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

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1.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.
(a)(−5, 2)
(b)(5, −2)
(c)(2, 5)
(d)(−5, −2)
2.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.
(a)arc
(b)segment
(c)chord
(d)sector
3.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°
4.A tank holds 3.2 m³ of water. Work out this volume in litres.
(a)320
(b)32000
(c)3200
(d)3.2
5.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
(a)30
(b)120
(c)90
(d)60
6.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
7.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.
(a)(−3, −4)
(b)(−4, 3)
(c)(4, −3)
(d)(4, 3)
8.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
9.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
(a)48
(b)14
(c)24
(d)28
10.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.
(a)Congruent circles
(b)Tangential circles
(c)Similar circles
(d)Concentric circles
11.A ladder of length 7 m leans against a vertical wall. The foot of the ladder is 3 m from the base of the wall. Work out how high up the wall the ladder reaches. Give your answer correct to 1 decimal place.
(a)4.0 m
(b)6.4 m
(c)6.3 m
(d)10.0 m
12.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
(a)18 cm
(b)3√3 cm
(c)9√3/2 cm
(d)9√3 cm
13.A polygon has 9 sides. What is the name of this polygon?
(a)Octagon
(b)Nonagon
(c)Heptagon
(d)Decagon
14.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.
(a)32 m
(b)242 m
(c)84 m
(d)121 m
15.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?
(a)(7, 0)
(b)(12, −9)
(c)(12, −3)
(d)(4, −9)

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