Constructions: WJEC GCSE Higher June 2023 Unit 1 Q4

Higher June 2023 Unit 1 Q4

WJECHigherCurrent spec4 marksConstructions

(a) Line \(AB\) is shown below.
Using only a ruler and a pair of compasses, construct an angle of 60° at point \(B\). [1]

(b) \(R\) is a point on the line \(LM\).
Using only a ruler and a pair of compasses, construct an angle of 90° at point \(R\). [1]

(c) Using only a ruler and a pair of compasses, construct a perpendicular line from the point \(P\) to the line \(XY\). [2]

Scheme	Marks	Comments
Correct construction of 60°	B1	Must be at point \(B\). Correct construction arcs (two or three) must be seen (initial and secondary). B0 if 60° and 30° drawn. Ignore additional lines provided intended 60° is clear (e.g any triangle, including equilateral \(ABC\)). For example:

Mark scheme (b)

Scheme	Marks	Comments
Correct construction of 90°	B1	Must be at point \(R\) above or below \(LM\). Correct construction arcs (initial and secondary) must be seen.

Mark scheme (c)

Scheme	Marks	Comments
All correct construction arcs shown	M1	Arc, centre P, intersecting \(XY\) at two points. (\(X\) may be one of the points with no arc seen at point \(X\).) [Note to markers: These arcs may be identified by the fact that they will ‘cross the line \(XY\) at an acute angle’. Arcs ‘crossing the line at 90°’ is evidence of an inappropriate method.] AND Intersecting arcs (equal radii) using the above two points as centres. Ignore line extended above \(XY\) for M1.
Line drawn	A1	Ignore line extended above \(XY\) for M1A1.

Scheme	Marks	Comments
(Using the properties of a kite.) All correct construction arcs shown.	M1	Intersecting arcs whose centres are any two points on the line XY and respective radii equal in length to the distance from the points to the point P. [Note to markers: The arcs will always intersect at a point that is a ‘reflection of point P’ in the line XY.]
Line drawn	A1