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.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?
(a)isosceles trapezium
(b)rhombus
(c)kite
(d)parallelogram
2.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?
(a)118°
(b)180°
(c)62°
(d)236°
3.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)
4.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.
(a)1/3
(b)3
(c)6
(d)1.8
5.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?
(a)No — any two angles enough alone
(b)Yes — third angle may differ
(c)Yes — side must be included
(d)No — third angle is also fixed
6.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)
7.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?
(a)Rectangle
(b)Triangle
(c)Trapezium
(d)Pentagon
8.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.
(a)(1, 6)
(b)(−1, 6)
(c)(−1, −6)
(d)(1, −6)
9.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
(a)159
(b)283
(c)182
(d)77
10.Write down the name given to a triangle whose three sides are all the same length.
(a)Right-angled
(b)Isosceles
(c)Scalene
(d)Equilateral
11.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
(a)sin 30°, cos 30°, tan 30°
(b)cos 30°, tan 30°, sin 30°
(c)tan 30°, sin 30°, cos 30°
(d)sin 30°, tan 30°, cos 30°
12.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.
(a)The tangent
(b)The radius
(c)The diameter
(d)The chord
13.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
14.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.
(a)65°
(b)115°
(c)25°
(d)295°
15.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.
(a)A rectangle with rounded ends
(b)An oval
(c)A circle
(d)A rectangle

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