Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher 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 Higher

Maths · GCSE Higher · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.O is the centre of a circle, and PT is a tangent to the circle at the point T. A is a point on the circle, with OA and OT both radii and angle AOT = 122°. At the point T, the chord TA lies between the radius TO and the tangent TP. Work out the size of angle ATP, the angle between the chord and the tangent.
(a)119°
(b)61°
(c)29°
(d)32°
2.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?
(a)Its rotational symmetry order is always 4
(b)Its diagonals cross at right angles
(c)Its diagonals are always equal in length
(d)It always has four right angles
3.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
4.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.
(a)9 : 4
(b)4 : 9
(c)2 : 3
(d)8 : 27
5.The perimeter of a square is 20 cm. Work out the area of the square.
(a)5 cm
(b)25 cm²
(c)100 cm²
(d)400 cm²
6.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.
(a)3.2 cm
(b)16 cm
(c)17 cm
(d)20 cm
7.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.
(a)It is the same length as the other two chords
(b)It is the longest of the three chords
(c)It is the shortest of the three chords
(d)It is half the length of each of the other two chords
8.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?
(a)∠QRS
(b)∠PQR
(c)∠TRP
(d)∠RST
9.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.
(a)68°
(b)170°
(c)78°
(d)184°
10.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
(a)£50.24
(b)£25.12
(c)£200.96
(d)£100.48
11.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?
(a)Pentagon
(b)Hexagon
(c)Rectangle
(d)Triangle
12.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
13.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.
(a)(5, 4)
(b)(14, 4)
(c)(8, 2)
(d)(4, 2)
14.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.
(a)The same as the cylinder's volume
(b)Two thirds of the cylinder's volume
(c)One third of the cylinder's volume
(d)Half the cylinder's volume
15.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?
(a)24
(b)6
(c)12
(d)9

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