2D Area & Perimeter: WJEC GCSE Numeracy Foundation June 2024 Unit 1 Q1

Numeracy Foundation June 2024 Unit 1 Q1

WJECFoundationCurrent spec19 marks2D Area & Perimeter FDPR Mixed Context Ratio & Basic Proportion

(a)

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Stuart, Annelise and their children like to keep fit.

The table below shows the prices of different membership types at a local fitness club.

Type of Membership	Price per year
Adult	£380
Senior (aged 60 or over)	£260
Junior (aged 16 or under)	£170
Family (2 adults and 2 juniors)	£920

Stuart and Annelise are both aged 42.
They have a son aged 14 and a daughter aged 12.
They all want to buy membership of the fitness club for a year.

How much less will the family pay in total by having a Family membership instead of a separate membership for each person?
You must show all your working. [4 + 2 OCW]

(b)

The table below gives the number of calories used in one minute when exercising on the gym equipment shown.

Equipment	Calories used in one minute
Rowing machine	11 calories
Exercise bike	14 calories
Treadmill	17 calories
Cross trainer	12 calories

(i) Stuart uses the rowing machine for 20 minutes.
How many calories will he use? [2]

(ii) Annelise uses the cross trainer.
How many minutes does it take her to use 360 calories? [2]

(c)

When Stuart uses the exercise bike, he keeps his upper body at an angle of 45° to the horizontal.

What type of angle is an angle of 45°?
Circle your answer. [1]

an acute angle an obtuse angle a straight line a right angle a reflex angle

(d)

The fitness club keeps weekly information about the number of people who attend different fitness classes.

The table below shows the information for the first week of April.

Fitness Class	Number of people
Spin	62
Step	96
Yoga	84
Circuits	88
Zumba	57

Annelise thinks that the modal fitness class is yoga.
Is she correct? [1]

Yes ☐ No ☐

Give a reason for your answer.

(e)

The fitness club wants to lay tiles on the bottom of the swimming pool.
The outline of the bottom of the pool is drawn to scale on the square grid below.
The scale of the drawing is 1 cm represents 1 m.

Scale: 1 cm represents 1 m

Outline of the bottom of a swimming pool, shaded, drawn on a square grid

The tiler will charge £30 per square metre for laying the tiles.
How much will the tiler charge in total for laying the tiles? [4]

(f)

The tiler has a small van.

The diagram below is a scale drawing of the van.
The scale of the drawing is 1 cm represents 50 cm.

Find the actual length of the van in metres. [3]

On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.

Length of the van = …………… metres

Mark scheme (a)

Scheme	Marks	Comments
(Total cost of individual membership) 380 × 2 + 170 × 2 or equivalent	M1	May be seen in stages
(£)1100	A1
(Amount saved) 1100 – 920	M1	FT ‘their derived 1100’ provided > than 920
(£)180	A1	If no marks awarded, award SC1 for 760 and 340 seen (not added)
Organisation and communication	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanations and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Writing	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.

Alternative

1(a) Alternative method 1: Subtraction method

Scheme	Marks	Comments
£920 – £170 – £170 – £380	M1
= £200	A1
£380 – £200	M1	FT 380 – ‘their 200’ provided M1 previously awarded
= £180.	A1

1(a) Alternative method 2: Subtraction method

Scheme	Marks	Comments
£920 – £170 – £380 – £380	M1
= – £10 OR is £10 more than the family membership	A1
£170 + £10	M1	FT 170 + ‘their 10’ provided M1 previously awarded
= £180.	A1

1(a) Alternative method 3: Subtraction method

Scheme	Marks	Comments
£920 – £170 – £170	M1
= £580	A1
£380 + £380 – £580	M1	FT 380 + 380 – ‘their 580’ provided M1 previously awarded
= £180.	A1

1(a) Alternative method 4: Subtraction method

Scheme	Marks	Comments
£920 – £380 – £380	M1
= £160	A1
£170 + £170 – £160	M1	FT 170 + 170 – ‘their 160’ provided M1 previously awarded
= £180.	A1

Scheme	Marks	Comments
Full subtraction method that would lead to an answer of £180	M2	Award M1 for sight of at least 2 values subtracted
Correct answer of £180	A2	Award A1 for answer from 1 error only.

The alternative methods are printed in italics in the original. In the original they come before the OC1 and W1 rows, which apply to any method.

Mark scheme (b)

Scheme	Marks	Comments
(i) 11 × 20	M1
220 (calories)	A1
(ii) 360 ÷ 12	M1	Allow 12 ÷ 360 written if the intention is 360 ÷ 12 e.g. counting up in 12s to at least 3 × 12 For 360 ÷ 12 not seen but counting up in 12s seen award M1 for the sight of ≥180
30 (minutes)	A1

Scheme	Marks	Comments
An acute angle	B1

Mark scheme (d)

Scheme	Marks	Comments
No indicated or unambiguously implied and correct reason given, e.g. ‘Because it is not the most popular class’ ‘As step is the modal fitness class’ ‘Because yoga doesn’t have the highest frequency’ ‘Because the most popular fitness class is step’ ‘Because other classes have more people in them’ ‘Because the number of people attending step class is higher’ ‘Because step is the most common class’ ‘Because circuits has more people attending’	E1	Allow, e.g. ‘It should be step’ ‘It’s not the highest number’ ‘It’s not the biggest’ ‘Because there are others with more’ ‘Because it’s step’ ‘More people do circuits’ ‘The steps have 12 more than yoga’ ‘Step does 96 people’ Do not accept ‘No, because it’s not in the middle of highest number and the lowest number’

Mark scheme (e)

Scheme	Marks	Comments
(Area of tiles) Evidence of counting squares within the shape	M1	Look at diagram Allow M1 for area within and some of the squares outside If no evidence of counting squares, award M1 if answer for area is in the range 22 – 40 Award M0 if clearly working with perimeter
Area in range 31 - 38 (cm² or m²)	A1	Number of squares in range with no evidence of counting award M1 A1
‘Their area’ × 30	M1	FT ‘their area’ × 30
Correct cost for their area	A1

Alternative

1(e) Alternative method

Scheme	Marks	Comments
(Area of tiles) Evidence of counting squares within the shape and counting up in 30s	M2	If no evidence of counting squares, award M1 for evidence of counting up in 30s to at least 300
Answer in the range (£)930 – (£)1140	A2	If A2 not awarded, award A1 for answer in the range (£)660 – (£)1200

The alternative method is printed in italics in the original.

Mark scheme (f)

Scheme	Marks	Comments
9(cm) (±2mm)	B1	(8.8 (cm) to 9.2(cm))
9 × 50 (÷100)	M1	FT ‘their 9’ provided it has come from a measurement of the height or length of the van, and is ≥ 3(cm)
4.5 (metres)	A1	Answer must be in metres only. Answer line takes precedence E.g. For an answer of 4m 50cm or 450cm using 9cm award B1 M1 A0 Measurements of: 8.8 cm gives 4.4 m 8.9 cm gives 4.45 m 9 cm gives 4.5 m 9.1 cm gives 4.55 m 9.2 cm gives 4.6 m If no marks awarded, award SC1 for an answer in the range 4.3m to 4.7m (but outside 4.4m to 4.6m)