Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

2.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

3.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

4.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

5.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

6.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.

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

8.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

9.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

10.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

11.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

12.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

13.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

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 packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?