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

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

MathsUKwww.geekhero.co.uk

1.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.
(a)The arc
(b)The chord
(c)The diameter
(d)The centre
2.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
(a)297
(b)117
(c)27
(d)63
3.A translation is described by the column vector $(- 2 7)$ . Write down a description of this translation in words, stating the horizontal and vertical movement.
(a)7 units left and 2 units up
(b)7 units right and 2 units down
(c)7 units right and 2 units up
(d)2 units right and 7 units down
4.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.
(a)5.6 m
(b)16 m
(c)3.87 m
(d)4 m
5.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.
(a)1600
(b)500
(c)8
(d)16
6.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
7.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
8.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?
(a)ASA (two angles and the included side)
(b)SAS (two sides and the included angle)
(c)RHS (right angle, hypotenuse, one side)
(d)SSS (three sides)
9.Write down which one of these statements about quadrilaterals is true.
(a)Every square is a rectangle
(b)Every rectangle is a rhombus
(c)Every rectangle is a square
(d)Every rhombus is a rectangle
10.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
(a)(1, 7)
(b)(6, 4)
(c)(6, 2)
(d)(−2, 4)
11.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?
(a)Two sides equal, with the angle between them equal
(b)Two angles equal, with the side between them equal
(c)All three pairs of sides equal
(d)Two sides equal, and any one angle equal
12.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.
(a)24 cm
(b)17 cm
(c)34 cm
(d)60 cm²
13.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?
(a)0
(b)4
(c)2
(d)1
14.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.
(a)31.4
(b)62.8
(c)3.14
(d)15.7
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.
(a)a² − b² = c²
(b)a² + b² = c
(c)a + b = c
(d)a² + b² = c²

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