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 circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.
(a)15.7 cm
(b)31.4 cm
(c)62.8 cm
(d)78.5 cm
2.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?
(a)4.4
(b)110
(c)11
(d)1.1
3.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
(a)18 units
(b)7 units
(c)14 units
(d)12 units
4.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.
(a)65°
(b)32.5°
(c)50°
(d)130°
5.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142
6.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?
(a)ABC ≅ ZXY
(b)ABC ≅ ZYX
(c)ABC ≅ XYZ
(d)ABC ≅ YXZ
7.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
(a)96 cm²
(b)24 cm²
(c)16 cm²
(d)64 cm³
8.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?
(a)ASA, vertically opposite angle at E
(b)Cannot prove — no angle measured
(c)SSS, three equal side pairs
(d)SAS, vertically opposite angle included
9.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
(a)a line parallel to both, 3 cm from each
(b)the perpendicular bisector of the gap
(c)a line parallel to both, 6 cm from each
(d)a circle of radius 3 cm, centred midway
10.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
11.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
12.A pin on a map is at grid reference (5, 2). It is moved by the vector $(4 - 3)$ . Write down its new grid reference.
(a)(2, 6)
(b)(8, 6)
(c)(9, −1)
(d)(2, 2)
13.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?
(a)the single point exactly halfway along AB
(b)points as far from A as the length AB
(c)points twice as far from A as from B
(d)points the same distance from A as from B
14.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).
(a)(7, −9)
(b)(5, 1)
(c)(4, 6)
(d)(2, 3)
15.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

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