Constructions: WJEC GCSE Numeracy Intermediate June 2024 Unit 1 Q7

Numeracy Intermediate June 2024 Unit 1 Q7

WJECIntermediateCurrent spec9 marksConstructions Percentages

(a) Josif produces a scale drawing to show where he wants a tree planted in his garden.

Scale: 1 cm represents 0·5 m

Scale drawing of a rectangular garden: Hedge along the top, House along the bottom, Wall on the left and Fence on the right. A dashed horizontal line near the top and a dashed diagonal line from the bottom left corner cross at the point marked Tree

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

He writes out instructions to show where the tree is to be planted.

Which two of the following instructions describe where the tree is to be planted?

A. The tree must be 2 m from the hedge.
B. The tree must be 1 m from the hedge.
C. The tree must be 6 m from the hedge.
D. The tree must be 3 m from the hedge.
E. The tree must be 1 m from the wall.

F. The tree must be equidistant from the hedge and the fence.
G. The tree must be equidistant from the hedge and the wall.
H. The tree must be equidistant from the wall and the house.
I. The tree must be equidistant from the hedge and the house.
J. The tree must be equidistant from the wall and the fence. [2]

The two instructions are …………… and ……………

(b) A garden centre buys trees from a grower for £30 each.
The garden centre sells the trees for £42 each.

(i) Calculate the percentage profit the garden centre makes from buying and selling one tree. [2]

(ii) The garden centre buys 10 of these trees to sell.
One of the trees gets damaged and cannot be sold.
The other 9 trees are sold.

Calculate the overall percentage profit or loss the garden centre makes from selling these trees.
You must state whether your answer is a profit or a loss.
You must show all your working. [4]

(iii) Of the 10 trees bought by the garden centre, what is the minimum number that need to be sold to ensure that the garden centre makes a profit?
Circle your answer. [1]

5 6 7 8 9

Scheme	Marks	Comments
B and H in either order	B2	B1 for either B or H selected

Mark scheme (b)

Scheme	Marks	Comments
(i) \(\dfrac{42-30}{30}\) (× 100) or \(\dfrac{42}{30}\) (× 100) – 1 (× 100)	M1	Or full reverse method, e.g. 20% of £30 is 30 ÷ 5 = £6, with either 6 × 2 = (£)12 or 6 × 7 = (£)42 10% of £30 is 30 ÷ 10 = £3, with either 3 × 4 = (£)12 or 3 × 14 = (£)42
40 (%)	A1	Allow an answer of £40 from correct working If no marks, award SC1 for an answer of 140(%)
(ii) (Percentage profit is) \(\dfrac{9 \times 42-10 \times 30}{10 \times 30}\) (× 100) or \(\dfrac{9 \times 12-30}{10 \times 30}\) (× 100) or \(\dfrac{9 \times 42}{10 \times 30}\) (× 100) – 1 (× 100) or \(\dfrac{378}{300}\) (× 100) – 1 (× 100) or 1.26 (× 100) – 1 (× 100) or equivalent	M2	Allow a reverse method of finding percentages of 300 used, these percentages must be correct and when added (or subtracted) could lead to an answer of 26% e.g. (2 × 10% =) 20% of 300 is 60 and 6% of 300 is 18 M1 for any one of the following: (difference between sales and costs) 9 × 42 – 10 × 30 (= 378 – 300) (sales) (£) 378 AND (cost) (£) 300 (difference between sales and costs) (£) 78
26 (%) AND states ‘profit’	A2	Mark final answer A1 for any one of the following: 26(%) \(\dfrac{78}{300}\) (× 100) or equivalent \(\dfrac{378}{300}\) × 100 = 126 (%) \(\dfrac{378}{300}\) = 1.26 \(\dfrac{(\text{‘their }9{\times}42\text{’} - 10 \times 30)}{10 \times 30}\) × 100 correctly evaluated and given as a percentage, allow if an error in the decimal part of their answer
(iii) 8	B1