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.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?
(a)I is the midpoint of side AB.
(b)I lies on side AC.
(c)I is the same distance from all three sides.
(d)I is the same distance from all three vertices.
2.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?
(a)a triangle
(b)a triangle with a rectangle attached
(c)two triangles joined at their bases
(d)a rectangle
3.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.
(a)100°
(b)260°
(c)80°
(d)50°
4.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?
(a)Not enough information
(b)Cuboid — not necessarily a cube
(c)Triangular prism
(d)Cube — only a cube fits this
5.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?
(a)0.3
(b)3
(c)6
(d)30
6.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.
(a)27°
(b)90°
(c)117°
(d)63°
7.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.
(a)1.5
(b)−10
(c)−1.5
(d)−24
8.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.
(a)−10
(b)47.5
(c)25
(d)20
9.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
(a)4
(b)0
(c)2
(d)1
10.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
11.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?
(a)Similar, but AAA alone does not prove congruence
(b)Congruent, because AAA proves congruence
(c)No relationship can be determined at all
(d)Congruent, because equal angles force equal sides
12.A circle has a diameter of 4 cm. Work out the radius of the circle.
(a)8 cm
(b)2 cm
(c)1 cm
(d)0.5 cm
13.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?
(a)A triangle-based pyramid standing on its triangular base
(b)A triangular prism standing on its triangular end
(c)A cuboid standing on a rectangular face
(d)A triangular prism lying on one of its rectangular faces
14.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.
(a)12 cm
(b)768 cm
(c)104 cm
(d)24 cm
15.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector $(4 6)$ and then by the vector $(- 9 - 1)$ . Write down the column vector that would take the drone straight back to its starting point.
(a) $(- 5 - 5)$
(b) $(5 - 5)$
(c) $(- 5 5)$
(d) $(- 13 - 7)$

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