Geometry and measures worksheet — GCSE Foundation

1.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

2.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

3.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

4.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

5.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

6.a is the column vector with top number 3 and bottom number 2. b is the column vector with top number −1 and bottom number 4. Work out a + b, giving your answer as a column vector in the form (top, bottom).

7.What does the statement AB = CD mean, where A, B, C and D are all points?

8.A hiker walks due west. What is the three-figure bearing for this direction?

9.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

10.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.

11.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

12.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

13.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

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.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?