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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?
(a)construct a perpendicular from the crossing point
(b)bisect the angle between the two lines
(c)construct the perpendicular bisector of the two lines
(d)draw a circle centred at the crossing point
2.Each of these has an exact value. Write down the one whose value is the greatest.
(a)cos 60°
(b)sin 45°
(c)tan 45°
(d)cos 30°
3.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
4.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.
(a)112°
(b)68°
(c)248°
(d)90°
5.How many vertices does a cuboid have?
(a)12
(b)6
(c)4
(d)8
6.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?
(a)where the angle bisector meets the posts' perpendicular bisector
(b)where the angle bisector meets the line joining the posts
(c)the perpendicular bisector of the posts, alone
(d)the angle bisector of the corner, alone
7.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.
(a)19
(b)10
(c)20
(d)14
8.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?
(a)No — hexagons can't be regular
(b)Yes — six equal sides means regular
(c)Yes — all sides are equal
(d)No — angles must be equal too
9.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.
(a)30 cm²
(b)54 cm²
(c)15 cm²
(d)27 cm²
10.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.
(a)Rhombus
(b)Trapezium
(c)Kite
(d)Parallelogram
11.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.
(a)(2, 6)
(b)(9, −1)
(c)(2, −2)
(d)(8, 6)
12.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.
(a)615.44 cm²
(b)1436.03 cm³
(c)153.86 cm²
(d)87.92 cm²
13.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
14.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.
(a)£0.31
(b)£1.57
(c)£0.16
(d)£6.28
15.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.
(a)30 m
(b)6 m
(c)300 m
(d)72 m

Build your own mix at the worksheet builder.