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 · 15 questions

MathsUKwww.geekhero.co.uk

1.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(a)7.0 cm
(b)14.0 cm
(c)9.9 cm
(d)5.0 cm
2.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.
(a)113.04 cm³
(b)28.26 cm³
(c)37.68 cm³
(d)84.78 cm³
3.Write down the column vector, from the options given, that would move a point to the right and downwards.
(a) $(3 - 4)$
(b) $(- 3 - 4)$
(c) $(- 3 4)$
(d) $(3 4)$
4.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
5.Which of these correctly compares a 'line' with a 'line segment'?
(a)A line has two endpoints; a segment has none
(b)A line segment is always curved
(c)A line has no endpoints; a segment has two
(d)A line segment is a closed shape
6.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?
(a)Yes, it folds into a cube
(b)No, it needs one more square
(c)No, it has one square too many
(d)Yes, but only if two squares overlap
7.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
(a)Angles in a triangle sum to 180°
(b)Angles on a straight line sum to 180°
(c)Vertically opposite angles are equal
(d)Base angles of an isosceles triangle are equal
8.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?
(a)5 cm by 2 cm
(b)5 cm by 3 cm
(c)3 cm by 2 cm
(d)5 cm by 5 cm
9.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?
(a)AAA applies, because both triangles have a right angle
(b)The triangles cannot be proved congruent from this information
(c)RHS applies: the right angle, hypotenuse and one matching side are all equal
(d)SSS applies, because all three sides must be equal in any right-angled triangle
10.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?
(a)335°
(b)025°
(c)155°
(d)065°
11.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
(a)120 units²
(b)60 units²
(c)30 units²
(d)65 units²
12.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector $(- 3 5)$ to a warehouse, then by the vector $(4 - 1)$ to the delivery address. Work out the coordinates of the delivery address.
(a)(7, −2)
(b)(11, −3)
(c)(8, −6)
(d)(6, 2)
13.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.
(a)0
(b)2
(c)4
(d)1
14.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?
(a)14
(b)104
(c)76
(d)90
15.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

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