Geometry and measures worksheet — GCSE Foundation

1.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

2.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

3.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

4.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

5.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

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

7.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.

8.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

9.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

10.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

11.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

12.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

14.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

15.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.