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

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1.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
(a) $(- 5 - 3)$
(b) $(- 3 5)$
(c) $(3 - 5)$
(d) $(- 3 - 5)$
2.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.
(a)12 cm
(b)768 cm
(c)104 cm
(d)24 cm
3.In this question, a curved surface counts as a face. How many faces does a sphere have?
(a)0
(b)2
(c)1
(d)3
4.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.
(a)Major arc
(b)Minor segment
(c)Chord
(d)Minor arc
5.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?
(a)8
(b)9
(c)3
(d)6
6.What does the statement AB = CD mean, where A, B, C and D are all points?
(a)AB is parallel to CD
(b)A, B, C and D all lie on one line
(c)AB and CD are equal in length
(d)AB is perpendicular to CD
7.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?
(a)ASA
(b)SSS
(c)SSA
(d)RHS
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 hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
(a)142°
(b)40°
(c)38°
(d)398°
10.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?
(a)3 squares
(b)5 squares
(c)2 squares
(d)4 squares
11.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.
(a)0.1 m
(b)2.4 m
(c)7.1 m
(d)0.9 m
12.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.
(a)45
(b)130
(c)90
(d)50
13.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.
(a)28 cm
(b)48 cm²
(c)80 cm²
(d)32 cm²
14.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?
(a)Two sides and the angle between them
(b)Right angle, equal hypotenuse, one more side
(c)Right angle and all three sides equal
(d)Right angle, hypotenuse, one more angle
15.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.
(a)(8, 2)
(b)(−1, 11)
(c)(−4, 8)
(d)(8, 8)

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