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.

Non-calculator

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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?
(a)Yes - SSS, the three side lengths all match
(b)Yes - SAS, two sides and an angle match
(c)Cannot be determined without the angles
(d)No - the sides are listed in a different order
2.The point R(−6, 9) is translated by the vector $(- 11 5)$ . Write down the coordinates of the image of R.
(a)(−1, 9)
(b)(−1, −2)
(c)(−6, −2)
(d)(−11, 20)
3.A designer plots a logo point at (3, 4) on a grid. She reflects it in the line y = 1 and then rotates the image 90° clockwise about the point (1, 1) to create a repeating tile pattern. Work out the coordinates of the point after both transformations.
(a)(−2, −3)
(b)(−2, −1)
(c)(−6, −1)
(d)(4, 3)
4.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?
(a)A reflection in the y-axis
(b)A reflection in the x-axis
(c)A rotation of 180° about the origin
(d)No transformation — the shape is unchanged
5.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
6.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
7.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.
(a)TU
(b)PQ
(c)VW
(d)RS
8.A rotation of 180° about the point (3, 2) can be written as a reflection in the line x = 3, followed by a reflection in a second line, for every point in the plane. Which line is the second line?
(a)x = 2
(b)y = 3
(c)y = x
(d)y = 2
9.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?
(a)ASA — angle between two sides
(b)SSS — but only two sides given
(c)Cannot prove — only one angle
(d)SAS — two sides, included angle
10.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.
(a)10√3 m
(b)5/√3 m
(c)5√3 m
(d)5√3/2 m
11.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.
(a)75°
(b)105°
(c)37°
(d)146°
12.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.
(a)4
(b)10
(c)8
(d)5
13.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.
(a)18
(b)9
(c)3
(d)2
14.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
15.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°

Build your own mix at the worksheet builder.