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.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15
2.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.
(a)28 cm
(b)14 cm
(c)49 cm
(d)11 cm
3.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.
(a)7 cm
(b)17 cm
(c)13 cm
(d)60 cm
4.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
5.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
(a) $(4 4)$
(b) $(4 - 4)$
(c) $(- 4 4)$
(d) $(- 4 - 4)$
6.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?
(a)Yes, it folds into a cube
(b)No, it needs one more square
(c)No, it has one square too many
(d)Yes, but only if two squares overlap
7.A shape is translated by the vector $(3 - 8)$ , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector $(- 5 2)$ . Work out the coordinates of the image of that same vertex under this second translation.
(a)(7, 8)
(b)(11, 3)
(c)(3, 1)
(d)(11, −2)
8.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.
(a)chord
(b)segment
(c)semicircle
(d)sector
9.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.
(a)54 cm
(b)50 cm²
(c)25 cm²
(d)27 cm
10.A vertical line passes through the point (5, 2). Write down the equation of this line.
(a)x = 2
(b)x = 5
(c)y = 2
(d)y = 5
11.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6
12.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.
(a)(−18, 23)
(b)(22, −13)
(c)(2, 5)
(d)(12, −4)
13.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?
(a)radius
(b)diameter
(c)circumference
(d)chord
14.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).
(a)(8, −3)
(b)(8, −6)
(c)(4, −6)
(d)(8, 6)
15.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?
(a)Right
(b)Acute
(c)Reflex
(d)Obtuse

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