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.
Geometry and measures worksheet — GCSE Higher
MathsUKwww.geekhero.co.uk
- 1.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
- 2.A shape is translated by the vector and then by the vector . Write down the single column vector that has the same effect as those two translations together.
- 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 cube has edges of length 5 cm. Work out the length of the diagonal that runs from one corner of the cube to the opposite corner. Give your answer as a surd in its simplest form.
- 5.Shape T has a vertex at (5, 3). T is enlarged by scale factor −1, centre (2, 1). Work out the coordinates of the image of the vertex (5, 3).
- 6.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.
- 7.Work out the exact value of tan 30° + tan 30°.
- 8.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.
- 9.A shape is translated by the vector , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector . Work out the coordinates of the image of that same vertex under this second translation.
- 10.Triangle T has a vertex A at (4, 6). It is enlarged by a scale factor of −1/2, centre (2, 2). Work out the coordinates of the image of point A.
- 11.A jug holds 750 ml of water. Work out what fraction of a litre this is.
- 12.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?
- 13.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?
- 14.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 15.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
Build your own mix at the worksheet builder.