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.
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Geometry and measures worksheet — GCSE Foundation
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- 1.Work out the exact value of cos 0° − sin 30°.
- 2.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.
- 3.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?
- 4.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
- 5.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
- 6.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
- 7.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.
- 8.A hiker walks due west. What is the three-figure bearing for this direction?
- 9.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.
- 10.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.
- 11.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.
- 12.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 13.Work out the exact value of sin 30° + cos 60°.
- 14.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?
- 15.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.
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