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.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.
(a)9
(b)5
(c)20
(d)4
2.p is the column vector with top number 5 and bottom number 2. q is the column vector with top number 1 and bottom number 6. Work out p + q, giving your answer as a column vector in the form (top, bottom).
(a)(4, −4)
(b)(8, 6)
(c)(6, 2)
(d)(6, 8)
3.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?
(a)y
(b)z
(c)x
(d)X
4.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?
(a)RHS - right angle, hypotenuse and one side equal
(b)SAS - two sides and the included angle equal
(c)AAS - two angles and a non-included side equal
(d)ASA - two angles and the included side equal
5.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).
(a)(9, −5)
(b)(1, 7)
(c)(12, −1)
(d)(7, −2)
6.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
(a)44
(b)22
(c)10
(d)5.5
7.How many edges does a triangular prism have?
(a)9
(b)5
(c)6
(d)12
8.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
(a)Angles in a triangle sum to 180°
(b)Angles on a straight line sum to 180°
(c)Vertically opposite angles are equal
(d)Base angles of an isosceles triangle are equal
9.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.
(a)5/12
(b)7/12
(c)5/6
(d)1/2
10.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?
(a)arc
(b)tangent
(c)chord
(d)radius
11.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
(a)125 g
(b)1025 g
(c)1000 g
(d)1250 g
12.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
(a)third quadrant
(b)second quadrant
(c)first quadrant
(d)fourth quadrant
13.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.
(a)314 cm²
(b)1256 cm²
(c)62.8 cm²
(d)628 cm²
14.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?
(a)Draw equal arcs from X and Y, meeting below line l.
(b)Draw an arc centred at P through only one of X or Y.
(c)Join X and Y with a straight line.
(d)Draw a circle through X, Y and P.
15.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
(a)20
(b)22
(c)18
(d)16

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