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

Maths · GCSE Higher · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.In triangle ABC, AB = x cm, AC = (x + 3) cm, BC = 7 cm and angle BAC = 60°. Work out the value of x.
(a)5
(b)37
(c)−8
(d)8
2.A crane's hook starts at the point (3.4, 9.5) on a construction site plan measured in metres. It moves along the vector $(- 4.5 - 1.2)$ to pick up a beam, then along the vector $(- 2.5 0.8)$ to place it. Work out the single column vector that describes the hook's overall movement from its start position to where it places the beam.
(a) $(- 2 - 2)$
(b) $(- 7 - 0.4)$
(c) $(7 - 0.4)$
(d) $(- 7 2)$
3.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?
(a)Square-based pyramid
(b)Cube
(c)Cuboid
(d)Triangular prism
4.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
(a)20
(b)22
(c)18
(d)16
5.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
6.A jug holds 750 ml of water. Work out what fraction of a litre this is.
(a)3/4
(b)1/4
(c)4/3
(d)3/10
7.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.
(a)SSS – all three corresponding sides are equal
(b)RHS – a right angle, hypotenuse and one other side are equal
(c)SAS – two sides and the included angle are equal
(d)ASA – two angles and the included side are equal
8.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.
(a)−10
(b)47.5
(c)25
(d)20
9.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
(a)49°
(b)41°
(c)82°
(d)98°
10.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).
(a)(5, 2)
(b)(3, 10)
(c)(0, 11)
(d)(1, 7)
11.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
(a)(3, −4)
(b)(3, −1)
(c)(3, −5)
(d)(−3, 5)
12.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.
(a)11.4 cm
(b)4.8 cm
(c)14.7 cm
(d)58.8 cm
13.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).
(a)(5, 3)
(b)(−1, −1)
(c)(−5, −3)
(d)(9, 5)
14.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
15.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$

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