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 shape is reflected in the line y = x, and the image is then reflected in the line y = 0. These two lines meet at the origin. Work out the single rotation, centre and angle, that is equivalent to this combination of two reflections, for every point.
y = x
(a)90° clockwise about (0, 0)
(b)45° clockwise about (0, 0)
(c)90° anticlockwise about (0, 0)
(d)180° about (0, 0)
2.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
(a)sin 30°, cos 30°, tan 30°
(b)cos 30°, tan 30°, sin 30°
(c)tan 30°, sin 30°, cos 30°
(d)sin 30°, tan 30°, cos 30°
3.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?
(a)angle C = angle F
(b)angle B = angle E
(c)AC = DF
(d)angle A = angle D
4.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?
(a)Not enough information
(b)Cuboid — not necessarily a cube
(c)Triangular prism
(d)Cube — only a cube fits this
5.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?
(a)3
(b)5
(c)7
(d)6
6.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.
(a)17
(b)7
(c)144
(d)13
7.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.
(a)441 cm
(b)21 cm
(c)35 cm
(d)9 cm
8.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?
(a)arc
(b)tangent
(c)chord
(d)radius
9.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.
(a)112°
(b)68°
(c)248°
(d)90°
10.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?
(a)Yes, it folds into a cube
(b)No, it needs one more square
(c)No, it has one square too many
(d)Yes, but only if two squares overlap
11.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?
(a)50
(b)5
(c)0.5
(d)0.05
12.A, B and C are points on a circle with centre O, and AC is a diameter of the circle. Work out the size of angle ABC.
(a)90°
(b)45°
(c)It cannot be worked out without knowing the radius
(d)180°
13.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
14.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?
(a)an arc of the same radius, centred at the midpoint of AB
(b)an arc of the same radius, centred at B
(c)a smaller arc, centred at A again
(d)a straight line joining the ends of the first arc
15.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) $(11 - 5.2)$

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