Foundation November 2017 Paper 1 Q21

AQACurrent spec4 marksConstructions

(a) Joe wants to bisect angle BCD.

Here is his method.

Use a pair of compasses to draw arcs of the same radius from B and D.
Draw a straight line from C through the intersection of the arcs.

Write down the error in his method. [1 mark]

(b) Kay wants to show all the points 3 km from point P.

Here is her answer.

What is wrong with her answer? [1 mark]

Using a pair of compasses and a straight edge, construct one line of symmetry.

Show clearly your construction arcs. [2 marks]

Mark scheme (a)

Answer	Mark	Comments
The arcs should be drawn from C or from points the same distance from C or The lines are different lengths, so you can’t go from the ends	B1	oe

CB ≠ CD	B1
Not drawn an arc from C	B1
He put compass in wrong place. He should have started at C but he started at B and D	B1
Should be an arc on each line CB and CD	B0
Arcs in wrong place	B0
Arcs aren’t equal	B0
His line isn’t in the centre of B and D	B0
D has a longer line than B	B0
Arcs aren’t the same radius	B0
Should be an arc from B to D	B0
Should be an arc from B to the line CD	B0
Should be an intersection on CB and CD	B0

Mark scheme (b)

Answer	Mark	Comments
It should be a circle, (not a square) or The corners are too far away	B1	oe eg accept circle constructed inside square, touching at midpoints of square to within 2mm

A correct diagram takes precedence over statements, otherwise ignore diagram
Any distances if quoted, eg to corners, should be accurate to within 2mm
Ignore any reference to the top point P
The corners are more than 3 (km or cm) away from the point	B1
Some points are more than 3 (km or cm) away	B1
It isn’t 3 (km or cm) to the corners	B1
Each corner is [4.1, 4.5] (km or cm) from P (values represent tolerance)	B1
Each corner is more than 4 away	B1
It should be a circle	B1
Each point is 4.2 km from P (not true)	B0
The corners of the square are 4 km (out of tolerance)	B0
The corners of the square are 4 km while the rest are 3 km	B0
Each corner will be more than 1 km away	B0
She’s measured 3 cm from P without checking the corners	B0
It is not supposed to be this shape (but what should it be?)	B0
She has measured 4.3 km not 3 (not stated corners)	B0
She hasn’t shown all the points that represent 3 km	B0
She hasn’t plotted where all the 3 km points are	B0
It shouldn’t be a square	B0

Answer	Mark	Comments
One pair of equal, intersecting arcs from the vertices of one side of the rectangle	M1	tolerance \(\pm\) 1 mm
Fully correct construction of line of symmetry with either two pairs of equal, intersecting arcs from the vertices of the same side of the rectangle or one pair of equal, intersecting arcs from the vertices of one side of the rectangle and the diagonals drawn	A1	tolerance \(\pm\) 1 mm line of symmetry may be solid or dashed but must touch opposite sides of rectangle