Stage 9 - Q1 - 2 marks
Find angle \(ABC\). Use the exterior angle and give a reason.
Hint
Combine the straight-line and triangle-angle sums.
Stage 9 - Q2 - 2 marks
Find angle \(E\) of the pentagon.
Hint
A pentagon contains three triangles.
Stage 9 - Q3 - 3 marks
Find one interior angle of a regular 9-gon.
Hint
Regular means all angles, as well as all sides, are equal.
Stage 9 - Q4 - 3 marks
For a regular polygon, find the exterior angle and side count.
Hint
Use 180 degrees first, then 360 degrees.
Stage 9 - Q5 - 4 marks
Construct a \(60^\circ\) angle on a base of 3.5 cm, then bisect it to make \(30^\circ\). Keep all construction arcs.
Hint
Use the equilateral triangle before applying the angle-bisector construction.
Stage 9 - Q6 - 4 marks
Construct a \(60^\circ\) angle on a base of 4.5 cm, then bisect it to make \(30^\circ\). Keep all construction arcs.
Hint
Use the equilateral triangle before applying the angle-bisector construction.
Stage 9 - Q7 - 5 marks
Draw a circle of radius 44 mm. Construct perpendicular diameters, bisect each right-angle sector and join the eight endpoints.
Hint
Bisect the central angles, not the polygon side lengths.
Stage 9 - Q8 - 5 marks
Find \(x\) to 1 decimal place. Lengths are in cm.
Hint
The final length is a root, not the sum of the squares.
Stage 9 - Q9 - 5 marks
\(AB=3\) cm, \(BC=3\) cm and \(CD=4\) cm. The marked angles \(ABC\) and \(ACD\) are right angles. Find \(AD\) exactly.
Hint
Avoid rounding the shared irrational length.
Stage 9 - Q10 - 3 marks
A regular hexagon and a square are inscribed in circles of the same radius, 5 cm. Find both exact side lengths and perimeters, then decide which perimeter is larger without relying only on rounded decimals.
Hint
The square diagonal, not its side, equals twice the radius.