Forming Equations: WJEC GCSE Higher June 2017 Unit 2 Q21

Higher June 2017 Unit 2 Q21

WJECHigherCurrent spec4 marksForming Equations Pythagoras

21. The cube below has an internal diagonal of length 20 cm.
Each edge of the cube is of length \(x\) cm.

Diagram not drawn to scale

Calculate the value of \(x\).
You must use an algebraic method and show all your working. [4]

Mark scheme

Scheme	Marks	Comments
Attempt to find the base diagonal	S1	e.g. diagonal² = x² + x² or x² + x² = 2x².
[‘Their face diagonal’]² + [‘Their edge’]²=20²	B1	Clear attempt at connecting their indicated face diagonal and edge of cube with the internal diagonal. This mark implies S1.
\(x^2 + x^2 + x^2 = 400\) OR \(3x^2 = 400\) OR \(x^2 = 400/3\) OR equivalent.	M1	Correct equation connecting edges and internal diagonal. This mark implies S1 B1.
x = √(400/3) OR 11.5(4700538…cm)	A1	CAO SC2 for an answer of 11.5(…cm) from a correct trial and improvement method, OR SC2 for an unsupported 11.5(…cm) SC1 for two correct evaluations of 11≤x≤12 from a correct trial and improvement method with one < 400 and one > 400.