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.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.
(a)180 cm³
(b)66 cm³
(c)15 cm³
(d)360 cm³
2.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
(a)24 cm
(b)26 cm
(c)6 cm
(d)10 cm
3.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
(a)zero
(b)negative
(c)cannot be determined
(d)positive
4.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.
(a)18 cm
(b)25 cm
(c)32 cm
(d)8 cm
5.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.
(a)3
(b)4
(c)0.25
(d)2.5
6.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?
(a)XP cannot be compared without knowing the line's length
(b)XP equals every other distance from X to the line
(c)XP is the longest distance from X to the line
(d)XP is the shortest distance from X to the line
7.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?
(a)where the angle bisector meets the posts' perpendicular bisector
(b)where the angle bisector meets the line joining the posts
(c)the perpendicular bisector of the posts, alone
(d)the angle bisector of the corner, alone
8.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?
(a)Two sides equal, with the angle between them equal
(b)Two angles equal, with the side between them equal
(c)All three pairs of sides equal
(d)Two sides equal, and any one angle equal
9.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.
(a)376.8 cm³
(b)452.2 cm³
(c)1130.4 cm³
(d)1884.0 cm³
10.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.
(a)42 cm
(b)21 cm
(c)34 cm²
(d)68 cm²
11.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?
(a)Cannot prove — no angle given
(b)Only two pairs of sides — not enough
(c)SAS, using the angle at Q
(d)SSS, using shared side QS
12.Work out the exact value of (cos 45°)² + (sin 45°)².
(a)2
(b)√2
(c)1
(d)1/2
13.An angle is measured with a protractor as 47°. What type of angle is this?
(a)Reflex
(b)Acute
(c)Obtuse
(d)Right angle
14.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
(a)(3, −4)
(b)(−4, 3)
(c)(4, 3)
(d)(−4, −3)
15.Work out the exact value of sin 30° + cos 60°.
(a)0
(b)√3
(c)1
(d)1/2

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