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.

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 Higher

Maths · GCSE Higher · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?
(a)Kite
(b)Rhombus
(c)Trapezium
(d)Parallelogram
2.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.
(a)16 cm³
(b)96 cm³
(c)144 cm³
(d)288 cm³
3.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.
(a)(6, 1)
(b)(1, 6)
(c)(1, 5)
(d)(9, 6)
4.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.
(a)30°
(b)45°
(c)120°
(d)60°
5.Triangle ABC has a right angle at B, hypotenuse AC = 13 cm and AB = 5 cm. Triangle DEF has a right angle at E, hypotenuse DF = 13 cm and DE = 5 cm. Which condition proves the two triangles are congruent?
(a)SSS - three sides equal
(b)RHS - right angle, hypotenuse and one side equal
(c)ASA - two angles and the included side equal
(d)SAS - two sides and the included angle equal
6.The vector $(- 2 5)$ describes a translation. A student writes it as $(5 - 2)$ by mistake. Write down what error the student has made.
(a)Doubled the x component
(b)Reversed both signs
(c)Swapped the x and y components
(d)Reversed only the y sign
7.OABC is a parallelogram, with OA = a and OC = c. M is the midpoint of AB. Express the vector MC in terms of a and c.
(a)(1/2)c + a
(b)c − a
(c)(1/2)c − a
(d)a − (1/2)c
8.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.
(a)2.25
(b)5.0625
(c)1.5
(d)1.125
9.A student is asked to rearrange the cosine rule a² = b² + c² − 2bc cos A to make cos A the subject. They write: cos A = (a² − b² − c²) / (2bc). Is the student's rearrangement correct?
(a)Yes — the sign does not matter for cos A.
(b)No — should divide by −2bc, not +2bc; sign is wrong.
(c)No — the denominator should be bc, not 2bc.
(d)Yes — the rearrangement is correct as written.
10.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°
11.Point P has coordinates (1, 3). P is reflected in the line x = 4, then the image is reflected in the line y = 1, and then that image is translated by the vector (2, −3). Work out the coordinates of the final image of P.
(a)(9, 2)
(b)(7, −1)
(c)(1, −6)
(d)(9, −4)
12.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?
(a)Wrong: 1 litre = 100 ml, so his number is off.
(b)Wrong: 1 litre = 1000 ml, so 3.2 l = 3200 ml.
(c)Wrong, but only because 3.2 should round to 3.
(d)Correct: ×100 converts litres to millilitres.
13.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
(a)60°
(b)20°
(c)120°
(d)80°
14.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.
(a)150°
(b)300°
(c)42°
(d)157°
15.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

Build your own mix at the worksheet builder.