Plans, Elevations & Nets: WJEC GCSE Numeracy Intermediate November 2024 Unit 1 Q12

Numeracy Intermediate November 2024 Unit 1 Q12

12. Shipping containers are used to transport goods around the world.
The dimensions of a shipping container are as follows:

(a) What is the least possible width of this shipping container?
Circle your answer. [1]

2·425 m 2·42 m 2·435 m 2·426 m 2·424 m

(b)

An end view of a stack of these shipping containers is shown below.

Diagram not drawn to scale

(i) Calculate the greatest possible height of the stack of shipping containers.
Give your answer in metres. [3]

(ii) There are 32 shipping containers in this stack.
Sketch the plan view of this stack of shipping containers in the space below. [1]

(c)

In 2012, there were \(2 \times 10^{7}\) shipping containers in the world.

Joshua says,

By 2025, I think that the number of shipping containers in the world will reach \(1{\cdot}2 \times 10^{8}\).

Assuming Joshua is correct, complete the statement below.

“By 2025, the percentage increase in the number of shipping containers in the world since 2012 will be …………… %.”

You must show all your working. [3]

Scheme	Marks	Comments
2.425 m	B1

Scheme	Marks	Comments
(i) Sight of 2.595 (m) or equivalent in cm or mm	B1	Award B1 for sight of 4 × 0.005 in an appropriate calculation Allow 0.004999(....) for 0.005, must clearly be a recurring 9 digit
4 × 2.595 or 4 × 2.59 + 4 × 0.005 (= 10.36 + 0.02) or equivalent	M1	Or equivalent in cm or mm If B0, FT provided unambiguously chosen: FT 2.59 < ‘their 2.595’ ≤ 2.6
10.38(0 m)	A1	CAO, must be given in metres
(ii)	B1	Intention to show 8 equal containers. Allow if: there is very small gap (≈1mm) is shown between each of the containers rectangles are not quite all the same size a couple of the rectangles appear to be closer to squares drawn free hand Do not accept if: rectangles are shown as all squares rectangles with shorter sides joined, e.g. B0 for an 8 by 4 grid of squares or rectangles drawn

Mark scheme (c)

Scheme	Marks	Comments
Complete method to calculate the percentage increase \(\dfrac{1.2 \times 10^{8} - 2 \times 10^{7}}{2 \times 10^{7}}\) (× 100) 5 (× 100) \(\dfrac{1.2 \times 10^{8}}{2 \times 10^{7}}\) (× 100) – 1(× 100) 6 (× 100) – 1(× 100)	M2	Allow place value errors in writing the given standard form numbers in full for M2 and M1 only M1 for any one of the following calculations or evaluations: \(1.2 \times 10^{8} - 2 \times 10^{7}\) (= \(1 \times 10^{8}\) = 100 000 000) \(\dfrac{1.2 \times 10^{8}}{2 \times 10^{7}}\) (= 0.6 × 10 (× 100) or 6(× 100) or 600(%))
500 (%)	A1	CAO Answer space completing the statement takes precedence Accept equivalents \(0.5 \times 10^{3}\) or \(5 \times 10^{2}\) Accept an unsupported correct answer or a correct answer from reverse calculations