Functional Skills Maths. Level 2 Answer Book v1.1

Transcription

1 Functional Skills Maths Level 2 Answer Book v1.1

2 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 Estimating and Checking Levels of Accuracy Apply the Skill Understand, use and calculate ratio and proportion, including problems involving scale Ratio Scale Diagrams Apply the Skill Understand and use equivalences between fractions, decimals and percentages Equivalent Fractions and Simplest Form Finding a Fraction of an Amount Evaluate One Number as a Fraction of Another Adding and Subtracting Fractions Rounding Decimals Add, Subtract, Multiply and Divide Decimals Percentages Percentage Increase and Decrease Converting between Fractions, Decimals and Percentages Apply the Skill Understand and use simple formulae and equations involving one- or two-step operations Bidmas Formulae Substitution Apply the Skill Recognise and use 2D representations of 3D objects D Shapes Nets Plans Parallel Lines Apply the Skill Find area and perimeter of common shapes Perimeter Circumference Area

3 Find volume of common shapes Volume Apply the Skill Use, convert and calculate using metric and, where appropriate, imperial measures Convert Currencies Dates Time Temperature Length Weight Capacity Apply the Skill Collect and represent discrete and continuous data, using ICT where appropriate Types of Data Gathering Discrete Data with Tally Charts Gathering Continuous Data Representing Data in a Bar Chart Representing Data in a Pie Chart Representing Data in a Line Graph Representing Data in a Scatter Graph Using ICT Apply the Skill Use and interpret discrete and continuous data Reading and Extracting Data from Tables Reading and Extracting Data from Bar Charts Reading and Extracting Data from Pie Charts Reading and Extracting Data from Line Graphs Reading and Extracting Data from Scatter Graphs Reading Continuous Data Apply the Skill Use statistical methods to investigate situations Mean, Median and Mode Range Apply the Skill Use probability to assess the likelihood of an outcome Probability Tree Diagrams & Tables Apply the Skill

4 Functional Skills Maths Level 2 Understand and use positive and negative numbers of any size in practical contexts v

5 Place Value 1) ) Yes 3) Five thousand and twenty One million five hundred and one thousand 52 Fifty one thousand and ten One billion five hundred and ten thousand Fifty two ) 200 miles 5) ) ) 7 Billion 8) )

6 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) ) -1 C 6) Stockholm 7) ) 9 C 6

7 Apply the Skill 1) a) Eve s account b) ) ) ) Yes 5) 17 C 6) ) )

8 Functional Skills Maths Level 2 Carry out calculations with numbers of any size in practical contexts, to a given number of decimal places v

9 Rounding 1) = = = ) = = = ) ) ) ) ) $ 2 billion 8) 454 billion 9) 64.5 million 10) 12.5 million 9

10 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)

11 Estimating and Checking 1) 56 = = = = = 9 2) Inverse calculation: / 12 = ) Inverse calculation: x 14= 245 4) 200 ~ 250 miles 5) $200 Levels of Accuracy 1) ) ) 11 glasses 4) 7 5) 333 mm 11

12 Apply the Skill 1) ) 4 million 3) ) 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 = ) 15 miles Inverse calculation: 1460 x 15 = ) 560 km 11)

13 Functional Skills Maths Level 2 Understand, use and calculate ratio and proportion, including problems involving scale v

14 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) m 3) 2.5 km 4) 14 cm 5) 8.5 cm 6) 1 cm : 2 m 14

15 Apply the Skill 1) 300 2) 1.5 kg 3) 300 4) 80 g 5) 19 : 15 6) ) 520 loaves 8) 180 9) 320 miles 10) 87.5 km 11) ) 34 cm 13) 1 :

16 Functional Skills Maths Level 2 Understand and use equivalences between fractions, decimals and percentages v

17 Equivalent Fractions and Simplest Form 1) 5 12 = = = = = = ) = = = = = = 3 4 Finding a Fraction of an Amount 1) 1 8 of 72 = of 1050 = of 1272 = 212 of 275 = of 135 = of 576 = 528 2) 152 bricks 3) 42 4) people 5)

18 Evaluate One Number as a Fraction of Another 1) 2) 3) 4) 5) 6) Adding and Subtracting Fractions 1) = = = ) = ) = = ) )

19 Rounding Decimals 1) = = = = 8.7 2) = = = = ) = = = = ) 1.5 cm 5) ) m 19

20 Add, Subtract, Multiply and Divide Decimals 1) = = ) = = ) 20.1 x 0.23 = x 2.5 = ) = = 1.9 5) m 6) ) ) ) )

21 Percentages 1) 405 2) 8 3) 21 4) 30% 5) 20% 6) 2% 7) ) ) 75% 10) 70% 11) 32% 21

22 Percentage Increase and Decrease 1) 455 2) 228 3) ) ) ) ) ) 320 9) 6% 10) 20% 22

23 Converting between Fractions, Decimals and Percentages 1) FS MATHS LEVEL 2 - ANSWERS 2) ) ) 57.8% 5) ) 15% 7) ) 37.5% 9)

24 Apply the Skill 1) a) 20% b) ) a) b) 4% 3) ) ) ) ) 6% 24

25 Functional Skills Maths Level 2 Understand and use simple formulae and equations involving one- or two-step operations 25

26 Bidmas 1) x 3 = 31 3 x 6 9 = x = 11 4 x = 19 (12 3) = 8 15 x 2 (8 + 4) = 18 (14 6) x (6 + 2) = 64 3 x 2² x 5 = (4² - 2³) = 11 8 x 5 (5² - 9) = 24 Formulae 1) 40y 2) T = h 3) C = m 4) T = e 5) T = 50y

27 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) ) C =

28 Apply the Skill 1) ) ) 20 C 4) 44 m 2 5) 70 6) 1.5 hours 7)

29 Functional Skills Maths Level 2 Recognise and use 2D representations of 3D objects v

30 3D Shapes 1) Shape Name Faces Edges Vertices Cube Cuboid Cylinder Pyramid Triangular Prism

31 Nets 1). 2) Pyramid 3) Triangular Prism Plans 1) Parallel Lines 1) 2) Bookcase, Carpet Tile, Door 3) 60 4) No 31

32 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 32

33 Functional Skills Maths Level 2 Find area and perimeter of common shapes v

34 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) cm 3) m 4) ) 13.4 m 6) m 34

35 Area 1) 703 m 2 2) 8.58 m 2 3) 10.6 m 2 4) m 2 5) 17 m 6) 4 tins 7) 36 tiles 35

36 Functional Skills Maths Level 2 Find volume of common shapes v

37 Volume 1) 105 cm 3 2) 1.5 cm 3) 12 cm 4) cm 3 5) 12.9 m 3 6) 288 cm 3 7) m 3 8) 47 cm 9) 50 cm 10) m 3 11) cm 3 12) 20 cm 13) cm

38 Apply the Skill 1) 5132 m 2) m 2 3) 1.35 m 3 4) a) cm 2 b) cm 3 5) 61.3 m 6) m 3 7) 5 8) Length = 15 cm Width = 15 cm Height = 16 cm 38

39 Functional Skills Maths Level 2 Use, convert and calculate using metric and, where appropriate, imperial measures v

40 Convert Currencies 1) 400 = = = ) 250 = $ = $ ) $165 = $770 = ) a) $855 b) ) Indian Rupees 6)

41 Dates 1) 25 / 12 / / 04 / / 07 / ) 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:

42 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) m 5) a) 3 ft 4 inches b) No 6) 20 miles 7) 1.75 metres 8) 128 kilometres 9) 23 cm 42

43 Weight 1) 7050 grams 2) Largest kg 4 kg 450 g 4.4 kg 4.04 kg 4004 kg 3) a) 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 43

44 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 44

45 Apply the Skill 1) ) 09 : 25 3) 15 : 45 4) 1.63 m 5) 8 stone 6) 48 km 7) 2 litres 8) 8 glasses 9) 29 / 04 / ) ) 59 F 12) 80 miles 13) 6 gallons 45

46 Functional Skills Maths Level 2 Collect and represent discrete and continuous data, using ICT where appropriate v

47 Types of Data 1) Continous Data, Primary Data 2) Discrete Data, Secondary Data Gathering Discrete Data with Tally Charts 1) ) Cities Tally Frequency Paris 4 Amsterdam 2 Rome 5 Berlin 2 Budapest 1 Madrid 2 London 4 3) 47

48 Gathering Continuous Data 1) < > > 2) 5 0 < n < < n < < n < < n < < n < 9 Distance (km) Tally Frequency 0 < distance < 3 3 3) 3 < distance < < distance < < distance <

49 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 Romance War Horror ) Other

50 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) 50

51 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 51

52 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 v

53 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)

54 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)

55 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% 55

56 c) FS MATHS LEVEL 2 - ANSWERS Functional Skills Maths Level 2 Use statistical methods to investigate situations v

57 Mean, Median and Mode 1) a) 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) ) 90 5) 92 6) a) 17 years b) 17 years c) 17 years Range 1) 78 2) 24 C 57

58 3) 5.2 m 4) a) 75 b) 50 c) No d) ) 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) Totals

59 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 v

60 Probability 1) 2 3 2) a) b) 3) a) b) ) 36% 5) 0.1 6) Daisy is more likely to land her spinner on red than pick a red ball 60

61 Tree Diagrams & Tables 1) 3 possible outcomes 2) 3) ) a) 16 possible outcomes b) c) 5) a) b) Apply the Skill 1) ) 1 4 3) 1 5 4) 80% 5) Bag

62 6) a) 0.1 b) 6 7) a) 1 2 Dice Dice b) c) ) a) 1 = Vanilla 2 = Strawberry 3 = Chocolate 4 = CS 5 = V V 6 = SS b) c) ) No, Molly is not correct because they both have the same chance of winning. 62

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