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 · 15 questions

MathsUKwww.geekhero.co.uk

1.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.
(a)(2, −5)
(b)(2, 3)
(c)(2, 5)
(d)(2, −1)
2.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).
(a)(7, −9)
(b)(5, 1)
(c)(4, 6)
(d)(2, 3)
3.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
4.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.
(a)28 cm
(b)7 cm
(c)7√3 cm
(d)14/√3 cm
5.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.
(a) $(- 6 5)$
(b) $(6 5)$
(c) $(6 - 5)$
(d) $(- 6 - 5)$
6.Two coastguard stations A and B are 18 km apart, with B due east of A. A boat at C is on a bearing of 062° from A and on a bearing of 315° from B. Work out the distance of the boat from station B. Give your answer to 1 decimal place.
(a)16.6 km
(b)13.3 km
(c)12.0 km
(d)8.8 km
7.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
8.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?
(a)(−6, −8)
(b)(6, −8)
(c)(6, −4)
(d)(9, −8)
9.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?
(a)9
(b)3
(c)1
(d)6
10.After a translation by the vector $(6 - 2)$ , a point lands on (4, 1). Write down the coordinates of the point before the translation.
(a)(2, −5)
(b)(2, 7)
(c)(6, −5)
(d)(6, 7)
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 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) $(4 0)$
13.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
(a)−32
(b)48
(c)32
(d)37
14.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15
15.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.
(a)50 m
(b)201 m
(c)25 m
(d)13 m

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