Geometry and measures worksheet — GCSE Foundation

1.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?

2.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

3.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

4.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

5.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².

6.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

7.Write down the term for the distance all the way around the edge of a circle.

8.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

9.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

10.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

11.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

12.A footpath is 3750 m long. Work out this distance in kilometres.

13.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

14.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

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