Geometry and measures worksheet — GCSE Foundation

1.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

2.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

3.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

4.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

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

6.A trapezium has parallel sides of 5 cm and 11 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

7.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

8.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).

9.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

10.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

11.A jug holds 750 ml of water. Work out what fraction of a litre this is.

12.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

13.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

14.Each of these has an exact value. Write down the one whose value is the greatest.

15.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.