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.A regular hexagon has sides of length 8 cm. By splitting the hexagon into 6 identical triangles that meet at its centre, work out the area of the hexagon. Give your answer to 1 decimal place.
(a)192.0 cm²
(b)166.3 cm²
(c)138.6 cm²
(d)27.7 cm²
2.In triangle ABC, AB = 6 cm, AC = 8 cm and angle BAC = 60°. Work out the exact area of triangle ABC, giving your answer in the form $a 3$ .
(a) $93$ cm²
(b) $243$ cm²
(c) $123$ cm²
(d) $163$ cm²
3.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
4.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.
(a)7.2 cm
(b)50 cm
(c)20 cm
(d)62.8 cm
5.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6
6.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
(a)64 cm²
(b)32 cm²
(c)20 cm²
(d)8 cm²
7.In cyclic quadrilateral ABCD, with vertices in that order around the circle, the diagonal BD is drawn. In triangle ABD, angle ABD = 35° and angle ADB = 65°. Side DC is extended beyond C to a point E. Work out the size of angle BCE.
(a)80°
(b)160°
(c)100°
(d)40°
8.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
9.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.
(a)(−5, 1)
(b)(5, 4)
(c)(−4, 7)
(d)(−2, 6)
10.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
11.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
12.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.
(a)A tangent always passes through the centre of the circle
(b)A tangent is always parallel to the radius it touches
(c)The angle in a semicircle is 90°
(d)The angle between a tangent and a radius is 90°
13.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.
(a)4 squares
(b)12 squares
(c)6 squares
(d)5 squares
14.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.
(a)6 cm
(b)21 cm
(c)12 cm
(d)7.5 cm
15.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5

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