Plans, Elevations & Nets: WJEC GCSE Numeracy Intermediate November 2019 Unit 2 Q9

Numeracy Intermediate November 2019 Unit 2 Q9

WJECIntermediateCurrent spec9 marksPlans, Elevations & Nets Prisms

9. The picture shows a solid concrete step.
The step:

stands on horizontal ground,
has all of its edges vertical or horizontal,
has a uniform cross-section.

Concrete step: a prism with an L-shaped cross-section (shaded), total height 50 cm, upper step 24 cm high and 20 cm deep, lower step tread 25 cm deep, and length marked along the front

Diagram not drawn to scale

(a) Draw a sketch of the plan view of the concrete step. [1]

(b)

The volume of concrete in the step is 66 000 cm³.

From the formula list: Volume of prism = area of cross-section × length

(i)

The concrete to make the step costs 39p per litre.

A builder charges a rate of £27 per hour.
Any fraction of an hour is charged as that fraction of his hourly rate.
(For example, half an hour is charged at half of £27.)

It takes him 1 hour 20 minutes to make the step.

There were no other costs.
Calculate the total cost of making the step. [3]

(ii) Calculate the length of the step.
Give your answer in cm.
You must show all your working. [5]

Plan view: a rectangle divided into two equal rectangles by a line across the middle — Mark scheme (a)

Scheme	Marks	Comments
in any orientation	B1	Allow: intention of straight lines and right angles two equal rectangles joined Do not accept if end elevation also drawn, unless plan view is labelled

Mark scheme (b)

Scheme	Marks	Comments
(i) (Concrete costs) 66 × 39(p) or equivalent	M1	(=£25.74) Allow M1 for sight of a multiplication involving the digits 66... with 39(p) or equivalent
(Builder charges) 27 + ⅓ × 27 or equivalent	M1	(= £36) Allow methods breaking down the hour to find the cost for 20 minutes provided sufficient evidence seen Do not allow: 27 + 0.3 × 27 = 27 + 8.10 = £35.10 27 + ⅓ × 27 = 27 + 8.10 = £35.10 Allow 27 + 0.33 × 27 = £35.91 or better
(Total cost of making the step) (£) 61.74	A1	CAO
(ii) (Area cross-section) as sum of two products: 50 × (20+25) – 24×25 (= 2250 – 600) or (20+25) × (50–24) + 20×24 (= 1170 + 480) or 50×20 + 25×(50–24) (= 1000 + 650) OR (Area cross-section) as sum of three products: 24×20 + 26×20 + 26×25 (= 480 + 520 + 650)	M2	Check diagram for working Accept a similar method given by an equation or expressions M1 for sight of either: difference or sum of 2 products, with 1 correct sum of 3 products with 2 correct all products correct but no attempt to sum
(Area cross-section) 1650 (cm²)	A1	CAO
(Length = Volume ÷ area cross-section) 66 000 ÷ 1650	M1	FT 66000 ÷ ‘their 1650’ provided ‘their 1650’ is dimensionally correct
40 (cm)	A1	ISW FT 66000 ÷ ‘their 1650’ only allowing rounding or truncation of decimals