Printable · GCSE Foundation · ages 14-16
Geometry and measures worksheet — GCSE Foundation
Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Geometry and measures worksheet — GCSE Foundation
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- 1.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.
- 2.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.
- 3.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.
- 4.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 5.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.
- 6.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.
- 7.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
- 8.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
- 9.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).
- 10.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 11.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
- 12.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 13.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.
- 14.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.
- 15.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².
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