Geometry and measures worksheet — GCSE Higher

1.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

2.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.

3.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

4.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

5.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

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

7.A parallelogram-shaped tile has two sides of 6 cm and 9 cm, with an angle of 60° between them. Work out the area of the tile. Give your answer to 1 decimal place.

8.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?

9.A circle has centre O and radius 13 cm. AB is a chord of the circle, and M is the midpoint of AB. OM is drawn, and OM = 5 cm. Work out the length of AB.

10.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?

11.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.

12.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?

13.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

14.An engineer models a technical drawing on a coordinate grid. A component is reflected in the line x = 2, and the image is then reflected in the line x = 6. Which single transformation has the same overall effect as these two reflections, for every point on the drawing?

15.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.