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 warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?
(a)22
(b)23
(c)21
(d)24
2.Work out the exact value of (sin 30°)² + (cos 30°)².
(a)1/4
(b)3/4
(c)−1/2
(d)1
3.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?
(a)angle A = angle D
(b)AB = DE
(c)AC is parallel to DF
(d)the triangles are drawn the same way up
4.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.
(a)Major segment
(b)Minor segment
(c)Semicircle
(d)Minor arc
5.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector $(4.5 - 6.2)$ to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
(a) $(6.5 1)$
(b) $(- 6.5 - 1)$
(c) $(6.5 - 4.4)$
(d) $(11 - 5.2)$
6.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?
(a)A parallelogram
(b)A rectangle
(c)An L-shape
(d)A T-shape
7.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.
(a)31.4
(b)62.8
(c)3.14
(d)15.7
8.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
(a)17
(b)24
(c)15
(d)7.5
9.A robot on a grid moves by the vector $(- 2 3)$ , then by the vector $(5 - 7)$ , then by the vector $(1 4)$ . Write down the single column vector that has the same overall effect as these three moves.
(a) $(- 6 14)$
(b) $(0 4)$
(c) $(3 - 4)$
(d) $(4 0)$
10.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.
(a)A rectangle 4 m wide, running along the wall.
(b)A semicircle of radius 4 m, away from the wall.
(c)A full circle of radius 4 m.
(d)A quarter circle of radius 4 m.
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.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).
(a)(5, 2)
(b)(3, 10)
(c)(0, 11)
(d)(1, 7)
13.A cube has all of its edges the same length. How many planes of symmetry does it have?
(a)9
(b)6
(c)12
(d)3
14.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
15.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
(a)96 cm²
(b)24 cm²
(c)16 cm²
(d)64 cm³

Build your own mix at the worksheet builder.