1. 1
   An architect is checking the properties of shapes used in a building design. Triangle ABC has AB = 5 cm, AC = 5 cm and BC = 8 cm.

   (a)

   Triangle ABC has AB = 5 cm, AC = 5 cm and BC = 8 cm. What type of triangle is ABC?

   [1 mark]

   • AIsosceles
   • BEquilateral
   • CScalene
   • DRight-angled

   (b)

   A quadrilateral in the same design has all four sides equal in length and its diagonals bisect each other at right angles, but its angles are not $90°$. What type of quadrilateral is this?

   [1 mark]

   • AKite
   • BRectangle
   • CTrapezium
   • DRhombus

   (c)

   A solid used for a decorative pillar has two parallel identical polygonal ends and rectangular side faces. What is this solid called?

   [1 mark]

   • ACone
   • BPyramid
   • CPrism
   • DFrustum

   Total for question 1: 3 marks

2. 2
   A designer is describing features of a circular clock face with centre $O$.

   (a)

   A circular clock face has centre $O$. A chord $PQ$ is drawn across the face, not passing through $O$. Name the term used for the straight line from $O$ perpendicular to $PQ$ that meets $PQ$ at its midpoint.

   [2 marks]

   (b)

   A straight line touches the edge of the clock face at exactly one point, $T$. Name this line and state the geometric relationship between this line and the radius $OT$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A landscape gardener is designing a garden bed shaped as a pentagon, and a separate feature shaped as a triangular prism for a water feature.

   (a)

   A pentagon-shaped garden bed has all sides and angles equal. State whether this pentagon is regular or irregular, and state the number of lines of symmetry it has.

   [3 marks]

   (b)

   The gardener also builds a solid water feature with two parallel triangular ends and three rectangular side faces. Name this solid, and state the number of edges it has.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A surveyor is mapping a field, ABCD, and a nearby hill modelled as a solid shape, for a construction report.

   (a)

   A surveyor describes a quadrilateral field ABCD where AB is parallel to DC, but AD is not parallel to BC, and no sides are equal in length. Name this quadrilateral, and state one further quadrilateral term that could NOT apply to it, giving a reason.

   [4 marks]

   (b)

   The surveyor models a nearby hill as a solid with one circular base and a curved surface narrowing to a single point at the top. Name this solid, and state the mathematical term for the flat circular part.

   [4 marks]

   (c)

   The surveyor also needs to classify an angle measured at $115°$ on the field boundary, and a second angle at $260°$ elsewhere on the site. Name the type of each angle (acute, right, obtuse, straight, or reflex), giving a brief justification for each.

   [5 marks]

   Total for question 4: 13 marks

End of questions