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 · 15 questions

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1.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°
2.Write down the exact value of tan 45°.
(a)0
(b)√3
(c)√3/3
(d)1
3.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.
(a)25.12 cm
(b)6.28 cm
(c)62.8 cm
(d)12.56 cm
4.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
5.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)
6.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?
(a)AAS - two angles and a non-included side equal
(b)SSS - three sides equal
(c)SAS - two sides and the included angle equal
(d)ASA - two angles and the included side equal
7.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?
(a)Wrong: multiply by angle ÷ 360, not divide by it.
(b)Wrong: multiply by the angle only, no division.
(c)Wrong: use radius × angle, not circumference.
(d)Correct: dividing by the angle in degrees works.
8.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.
(a)Isosceles
(b)Right-angled
(c)Scalene
(d)Equilateral
9.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.
(a)The same as the cylinder's volume
(b)Two thirds of the cylinder's volume
(c)One third of the cylinder's volume
(d)Half the cylinder's volume
10.Write down the exact value of tan 60°.
(a)1/√3
(b)3
(c)√3/2
(d)√3
11.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².
(a)300 cm²
(b)204 cm²
(c)150 cm²
(d)600 cm²
12.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.
(a)180°
(b)59°
(c)62°
(d)118°
13.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.
(a)27 cm
(b)45 cm
(c)15 cm
(d)11 cm
14.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.
15.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.
(a)59°
(b)118°
(c)62°
(d)31°

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