EDEXCEL FUNCTIONAL SKILLS PILOT

Maths Level 2 Test your skills Su Nicholson

Practice test Time: 1 hour 15 minutes

Materials required Ruler graduated in centimetres and millimetres, protractor, pen, HB pencil, eraser, calculator. Information for Candidates The marks for individual questions and the parts of questions are shown in round brackets; e.g. (2). In this question paper there are 3 questions in Task 1, 5 questions in Task 2, and 5 questions in Task 3. The total mark for this paper is 48. Calculators may be used. Advice to Candidates Show all stages in any calculations. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out.

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Functional Maths Level 2 • Chapter 8 Test • page 1

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TASK 1: PLANNING A GARDEN Answer all three questions in this task. Write your answers in the spaces provided. Where you see this sign you must show clearly how you get your answers as marks may be awarded for your working out. Brad has moved into a new house. He plans how to use his garden space. The diagram shows a plan of the garden. (Not drawn to scale.) 8.7 m

Flower beds

4.5 m

6.6 m

0.6 m Paving

2.1 m

back of house

4.5 m

1

The three outside edges of the garden are to be fenced, (marked in the plan). Fencing comes in 2 metre lengths. How many lengths of fencing does Brad need to buy?

Number of lengths (Total 3 marks) © Pearson Education 2009 FS-Ma-L2test-PracTest.indd 2

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Practice test materials  8 2

Brad decides to pave the area labelled ‘Paving’ with paving stones. The paving stones each measure 0.5 m by 0.5 m. The paving stones cost £8.75 each. The paving stones can be cut to size. Brad does not want to buy more paving stones than he has to. Calculate the lowest total cost of the paving stones for Brad’s garden. Use the box below to show clearly how you get your answer. You may find it helpful to draw on the diagram of the garden.

Total cost £ (Total 8 marks) 3

Brad buys some cylindrical terracotta flower tubs for the garden. The flower tubs have an internal diameter of 50 cm and a height of 60 cm. The volume, V, of a cylinder with base radius π × h × d2 r and height h is given by V = ________ 4 where π = 3.14, d = 50 cm.

60 cm

Brad fills two-thirds of each flower tub with potting compost. 1000 cm3 = 1 litre 50 cm

a) How much potting compost is needed for each flower tub to the nearest litre?

litres

Amount of potting compost

(4) The potting compost is made up of loam, peat and sand in the ratio 7:3:2. b) How much loam, peat and sand are used to make up 300 litres of potting compost? loam

litres

peat

litres

sand

litres (3) (Total 7 marks)

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TASK 2: PLANNING A JOURNEY Answer all five questions in this task. Write your answers in the spaces provided.  here you see this sign you must show clearly how you get your W answers as marks may be awarded for your working out. The table below shows part of the journey to the Trafford Centre worked out by a route planner. distance 1 Slight left at Broadway

299 feet

2 Slight left at A5063/Trafford Rd Continue to follow A5063

0.2 miles

3 Merge onto M602 to Ring Rd/M60

3.7 miles

4 At junction 1, take the M60 exit to Ring Rd

0.8 miles

5 Follow signs for Ring Road (S)/M60 and merge onto M60

1.2 miles

6 At junction 10, take the B5214 exit to Trafford Centre

0.1 miles

4

The distances are given in imperial units. 5 miles is approximately 8 kilometres. Convert 3.7 miles to kilometres.

km

3.7 miles

(Total 2 marks) 5

Three sections of the journey are on the motorway, shown by the

symbol.

The maximum speed on the motorway is 70 mph. a) U  se the maximum speed to estimate a time for the journey on the motorway to the nearest minute.

Total time

minutes (3)

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Practice test materials  8 b) Explain why this is not a good estimate of the time for the journey on the motorway.

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(1) (Total 4 marks) 6

The 1.2 mile section of the journey actually takes 1 12 minutes. Calculate the average speed for this section of the journey.

mph

Average speed

(Total 4 marks) 7

A car is filled with petrol before the journey. The petrol tank holds 42 litres of petrol. The petrol tank was 25% full before it was filled. Petrol costs 109.2p per litre. How much does it cost to fill up the petrol tank?

Cost of petrol £ (Total 3 marks) © Pearson Education 2009 FS-Ma-L2test-PracTest.indd 5

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8

A motorist uses the M602 motorway to travel to work in the mornings from Monday to Friday. In a six-week period he is delayed by more than 10 minutes on 12 occasions. The motorist travels to work on 230 days in a year. a) E stimate the probability that the motorist is delayed by more than 10 minutes on his way to work.

Probability (2) b) H  ow many days in the year can the motorist expect to be delayed by more than 10 minutes?

Number of days (1) (Total 3 marks)

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Practice test materials  8

TASK 3: HEALTHY EATING Answer all five questions in this task. Write your answers in the spaces provided.  here you see this sign you must show clearly how you get your W answers as marks may be awarded for your working out. Jessica plans her meals for a day to include five portions of fruit or vegetables. Meal

Menu

Calories

Fat (g)

Breakfast

cereal

115

0

22

6

orange juice *

132

0

33

0

chicken

221

5

0

42

baked potato

115

0

27

2

green beans *

44

0

10

2

yoghurt

155

4

17

13

lasagne

734

36

63

38

green salad *

9

0

2

1

tomatoes *

31

0

7

1

garlic bread

64

2

9

2

fruit salad *

141

1

36

2

1760

49

225

110

Lunch

Dinner

TOTAL 9

Carbohydrate (g) Protein (g)

The menu items which count as Jessica’s five portions of fruit or vegetables are marked with a *. E xpress the total number of calories in Jessica’s five portions of fruit and vegetables as a percentage of the total number of calories in her meals for the day.

Calories

% (Total 3 marks)

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10

The table shows the total number of grams of fat, carbohydrate and protein in Jessica’s planned meals for the day. Nutrients Fat Carbohydrate Protein

Grams 49 225 110

Draw an accurate pie chart to show this information.

(Total 4 marks) 11

The Department of Health suggests a good ratio of fat to carbohydrate to protein in a daily diet is 5:12:3. How does the proportion of fat in Jessica’s planned meals compare with the proportion suggested by the Department of Health?

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Practice test materials  8 12

The table compares the calories and fat content of portions of different foods for your meals. Food Roast beef Roast pork Bacon Lamb Chicken Fish Scrambled egg Tomato soup

Fat (g) 23 20 39 27 5 4 17 4

Calories 356 331 461 368 221 173 273 171

a) Draw a scatter graph to investigate the connection between calories and fat content. Plot the points in the table on the graph paper below.

500

400

Calories

300

200

100

0 10

20

30

40

50

Fat in grams

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b) Suggest a possible connection between the calories and fat content of the food items.

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.....................................................................................................................................................................................

(1) (Total 3 marks) 13

There are 387 calories in a portion of baked beans. Draw a line of best fit on the scatter graph and use it to estimate the fat content of a portion of baked beans.

Fat content

g

(Total 2 marks) TOTAL FOR PAPER: 48 MARKS

END

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Q2

Finds results and solutions

Selects and uses appropriate mathematical procedures for detailed calculation leading to the number of paving stones needed; undertakes the calculations to find results and solutions

Selects and uses appropriate mathematical procedures for overall method, decides on the overall methods to use

Quest. Process Selects and uses Q1 appropriate mathematical procedures for detailed calculation leading to the number of lengths

e.g. 48 × £8.75 e.g. £420

3

Demonstrates complete method to find the number of paving stones needed Calculates number of paving stones needed Attempts to find total cost Correct solution 2 or 3

2 or

Calculates the sum of the number of paving stones OR combined area of paving

1 or

1 or

Calculates the number of paving stones OR combined area of the paving

2

Chooses a correct process and finds any missing information needed for solution process

squares drawn on diagram OR divides into two rectangles e.g. missing length of 4.2 m shown, and associated with complete process e.g. 36 and 8 and 4 for paving stones OR 4.2 × 0.6 and 4.5 × 2.1 for area e.g. 36 + 8 + 4 for paving stones OR (4.2 × 0.6) + (4.5 × 2.1) for area shows complete method which should lead to 48 e.g. 48

1 or

Mark Notes 1 or e.g. 4.5 ÷ 2 2 or shows complete method which should lead to 10 or 11 3 accept 10 or 11

Chooses a diagrammatic OR area approach

Evidence Process of dividing length by 2 4.5 m – 2 lengths + 0.5 8.7 m – 4 lengths + 0.7 6.6 m – 3 lengths + 0.6 States correct number of lengths

Functional Maths Level 2 • Chapter 8  Test • page 11

Total 8 marks

A: use appropriate mathematical procedures; find results and solutions

R; make an initial model of a situation using suitable forms of representation; decide on the methods, operations and tools, including ICT, to use in a situation; select the mathematical information to use

Total 3 marks R; recognise that a situation has aspects that can be represented using mathematics; make an initial model of a situation using suitable forms of representation

Attribute A: use appropriate mathematical procedures; find results and solutions

Practice test materials  8

Functional skills test (Mathematics)

Practice test mark scheme – Level 2

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Converts from miles to kilometres

Calculates total length and speed

Consider the appropriateness and accuracy of the results

5a)

5b)

Correct use of ratio

4

3b)

Calculates 23 of volume and converts to litres

Quest. Process 3a) Calculates volume

Calculates total length Divides by 70 and multiplies by 60 Correct solution Explanation given

Division by 5 and multiplication by 8 Correct solution

Division by 12 Correct process to find all three weights Correct solution

Correct solution

3.7 + 0.8 +1.2 5.7 ÷ 70 × 60 answer rounds to 5 e.g. takes time to reach a speed of 70 when joining the motorway

3 1

5.92

2 1 or 2 or

3.7 ÷ 5 × 8

175, 75 and 50

1 or

3

1 or 2 or

2

Attribute A: use appropriate mathematical procedures; find results and solutions

(Total 4 marks)

I: interpret results and solutions; draw conclusions in the light of the situation

(Total 2 marks) R: decide on the methods, operations and tools, including ICT to use in a situation; select the mathematical information to use

(Total 7 marks) R: decide on the methods, operations and tools, including ICT to use in a situation; select the mathematical information to use

A: use appropriate mathematical procedures; change values and assumptions or adjust relationships to see the effects on answers in answer rounds to 78.5 the model 300 ÷ 12 R: decide on the methods, operations and 25 × 7, 25 x 3 and 25 tools, including ICT to use in a situation; select the mathematical information to use ×2

Mark Notes 1 or 3.14 × 60 × 502 ÷ 4 2 answer in range 117750–117810 2 Correct process of multiplication 1 or e.g. 117750 × 3 ÷ 2 1000 by 3 and division by 1000

Evidence Substitutes values into formula Calculates volume correctly

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Calculates probability

Calculates number of days

Calculates calories as a percentage

8a)

8b)

9

2

Correct solution

Calculates total number of calories Process of converting to a percentage Correct solution

Answer rounds to 13

3

2 or

132 + 44 + 9 + 31 + 141 357 ÷ 1760 × 100

1 or

Process of multiplication by 230 1 to give correct solution

1 or

3

Correct solution Calculates number of days

2 or

Attempts to find total cost

48

3 1 or

Calculates amount of petrol and cost

7

e.g. 0.8 × 60

2 or

R: decide on the methods, operations and tools, including ICT to use in a situation; select the mathematical information to use

Attribute

(Total 3 marks)

(Total 3 marks) R: decide on the methods, operations and tools, including ICT to use in a situation; select the mathematical information to use

(Total 3 marks) e.g. 0.75 × 42 R: decide on the methods, operations and e.g. 31.5 × 109.2 ÷ 100 tools, including ICT to use in a situation; select the mathematical information to use 48 (Total 3 marks) 6×5 R: decide on the methods, operations and 12 tools, including ICT to use in a situation;    30 or equivalent select the mathematical information to use 92 I: interpret results and solutions; draw conclusions in the light of the situation

1.2 ÷ 1.5

1 or

Mark Notes

Calculates amount of petrol

Calculates total distance Uses ‘distance ÷ time’ and speed Attempts to find speed in correct units Correct solution

Evidence

6

Quest. Process

Practice test materials  8

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13

Draws and uses line of best fit

Interpret and find solution

12b)

2

1

1

Line of best fit drawn

Uses 387 calories

between (5, 150), (5,220) and (35, 400), (35, 470) answer from a single I: interpret results and solutions; draw conclusions in the light of the situation line segment with positive gradient ± 1 full (2 mm) square (Total 2 marks) (Total 48 marks)

(Total 3 marks) A: use appropriate mathematical procedures

I: interpret results and solutions; draw conclusions in the light of the situation

I: interpret results and solutions; draw conclusions in the light of the situation (Total 3 marks) no more than 2 errors A: use appropriate mathematical procedures

1

points not joined 14 square tolerance e.g. higher fat content means higher calories

e.g. 0.25 and 0.1276…..

2

1 or

 5 OR 49 e.g. 20 384

I: choose appropriate language and forms of presentation to communicate results and conclusions (Total 4 marks) R: decide on the methods, operations and tools, including ICT to use in a situation; select the mathematical information to use

Attribute A: use appropriate mathematical procedures

1 or

Comment on connection between 1 fat content and calories

Plots points correctly on Points plotted scatter graph All points plotted accurately

12a)

Calculates fat as a proportion of total Converts to same form and compares Identifies Department of Health as a higher proportion

Selects and uses appropriate mathematical procedures for detailed calculation leading to a comparison

1

Correct labels on sectors (dependent on at least 1 angle drawn correctly) fat, carbohydrate and protein

Mark Notes 1 or e.g. 46 or 211 or 103 seen 2 or e.g. 46 and 211 and 103 seen 3 ± 2o tolerance

Evidence Calculates angles OR method shown Second angle drawn correctly, OR correct values for all angles seen All 3 angles drawn correctly

11

Quest. Process Selects and uses 10 appropriate mathematical procedures for overall method