Constructions

OCR

GCSE

Geometric constructions necessitate the rigorous application of straightedge and compass techniques to derive exact figures independent of numerical measurement. The study of loci defines a set of points satisfying specific geometric conditions, such as equidistance from fixed elements, forming the basis for defining regions through inequalities. Candidates must demonstrate precision in manual drafting while applying deductive logic to solve complex boundary problems and verify construction validity through congruence proofs.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

What You Need to Demonstrate

Key skills and knowledge for this topic

Award 1 mark for drawing correct intersecting arcs to establish the perpendicular bisector
Award 1 mark for a continuous, accurate curve or line within the tolerance of ±2mm
Credit responses that clearly distinguish between strict inequalities (dashed lines) and inclusive inequalities (solid lines)
Award 1 mark for correctly shading the region satisfied by multiple locus conditions
Do not award method marks for 'bald' correct lines where construction arcs are not visible

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have drawn the correct line, but you lost marks because your construction arcs were not visible — never erase them"
"Check your boundary lines: you used a solid line for 'less than', which implies 'less than or equal to'"
"Your accuracy is slightly out; ensure your compass setting doesn't slip when drawing the arc"
"Excellent identification of the region; to ensure full marks, clearly label the region R as requested"

Marking Points

Key points examiners look for in your answers

Award 1 mark for drawing correct intersecting arcs to establish the perpendicular bisector
Award 1 mark for a continuous, accurate curve or line within the tolerance of ±2mm
Credit responses that clearly distinguish between strict inequalities (dashed lines) and inclusive inequalities (solid lines)
Award 1 mark for correctly shading the region satisfied by multiple locus conditions
Do not award method marks for 'bald' correct lines where construction arcs are not visible

Examiner Tips

Expert advice for maximising your marks

💡Ensure your compass pencil is sharp and aligned with the metal point; thick lines can lead to accuracy penalties outside the ±2mm tolerance
💡Never erase your construction arcs; the command word 'Construct' explicitly requires evidence of the method used
💡When shading a region defined by inequalities, test a coordinate point inside your region to verify it satisfies all conditions
💡For loci involving a fixed distance from a line (running track shape), ensure the semi-circular ends join the straight lines smoothly

Common Mistakes

Pitfalls to avoid in your exam answers

Erasing construction arcs after drawing the final line, resulting in a loss of method marks (M-marks)
Confusing the locus equidistant from two lines (angle bisector) with the locus equidistant from two points (perpendicular bisector)
Drawing solid boundary lines for strict inequalities (e.g., < or >) instead of the required dashed lines
Failing to check the scale of the axes, resulting in distorted circles (ellipses) when drawing a fixed distance from a point

Key Terminology

Essential terms to know

Standard compass and straightedge constructions

Loci defined by equidistance rules

Region identification via inequalities

Geometric proof of construction validity

Likely Command Words

How questions on this topic are typically asked

Construct

Draw

Shade

Describe

Indicate

Ready to test yourself?

Practice questions tailored to this topic