functional skills maths

Level 2 Answer Book v1.1

Functional Skills Maths

FS MATHS LEVEL 2 - ANSWERS

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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

Contents


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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


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Level 2 Understand and use positive and negative numbers of any size in practical contexts

v1.0


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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


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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


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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


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

v1.0


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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


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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 32

6)

x

x x x 7) 22 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

24 2

2 12

2 6

48

3 2


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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


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Apply the Skill 1) 177 600 000

2) 4 million

3) 600 000

4) 1, 2, 4, 8, 16, 32

5) 22 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


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Level 2 Understand, use and calculate ratio and proportion, including problems involving scale

v1.0


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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


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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


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Level 2 Understand and use equivalences between fractions, decimals and percentages

v1.0


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Equivalent Fractions and Simplest Form

1) 512

= 1536

314

= 942

824

= 13

1640

= 25

1421

= 23

35 =

3050

2) 1520

= 34

1166

= 16

624

= 14

2832

= 78

927

= 13

4864

= 34

Finding a Fraction of an Amount

1) 18 of 72 = 9

16 of 1272 = 212

17 of £1050 = £150

25 of 275 = 110

59 of 135 = 75

1112

of £576 = £528

2) 152 bricks

3) £42

4) 8 828 000 people

5) £1140.00


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Evaluate One Number as a Fraction of Another

1) 710

2) 110

3) 23

4) 725

5) 1120

6) 225

Adding and Subtracting Fractions

1) 34 +

18 =

7

8

2 12 +

35 = 3

1

10

4 38 + 1

23 = 6

1

24

2) 3 12 +

56 = 2

2

3

4 34 - 1

38 = 3

1

8

3 35 - 1

910

= 1 7

10

3) 6 7

12

4) 524

5) 120


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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


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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


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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%


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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%


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Converting between Fractions, Decimals and Percentages

1) 0.875

2) 3340

3) 0.075

4) 57.8%

5) 1625

6) 15%

7) 0.125

8) 37.5%

9) 425


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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%


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Level 2 Understand and use simple formulae and equations involving one- or two-step operations


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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


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Substitution

1) 3a + b = 18

4a + 2b = 26

5a + 3b – c = 25

6(a + b) = 48

5(b + c) = 12

a

2) 160 cm3

3) 2500 p

4) £61.00

5) C = 30°


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Apply the Skill 1) £550.00

2) £19.00

3) 20 °C

4) 44 m2

5) €70

6) 1.5 hours

7) £39


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Level 2 Recognise and use 2D representations of 3D objects

v1.0


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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


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Nets 1) .

2) Pyramid

3) Triangular Prism

Plans

1)

Parallel Lines 1)

2) Bookcase, Carpet Tile, Door

3) 60

4) No


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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


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Level 2 Find area and perimeter of common shapes

v1.0


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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


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Area

1) 703 m2

2) 8.58 m2

3) 10.6 m2

4) 10 344.47 m2

5) 17 m

6) 4 tins

7) 36 tiles


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Level 2 Find volume of common shapes

v1.0


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Volume

1) 105 cm3

2) 1.5 cm

3) 12 cm

4) 502.4 cm3

5) 12.9 m3

6) 288 cm3

7) 2.772 m3

8) 47 cm

9) 50 cm

10) 21.28 m3

11) 461.58 cm3

12) 20 cm

13) 18 840 cm3


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Apply the Skill

1) 5132 m

2) 75.42 m2

3) 1.35 m3

4) a) 706.5 cm2

b) 28 260 cm3

5) 61.3 m

6) 163.28 m3

7) 5

8) Length = 15 cm

Width = 15 cm

Height = 16 cm


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Level 2 Use, convert and calculate using metric and, where appropriate, imperial measures

v1.0


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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


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Dates

1) 25 / 12 / 2017

01 / 04 / 1999

29 / 07 / 2010

2)

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

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


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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


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Weight

1) 7050 grams

2) Largest 4 12 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


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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


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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


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Level 2 Collect and represent discrete and continuous data, using ICT where appropriate

v1.0


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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 |||| |||| |||| |||| ||

3)

Cities Tally Frequency

Paris |||| 4

Amsterdam || 2

Rome |||| 5

Berlin || 2

Budapest | 1

Madrid || 2

London |||| 4


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Gathering Continuous Data

1) <

>

>

2)

3)

Distance (km)

Tally

Frequency

0 < distance < 3

|||

3

3 < distance < 6

||

2

6 < distance < 9

||||

5

9 < distance < 12

||||

5

5

1

8

7

2

0 < n < 2

2 < n < 4

6 < n < 8

4 < n < 6

8 < n < 9


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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

1)

Film Genres

Number of people

Number of degrees

Western

20

80 °

Romance

10

40 °

War

15

60 °

Horror

25

100 °

Other

20

80 °


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2)

Representing Data in a Line Graph

1)

2)

Month

Paula

Stuart

January

20 miles

20 miles

March

30 miles

30 miles

April

40 miles

40 miles

July

55 miles

30 miles


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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)

b) Pie Chart

c) Scatter Graph

2)

Department Number of People

Rocket 120

Logistics 80

Firefighting 10

Catering 50

Design and Engineering 75

Accounting 25

Time in Air (seconds) Tally Frequency

X AXIS

Y AXIS

TITLE

X AXIS VALUE

TEST LAUNCHES

HEIGHT (ft)

ROCKET TEST LAUNCH HEIGHTS

TEST 3


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3)

4) a) Anne

b) Charlotte

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


Level 2 Use and interpret discrete and continuous data

v1.0


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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


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3) Snow Sports Magazine

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


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b) 14.9 ̇ m

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%


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c) 70 000


Level 2 Use statistical methods to investigate situations

v1.0


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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


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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

6)

Number of apples (a) Frequency (f) af

28 2 56

29 4 116

30 8 240

31 4 124

32 2 64

Totals 20 600


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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


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Probability

1) 23

2) a) 113

b) 126

3) a) 15

b) 710

4) 36%

5) 0.1

6) Daisy is more likely to land her spinner on red than pick a red ball


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Tree Diagrams & Tables

1) 3 possible outcomes

2) 78

3) 59

4) a) 16 possible outcomes

b) 1316

c) 38

5) a) 14

b) 1112

Apply the Skill

1) 1

12

2) 14

3) 15

4) 80%

5) Bag 2


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6) a) 0.1

b) 6

7) a)

b) 112

c) 518

8) a) 1 = Vanilla

2 = Strawberry

3 = Chocolate 4 = CS 5 = V V 6 = SS

b) 13

c) 59

9) No, Molly is not correct because they both have the same chance of winning.

Dice 1

1 2 3 4 5 6

1

2

3

4

5

6

7

2

3

4

5

6

7

8

Dice 2 3

4

5

6

7

8

9

4

5

6

7

8

9

10

5

6

7

8

9

10

11

6

7

8

9

10

11

12


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functional skills maths

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