2D Area & Perimeter: WJEC GCSE Numeracy Foundation November 2017 Unit 1 Q8

Numeracy Foundation November 2017 Unit 1 Q8

WJECFoundationCurrent spec10 marks2D Area & Perimeter Decimals

8. Mehmet needs a new fence for one end of his garden.
Fences are constructed using panels and posts.

(a) Posts are needed between each fence panel and at both ends.
How many posts are needed for a fence made with 34 panels?
Circle your answer. [1]

33 35 37 34 36

(b)

Mehmet wants a new 1·5 m high fence for his garden.
The fence panels come in different lengths.
The posts Mehmet wants to use are all the same size.
Mehmet has the following information.

Post: 1.5 m high, 10 cm square base, posts cost £14 each. Panels, all 1.5 m high: Large 2.5 m long £40 each; Medium 2 m long £30 each; Small 1.5 m long £26 each; Extra small 1 m long £18 each

The fence Mehmet wants to make is 8·5 m long, including the posts.
He has started to sketch a plan, as shown below.

Plan of the fence, 8.5 m long overall: Post, Panel, Post at the left end and a Post at the right end

Diagram not drawn to scale

Mehmet needs to use 5 posts.
Work out one possible choice of panels that Mehmet could use.
You may use the plan to help you.
Calculate the total cost of the posts and panels for this choice of fence. [6]

Total cost of making the 8·5 m fence is £ ……………………

(c) It costs 2p to paint each 100 cm² of a fence post.
How much will it cost to paint the 4 vertical sides of 1 fence post? [3]

Scheme	Marks	Comments
35	B1

Mark scheme (b)

Scheme	Marks	Comments
Need 8 metres of panels	S1	Stated or implied
Panels, any indication of 1 the following: 4 × 2 (m) 2.5(m), 2(m), 2(m), 1.5(m) 2.5(m), 2.5(m), 2(m), 1(m) 2.5(m), 2.5(m), 1.5(m), 1.5(m)	B2	Posts and panels do not have to be shown in any particular order (also see diagram) FT from 8.5 – ‘their width for post(s)’, provided 4 possible whole panels are selected B1 for any 1 of the following: if total length of their 4 panels adds to 8.5 m (posts forgotten) if total length of their number of panels, ≠4, adds to 8 m using 4 panels (not adding to 8m) FT 8.5 – ‘their width for post(s)’ provided 2 or 3 whole panels are selected Do not accept any panels cut into fractions
Cost for the fence as appropriate: 5 × 14 + 4 × 30 5 × 14 + 40 + 2 × 30 + 26 5 × 14 + 2 × 40 + 30 + 18 5 × 14 + 2 × 40 + 2 × 26	M2	Ignore any incorrect units for M2 or M1 FT provided B1 or S1 previously awarded for M2 or M1 (but A0) M1 for 1 of the following: calculation costing ‘their panels’ only (posts not included), cost of posts (5 × 14 =) (£) 70, which may be elicited from within a calculation
(£) 190 OR (£) 196 OR (£) 198 OR (£) 202	A1	CAO Only these answers accepted and must be from correct working. Do not ignore incorrect units, if a unit is given it must be correct

Mark scheme (c)

Scheme	Marks	Comments
1(.)50 × 0(.)10 × 4 × (0.0)2	M2	Allow inconsistent units for M marks Ignore any extra faces painted M1 for 1(.)50 × 0(.)10 with either × 4 or × (0.0)2
120(p) OR (£)1.2(0)	A1	CAO, if units are given they must be correct for A1 Do not ignore further working, such as painting top and/or bottom of the post (for A mark)