Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

2.Write down the exact value of tan 60°.

3.Write down the exact value of sin 60°.

4.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

5.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

6.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

7.How many edges does a triangular prism have?

8.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

9.A submarine travels due south. What is the three-figure bearing for this direction?

10.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

11.In this question, a curved surface counts as a face. How many faces does a sphere have?

12.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

13.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

15.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.