Printable · GCSE Higher · ages 14-16
Geometry and measures worksheet — GCSE Higher
Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Geometry and measures worksheet — GCSE Higher
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- 1.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?
- 2.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.
- 3.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.
- 4.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?
- 5.Work out the exact value of (cos 45°)² + (sin 45°)².
- 6.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?
- 7.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
- 8.OABC is a parallelogram, with OA = a and OC = c. M is the midpoint of OC, and N is the point on AC such that AN is twice NC. By finding the vectors MN and MB, show that M, N and B are collinear, and give the scalar k such that MN = k × MB.
- 9.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 10.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?
- 11.OABC is a parallelogram, with OA = a and OC = c. X is the point on AC such that AX is a third of XC. Express the vector OX in terms of a and c.
- 12.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 13.Triangle E has vertices (1, 2), (4, 2) and (1, 5). It is rotated 90° anticlockwise about the origin, and the image is then reflected in the line y = x. Work out the coordinates of the image of (4, 2).y = x
- 14.Shape S has an area of 5 cm². Shape S is enlarged by a scale factor of −3 to give shape T. Work out the area of shape T.
- 15.What does the statement AB = CD mean, where A, B, C and D are all points?
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