 104 F 5) 10 C Length 1) a) 96 cm b) 0.96 m 2) 3 yards = approximately 3 m 3 feet = approximately 90 cm 8 inches = approximately 20 cm 3) Largest 1 km 50 m 1100 cm 1875 mm 185 cm 200 mm 4) a) 5.05 m b) 20.85 m 5) a) 3 ft 4 inches b) No 6) 20 miles 7) 1.75 metres 8) 128 kilometres 9) 23 cm www.bksb.co.uk 42
Weight 1) 7050 grams 2) Largest 4 1 2 kg 4 kg 450 g 4.4 kg 4.04 kg 4004 kg 3) a) 2.547 kg b) 2.97 kg 4) a) 300 g b) 15 kg 5) 200 g 6) 5.5 lbs 7) a) 2.5 ~ 3 lbs b) No 8) 4 kg 250 g 9) 9 kg www.bksb.co.uk 43
Capacity 1) 0.06 litres 2) 7 pints = approximately 4 litres 27 litres = approximately 6 gallons 3) Largest 222 cl 2.2 L 2022 ml 2.02 L 2002 ml 4) 8.9 litres 5) Smallest 2 gals 400 fluid ounces 24 pints 6) 35 fluid ounces 7) 2 containers 8) 16 gallons www.bksb.co.uk 44
Apply the Skill 1) 504.00 2) 09 : 25 3) 15 : 45 4) 1.63 m 5) 8 stone 6) 48 km 7) 2 litres 8) 8 glasses 9) 29 / 04 / 2015 10) 345 11) 59 F 12) 80 miles 13) 6 gallons www.bksb.co.uk 45
Functional Skills Maths Level 2 Collect and represent discrete and continuous data, using ICT where appropriate v1.0 www.bksb.co.uk 46
Types of Data 1) Continous Data, Primary Data 2) Discrete Data, Secondary Data Gathering Discrete Data with Tally Charts 1) 4 20 9 23 2) 8 14 12 22 Cities Tally Frequency Paris 4 Amsterdam 2 Rome 5 Berlin 2 Budapest 1 Madrid 2 London 4 3) www.bksb.co.uk 47
Gathering Continuous Data 1) < > > 2) 5 0 < n < 2 1 2 < n < 4 7 4 < n < 6 8 6 < n < 8 2 8 < n < 9 Distance (km) Tally Frequency 0 < distance < 3 3 3) 3 < distance < 6 2 6 < distance < 9 5 9 < distance < 12 5 www.bksb.co.uk 48
Representing Data in a Bar Chart 1) There is no title. The y-axis and x-axis are the wrong way round. The scale is much too large to meaningfully represent the data. There is no key. 2) Conservative Lib Dems Representing Data in a Pie Chart Film Genres Number of people Number of degrees Western 20 80 Romance 10 40 War 15 60 Horror 25 100 1) Other 20 80 www.bksb.co.uk 49
2) Representing Data in a Line Graph 1) Month Paula Stuart January 20 miles 20 miles March 30 miles 30 miles April 40 miles 40 miles July 55 miles 30 miles 2) www.bksb.co.uk 50
Representing Data in a Scatter Graph 1) Plot B is incorrect Plot F is incorrect Plot G is incorrect Using ICT 1) Tutor Mark Apply the Skill 1) a) Department Number of People Rocket 120 Logistics 80 Firefighting 10 Catering 50 Design and Engineering 75 Accounting 25 b) Pie Chart c) Scatter Graph 2) ROCKET TEST LAUNCH HEIGHTS TEST 3 TEST LAUNCHES HEIGHT (ft) X AXIS Y AXIS TITLE X AXIS VALUE Time in Air (seconds) Tally Frequency www.bksb.co.uk 51
3) FS MATHS LEVEL 2 - ANSWERS 0 < t < 5 I 1 5 < t < 10 II 2 10 < t < 15 I 1 15 < t < 20 III 3 20 < t < 25 II 2 25< t < 30 III 3 4) a) Anne b) Charlotte Functional Skills Maths Level 2 Use and interpret discrete and continuous data v1.0 www.bksb.co.uk 52
Reading and Extracting Data from Tables 1) a) Network: Mob4Me Model: The Brick b) 22 2) a) Mint Chips b) 53 Reading and Extracting Data from Bar Charts 1) a) 3-door b) Sport c) July d) 230 e) No Reading and Extracting Data from Pie Charts 1) a) Bills b) 24% c) 14% d) 56 Reading and Extracting Data from Line Graphs 1) Real Runner Monthly 2) 2600 www.bksb.co.uk 53
3) Snow Sports Magazine FS MATHS LEVEL 2 - ANSWERS 4) Snow Sports are typically sports that take place during the winter. Or words to that effect. Reading and Extracting Data from Scatter Graphs 1) The graph shows a negative correlation. The two pieces of data are caused by one another. 2) This graph shows no correlation. There is no causality between the two sets of data. 3) Does not imply causality / Implies causality Does not imply causality / Implies causality Does not imply causality / Implies causality Does not imply causality / Implies causality Reading Continuous Data 1) a) 20 < age < 25 b) 8 kg c) 31 kg 2) a) 6 www.bksb.co.uk 54
b) 14.9 m FS MATHS LEVEL 2 - ANSWERS Apply the Skill 1) a) Design 2 b) Design 3 c) 100 2) The graph suggests causality The graph shows causality The graph shows negative correlation The graph shows positive correlation The graph shows no correlation The graph suggests that there is no change in sales as price is reduced The graph suggests that there is an increase in sales as price is reduced The graph suggests that there is a decrease in sales as the price is reduced When the price is reduced by 60p, 100,000 drinks are sold When the price is reduced by 60p, 10,000 drinks are sold When the price is reduced by 60p, 100 drinks are sold 3) a) Driver A b) Driver B c) Driver A d) Driver B e) 70 km 4) a) Cola b) 18% www.bksb.co.uk 55
c) 70 000 FS MATHS LEVEL 2 - ANSWERS Functional Skills Maths Level 2 Use statistical methods to investigate situations v1.0 www.bksb.co.uk 56
Mean, Median and Mode 1) a) 109.4 p b) 109 p c) 109 p 2) a) 24 C b) 23.5 C c) 24 C and 23 C 3) a) 1.17 b) 1.17 c) 1.17 4) 90 5) 92 6) a) 17 years b) 17 years c) 17 years Range 1) 78 2) 24 C www.bksb.co.uk 57
3) 5.2 m 4) a) 75 b) 50 c) No d) 55.20 5) The median, because the mean is distorted by a high value 6) Less money was donated in Year 1 than Year 2 The amounts donated in Year 1 were more consistent than Year 2 Apply the Skill 1) a) 140 b) 174 c) 385 d) 226 2) Median, because the mean is distorted by a high wage 3) 97% 4) a) 125 b) 96 5) 3 Number of apples (a) Frequency (f) af 6) 28 2 56 29 4 116 30 8 240 31 4 124 32 2 64 Totals 20 600 www.bksb.co.uk 58
a) 30 b) 30 c) 30 7) Farm Fresh 8) a) Brevi 12 mins Snappy 9 mins b) Brevi 6 mins Snappy 4 mins c) The range is lower so the times are more consistent The mean is lower so buses are less minutes late More Snappy buses run on time Functional Skills Maths Level 2 Use probability to assess the likelihood of an outcome v1.0 www.bksb.co.uk 59
Probability 1) 2 3 2) a) b) 3) a) b) 1 13 1 26 1 5 7 10 4) 36% 5) 0.1 6) Daisy is more likely to land her spinner on red than pick a red ball www.bksb.co.uk 60
Tree Diagrams & Tables 1) 3 possible outcomes 2) 3) 7 8 5 9 4) a) 16 possible outcomes b) c) 5) a) b) 13 16 3 8 1 4 11 12 Apply the Skill 1) 1 12 2) 1 4 3) 1 5 4) 80% 5) Bag 2 www.bksb.co.uk 61
6) a) 0.1 b) 6 7) a) 1 2 Dice 2 3 4 5 6 Dice 1 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12 b) c) 1 12 5 18 8) a) 1 = Vanilla 2 = Strawberry 3 = Chocolate 4 = CS 5 = V V 6 = SS b) c) 1 3 5 9 9) No, Molly is not correct because they both have the same chance of winning. www.bksb.co.uk 62
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