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 sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.
- 2.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.
- 3.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
- 4.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?
- 5.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?
- 6.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.
- 7.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.
- 8.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
- 9.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.
- 10.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.
- 11.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
- 12.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
- 13.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).
- 14.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.
- 15.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.
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