Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation 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 Foundation

Maths · GCSE Foundation · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?
(a)∠YZW
(b)∠WXY
(c)∠XYZ
(d)∠ZWX
2.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
(a)62°
(b)59°
(c)90°
(d)118°
3.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
4.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.
(a)SSS
(b)SAS
(c)RHS
(d)AAS
5.A square has sides of length 7 cm. Work out its area.
(a)49 cm²
(b)21 cm²
(c)28 cm²
(d)14 cm²
6.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?
(a)7.7 m
(b)4.5 m
(c)7.6 m
(d)15.4 m
7.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?
(a)A cylinder
(b)A pyramid
(c)A cone
(d)A prism
8.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.
(a)65°
(b)32.5°
(c)50°
(d)130°
9.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?
(a)The radius must equal the full length of AB.
(b)The arcs only meet exactly on AB, not above or below it.
(c)That radius is always too short to draw any arc.
(d)The arcs would not cross the line AB at all.
10.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
(a)40 cm²
(b)80 cm²
(c)20 cm²
(d)13 cm²
11.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.
(a)1600
(b)500
(c)8
(d)16
12.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate
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.Write down the exact value of sin 45°.
(a)√3/2
(b)√2/2
(c)1/2
(d)1
15.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.
(a)(2, 6)
(b)(9, −1)
(c)(2, −2)
(d)(8, 6)

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