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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 solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.
(a)14
(b)10
(c)16
(d)12
2.An enlargement with scale factor 5 maps the point (4, 1) to the point (12, 9). Which of these points is invariant (does not move) under this enlargement?
(a)(−2, −2)
(b)(−2, 1)
(c)(8, 5)
(d)(2, −1)
3.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15
4.Triangle D has vertices (3, 1), (3, 5) and (6, 1). It is reflected in the line x = 3. Write down the number of vertices of the triangle that are invariant under this reflection.
(a)3
(b)1
(c)0
(d)2
5.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.
(a)(5, 4)
(b)(14, 4)
(c)(8, 2)
(d)(4, 2)
6.In triangle ABC, AB = 8 cm, AC = 5 cm and angle BAC = 60°. Work out the value of BC².
(a)49 cm²
(b)129 cm²
(c)69 cm²
(d)89 cm²
7.AT is a diameter of a circle with centre O. PT is a tangent to the circle at the point T, and P is a point on this tangent such that A, T and P form a triangle. Angle PAT = 28°. Work out the size of angle APT.
(a)118°
(b)62°
(c)28°
(d)90°
8.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.
(a)Major segment
(b)Minor segment
(c)Semicircle
(d)Minor arc
9.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
10.OABC is a parallelogram, with OA = a and OC = c. X is the midpoint of the diagonal AC. Express the vector OX in terms of a and c, and use it to show that X also lies on the diagonal OB.
(a)a + c
(b)(1/2)a + c
(c)(1/2)a − (1/2)c
(d)(1/2)a + (1/2)c
11.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.
(a)18
(b)9
(c)3
(d)2
12.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
13.Triangle J is mapped onto triangle K by a single transformation with centre O. Triangle K is half the size of triangle J and is inverted (turned through 180°). Which of these transformations maps J onto K?
(a)An enlargement, centre O, scale factor −2.
(b)An enlargement, centre O, scale factor −1/2.
(c)A rotation of 180° about O, with no change in size.
(d)An enlargement, centre O, scale factor 1/2.
14.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
(a)142°
(b)40°
(c)38°
(d)398°
15.Work out the exact value of sin 30° + cos 60°.
(a)0
(b)√3
(c)1
(d)1/2

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