Geometry and measures worksheet — GCSE Foundation

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

2.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

3.Write down how many right angles a right-angled triangle has.

4.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

5.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

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

7.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

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

9.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

10.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

11.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

12.Work out the exact value of (cos 45°)² + (sin 45°)².

13.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

14.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

15.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.