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.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.
(a)8,000,000 cm³
(b)8,000 cm³
(c)8 cm³
(d)80,000 cm³
2.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?
(a)angle C = angle F
(b)angle B = angle E
(c)AC = DF
(d)angle A = angle D
3.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
(a)10.5 cm²
(b)21 cm²
(c)27 cm²
(d)30 cm²
4.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).
(a)(7, 2)
(b)(12, −8)
(c)(3, −8)
(d)(12, −2)
5.Write down the term for the distance all the way around the edge of a circle.
(a)diameter
(b)circumference
(c)area
(d)radius
6.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?
(a)5
(b)4
(c)3
(d)2
7.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?
(a)I is the midpoint of side AB.
(b)I lies on side AC.
(c)I is the same distance from all three sides.
(d)I is the same distance from all three vertices.
8.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
(a)12√3 cm
(b)6 cm
(c)4√3 cm
(d)6√3 cm
9.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.
(a)59°
(b)118°
(c)62°
(d)31°
10.After a translation by the vector $(6 - 2)$ , a point lands on (4, 1). Write down the coordinates of the point before the translation.
(a)(2, −5)
(b)(2, 7)
(c)(6, −5)
(d)(6, 7)
11.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?
(a)9
(b)3
(c)1
(d)6
12.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.
(a)π cm²
(b)4π cm
(c)2π cm
(d)π cm
13.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.
(a)Chord
(b)Diameter
(c)Radius
(d)Arc
14.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
(a) $(2 - 5)$
(b) $(8 9)$
(c) $(- 2 5)$
(d) $(2 5)$
15.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

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