Geometry and measures worksheet — GCSE Foundation

1.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

2.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.

3.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

4.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

5.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

6.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

7.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

8.Work out the exact value of sin 45° × cos 45°.

9.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

10.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

11.Write down how many right angles a rectangle has.

12.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

13.Which of the following correctly describes what it means for two lines to be perpendicular?

14.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

15.A cube has all of its edges the same length. How many planes of symmetry does it have?