Geometry: Constructions Practice Test

Geometry: Constructions Practice Test: 10 questions, graded instantly with every answer explained. Free, no sign-up, no ads in the test. This test is for Geometry, a US high school math course. In the UK, the same topics come up in GCSE maths (Years 10 and 11).

Before you start

10 questions on constructions with a compass and straightedge, bisectors and loci, picked at random from a bank of 27, so every try is different. Type a number or a short answer, or choose an answer. To draw a shape or an angle, drag the corners with the on-screen ruler and protractor, or use the arrow keys. Questions with units tell you which unit to use. Choose Practice to see each answer explained as you go, or Test to see your score and explanations at the end.

10 questions – a new mix each time you try
Drawing questions work with a mouse, a finger or the keyboard
Plus written questions for your teacher or a parent to check

Choose how to do it Test – answers and explanations at the end; no time limit Practice – see the answer after each question; no time limit

No sign-up and no ads. Your answers stay on this device. Nothing you type in the test is sent to us – unless you choose to report a problem with a question.

How it is graded: by Classfern's own checks, in your browser, straight away. Drawings are graded by what they show: any correct drawing counts (a shape started from any corner, any net that folds up), within the small allowance the question shows. Spot a mistake? Use the Report button.

Written questions – check with your teacher

Classfern does not grade these questions, and they are not part of your score above. They need a written answer or a drawing that a person has to read. Answer each one in the box or on paper, then ask your teacher or a parent to check it with the marking guide. What you type here stays on this device and is not sent anywhere.

Draw an angle of 90° with a protractor. Then, using only a ruler and a compass, construct the bisector of the angle. Leave in your construction arcs.
3 marks
Do the drawing on paper with a ruler and a compass. Notes (optional):
Marking guide (for your teacher or a parent)

Give a mark for each point the answer shows. Tick as you go:
- Angle drawn as 90° (to within 2°). (1 mark)
- An arc centered on the vertex cuts both arms; equal arcs from those two points cross inside the angle. (1 mark)
- A line from the vertex through the crossing point, making two angles of 45° (to within 2°). (1 mark)
One answer that would get full marks:
Draw the 90° angle. Put the compass point on the vertex and draw an arc cutting both arms. From each of those two points draw arcs of the same radius so they cross inside the angle. Join the vertex to the crossing point: each half is 45°.
Draw a circle of radius 6 cm. Using only a ruler and a compass, construct a square with all its corners on the circle. Leave in your construction lines.
3 marks
Do the drawing on paper with a ruler and a compass. Notes (optional):
Marking guide (for your teacher or a parent)

Give a mark for each point the answer shows. Tick as you go:
- Circle of radius 6 cm (to within 2 mm). (1 mark)
- Two perpendicular diameters constructed (a diameter and its perpendicular bisector). (1 mark)
- The four ends of the diameters joined to give a square. (1 mark)
One answer that would get full marks:
Draw a diameter. Construct its perpendicular bisector through the center to get a second diameter at 90°. Join the four points where the diameters meet the circle.
Draw a line AB 7 cm long. Using only a ruler and a compass, construct the perpendicular bisector of AB. Leave in your construction arcs.
3 marks
Do the drawing on paper with a ruler and a compass. Notes (optional):
Marking guide (for your teacher or a parent)

Give a mark for each point the answer shows. Tick as you go:
- AB drawn 7 cm long (to within 2 mm). (1 mark)
- Two pairs of arcs of the same radius (more than half of AB), one centered on A and one on B, crossing above and below AB. (1 mark)
- A straight line through both crossing points, cutting AB at its midpoint at 90°. (1 mark)
One answer that would get full marks:
Draw AB = 7 cm. Set the compass to more than 3.5 cm. With the point on A draw arcs above and below AB; keep the same radius and repeat from B. Join the two places where the arcs cross. This line meets AB at its midpoint (3.5 cm from A) at a right angle.

Classfern practice material. Not an official test and not affiliated with or endorsed by any state, testing program or the Common Core State Standards Initiative.

Lines up with these Common Core State Standards for Mathematics: 7.G.A.2, HSG.CO.D.12, HSG.CO.D.13. © Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.