Constructions: WJEC GCSE Numeracy Foundation November 2022 Unit 2 Q2

Numeracy Foundation November 2022 Unit 2 Q2

WJECFoundationCurrent spec13 marksConstructions FDPR Mixed Context

(a)

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

Mrs Smith is planning to hold a tea party in her garden.

The costs for the party are shown in the table below.

Item	Cost
36 scones	52 pence each
4 pots of cream	£1.27 per pot
3 jars of strawberry jam	£2.16 per jar
9 plates of sandwiches	£7.98 per plate
Drinks and decorations	£230

Mrs Smith has already saved £250 towards the cost of the party.

How much more money does Mrs Smith need for the party?
You must show all your working. [6 + 2 OCW]

(b)

Mrs Smith wants to make her own bunting to decorate the garden.

The triangles for the bunting are in the shape of isosceles triangles.

A sketch of the pattern that Mrs Smith is going to use to make her bunting is shown below.

Sketch of an isosceles triangle: base 14 cm, angle 40° at the right-hand end of the base, the base and the right-hand side marked equal

Diagram not drawn to scale

Make an accurate drawing of the pattern for the bunting.
One side has already been drawn for you. [3]

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

(c)

Mrs Smith is planning to use a number of identical rectangular tables for her party.
There will be 18 people at the party, including Mrs Smith.

Six chairs fit around one table, as shown in the diagram below.

A rectangular table with two chairs along each longer side and one chair at each shorter side

She would like all the tables to be joined together.

All the tables must be joined together either:

with their shorter sides touching
or
with their longer sides touching.

Mrs Smith wants to use the least number of tables possible.
Draw a diagram in the space below to show how the tables and chairs for the 18 people at the party should be arranged. [2]

Mark scheme (a)

Scheme	Marks	Comments
(Cost of fruit scones 36 × 52p=) 1872(p) or (£)18.72 (Cost of cream 4 × 1.27 =) (£)5.08 (Cost of jam 3 × 2.16 =) (£)6.48 (Cost of sandwiches 9 × 7.98=)(£)71.82	B3	Ignore incorrect units for the first B3 marks Award B3 for all 4 costs correct Award B2 for any 3 costs correct Award B1 for any 2 costs correct
(Total costs 18.72 + 5.08 + 6.48+ 71.82 + 230 =) (£)332.1(0)	B1	FT ‘their costs’ provided B1 previously awarded and 5 costs, all in consistent units, added
(Needs to save) (£)332.1(0) - (£)250	M1	FT ‘their derived’ total costs providing greater than (£)250
(£)82.1(0)	A1	If units given they must be correct. Allow £82.1(0)p If no marks awarded, award SC1 for an answer of £241.93 for ‘their total costs’

Alternative

In the mark scheme the heading and the last three rows of the alternative method are printed in italics; the first row is not.

Alternative method

Scheme	Marks	Comments
(Cost of fruit scones 36 × 52p=) 1872(p) or (£)18.72 (Cost of cream 4 × 1.27 =) (£)5.08 (Cost of jam 3 × 2.16 =) (£)6.48 (Cost of sandwiches 9 × 7.98=)(£)71.82	B3	Ignore incorrect units for the first B3 marks Award B3 for all 4 costs correct Award B2 for any 3 costs correct Award B1 for any 2 costs correct
(Food costs 18.72 + 5.08 + 6.48+ 71.82 =) (£)102.1(0)	B1	FT ‘their food costs’ provided B1 previously awarded and 4 costs, all in consistent units, added
(Needs to save) 102.1(0) – (250 – 230)	M1	FT ‘their derived’ total food costs
(£)82.1(0)	A1

Scheme	Marks	Comments
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.

Mark scheme (b)

Scheme	Marks	Comments
Correct completed triangle drawn within tolerance. (Use overlay)	B3	Allow if triangle is reflected. B3 or B2 can only be awarded if the measurements are from the given14cm base line or a new 14cm base line is drawn on the page. Award B2 for 40° (±2°) and 14 cm (±2mm) correct but triangle not completed Either 40° (±2°) or 14 cm (±2mm) correct in a completed triangle If B2 not awarded, award B1 for Either 40° (±2°) or 14 cm (±2mm) (not the base line) correct in a triangle not completed or using a new base line drawn of any size.

Scheme

Marks

Comments

Correct completed triangle drawn within tolerance. (Use overlay)

Allow if triangle is reflected.
B3 or B2 can only be awarded if the measurements are from the given14cm base line or a new 14cm base line is drawn on the page.
Award B2 for

40° (±2°) and 14 cm (±2mm) correct but triangle not completed
Either 40° (±2°) or 14 cm (±2mm) correct in a completed triangle

If B2 not awarded, award B1 for

Either 40° (±2°) or 14 cm (±2mm) (not the base line) correct in a triangle not completed or using a new base line drawn of any size.

Four tables in a row joined at their shorter sides, with 8 chairs along each long edge and 1 chair at each end — Mark scheme (c)

Four tables in a row joined at their shorter sides, no chairs — Mark scheme (c)