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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?
(a)Triangular-based pyramid (tetrahedron)
(b)Square-based pyramid
(c)Cube
(d)Triangular prism
2.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
(a)24 cm
(b)26 cm
(c)6 cm
(d)10 cm
3.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.
(a)circumference
(b)segment
(c)sector
(d)tangent
4.A student is asked to rearrange the cosine rule a² = b² + c² − 2bc cos A to make cos A the subject. They write: cos A = (a² − b² − c²) / (2bc). Is the student's rearrangement correct?
(a)Yes — the sign does not matter for cos A.
(b)No — should divide by −2bc, not +2bc; sign is wrong.
(c)No — the denominator should be bc, not 2bc.
(d)Yes — the rearrangement is correct as written.
5.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.
(a)17.5 cm
(b)24 cm
(c)12 cm
(d)6 cm
6.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
7.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.
(a) $(- 6 5)$
(b) $(6 5)$
(c) $(6 - 5)$
(d) $(- 6 - 5)$
8.A trapezium has vertices (2, 1), (6, 1), (5, 4) and (3, 4). It is rotated 180° about the vertex (2, 1). Work out the number of points on the trapezium — including its vertices, edges and interior — that are invariant under this rotation.
(a)0 points
(b)1 point
(c)2 points
(d)4 points
9.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)
10.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.
y = x
(a)(−7, −3)
(b)(7, 3)
(c)(−3, 7)
(d)(3, −7)
11.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?
(a)Angle D = angle A
(b)BC = 8 cm
(c)EF = 8 cm
(d)DE = 8 cm
12.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
13.A garden plan is drawn to a scale of 1 cm : 1.8 m. A path on the plan measures 4.5 cm. What is the real length of the path, in metres, to 1 decimal place?
(a)8.1 m
(b)9.0 m
(c)6.3 m
(d)2.5 m
14.An enlargement has a scale factor of −2. Priti says the image must be a mirror image of the original shape. Is Priti correct?
(a)No — it's a 180° rotation, not a reflection.
(b)Yes — negative numbers always mean a reflection.
(c)Yes — upside down is the same thing as mirrored.
(d)No — negative factors change size, not orientation.
15.A tank holds 3.2 m³ of water. Work out this volume in litres.
(a)320
(b)32000
(c)3200
(d)3.2

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