Geometry and measures worksheet — GCSE Foundation

1.Which of these correctly compares a 'line' with a 'line segment'?

2.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

3.A square has sides of length 7 cm. Work out its area.

4.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

5.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

6.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

7.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

9.A circle has a diameter of 4 cm. Work out the radius of the circle.

10.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.

11.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

12.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

13.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

14.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

15.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?