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.Vector A is $(- 5 2)$ and vector B is $(5 - 2)$ . Write down how vector B compares to vector A.
(a)B is the same as A
(b)B is unrelated to A in direction
(c)B is twice A
(d)B is the reverse of A
2.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?
(a)2
(b)1
(c)4
(d)0
3.A circle has a radius of 3 cm. Work out the diameter of the circle.
(a)6 cm
(b)1.5 cm
(c)3 cm
(d)5 cm
4.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.
(a)(−5, 1)
(b)(5, 4)
(c)(−4, 7)
(d)(−2, 6)
5.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
6.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
7.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
(a)12√3 cm
(b)6 cm
(c)4√3 cm
(d)6√3 cm
8.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.
(a)27 cm³
(b)400 cm²
(c)150 cm³
(d)300 cm³
9.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.
(a)113°
(b)48°
(c)67°
(d)180°
10.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
11.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
12.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.
(a)3 m
(b)3√2/2 m
(c)6 m
(d)3√2 m
13.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)
14.A water tank holds 2.5 m³. Work out this volume in cm³.
(a)2500 cm³
(b)2 500 000 cm³
(c)25 000 cm³
(d)250 cm³
15.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.
(a)59°
(b)118°
(c)62°
(d)236°

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