Geometry and Shape: Practice Set 4 - Worksheets, Questions and Revision

26 original exam-style questions - 15 pages of questions with a full mark scheme - free printable PDF.

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EP.M80 Geometry and Shape: Practice Set 4

GL ASSESSMENT GL · Calculators not allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
An angle measures 155 degrees. Which type of angle is this?
  • A) Acute
  • B) Right angle
  • C) Obtuse
  • D) Reflex
(Total for Question 1 is 1 mark)
2
A straight line AB passes through point M. A ray MC is drawn from M, splitting angle AMB into two angles: angle AMC = 47 degrees and angle CMB = y degrees. Calculate the value of y.
Diagram NOT accurately drawn
47° y° A B C M (not to scale)
(Total for Question 2 is 2 marks)
3
Four angles meet at a point O: 63 degrees, 78 degrees, 91 degrees and w degrees. Calculate the value of w.
Diagram NOT accurately drawn
63° 78° 91° w° O (not to scale)
(Total for Question 3 is 2 marks)
4
For each description below, write down the correct circle term (radius, diameter, chord, tangent or circumference).
Diagram NOT accurately drawn
radius diameter chord tangent (not to scale)
(a)A straight line from the centre of a circle to any point on its edge.(1)
(b)A straight line that touches a circle at exactly one point without crossing into it.(1)
(c)A straight line segment joining any two points on the circumference, not necessarily through the centre.(1)
(d)The distance all the way around the outside of a circle.(1)
(Total for Question 4 is 4 marks)
5
Which of these shapes is NOT a type of quadrilateral?
  • A) Rhombus
  • B) Kite
  • C) Pentagon
  • D) Trapezium
(Total for Question 5 is 1 mark)
6
State how many sides each polygon has.
(a)A heptagon.(1)
(b)A nonagon.(1)
(c)A hendecagon (also called an undecagon).(1)
(d)A dodecagon.(1)
(Total for Question 6 is 4 marks)
7
Identify the quadrilateral described in each statement.
(a)A quadrilateral with exactly one pair of parallel sides, where the two non-parallel sides are equal in length.(1)
(b)A quadrilateral with four right angles and two pairs of equal opposite sides, but where not all four sides are equal.(1)
(c)A quadrilateral with two pairs of adjacent equal sides, exactly one pair of equal opposite angles, and diagonals that cross at right angles.(1)
(Total for Question 7 is 3 marks)
8
Triangle XYZ is isosceles with XY = XZ. The apex angle X is 3 times the size of each base angle (angle XYZ and angle XZY). Calculate the size of the apex angle and each base angle.
Diagram NOT accurately drawn
X Y Z 3b° b° b° (not to scale)
(Total for Question 8 is 3 marks)
9
Quadrilateral PQRS has angle P = 73 degrees, angle Q = 108 degrees, angle R = 95 degrees and angle S = k degrees. Calculate the value of k.
Diagram NOT accurately drawn
73° 108° 95° k° P Q R S (not to scale)
(Total for Question 9 is 2 marks)
10
In triangle LMN, angle L = 61 degrees and angle M = 84 degrees. Side MN is extended beyond N to a point K, so that angle LNK is the exterior angle of the triangle at N. Calculate the size of angle LNK.
Diagram NOT accurately drawn
L M N K 61° 84° Not to scale
(Total for Question 10 is 2 marks)
11
Two parallel lines FG and HI are cut by a transversal. One of the angles formed, at the intersection with line FG, is 118 degrees.
Diagram NOT accurately drawn
118° F G H I Not to scale
(a)State the size of the corresponding angle to the 118 degree angle at line HI, giving a reason.(2)
(b)Calculate the size of the co-interior (allied) angle to the 118 degree angle at line HI, giving a reason.(2)
(Total for Question 11 is 4 marks)
12
A regular pentagon has five equal sides and five equal angles.
Diagram NOT accurately drawn
regular pentagon (not to scale)
(a)Calculate the size of one exterior angle of the pentagon.(2)
(b)Hence calculate the size of one interior angle of the pentagon.(2)
(Total for Question 12 is 4 marks)
13
Calculate the sum of the interior angles of a polygon with 13 sides.
(Total for Question 13 is 2 marks)
14
The exterior angles of a pentagon are x degrees, 58 degrees, 71 degrees, 84 degrees and 65 degrees. The exterior angles of any convex polygon sum to 360 degrees. Calculate the value of x.
(Total for Question 14 is 2 marks)
15
Triangle P has sides 4 cm, 6 cm and 9 cm. Triangle Q has sides 6 cm, 9 cm and 4 cm. Triangle R has sides 4 cm, 6 cm and 8 cm. State which two of the triangles are congruent to each other, and give a reason.
(Total for Question 15 is 2 marks)
16
Rectangle A measures 4 cm by 6 cm. Rectangle B is similar to rectangle A and has a shorter side of 10 cm. Calculate the length of the longer side of rectangle B.
(Total for Question 16 is 3 marks)
17
The diagram shows a net made from a regular pentagon in the centre, with five identical isosceles triangles attached, one to each side of the pentagon. Which 3D solid does this net fold up to make?
Diagram NOT accurately drawn
pentagon (not to scale)
  • A) Pentagonal prism
  • B) Pentagonal pyramid
  • C) Hexagonal pyramid
  • D) Cone
(Total for Question 17 is 1 mark)
18
Euler's formula for solids states that F + V - E = 2, where F is the number of faces, V is the number of vertices and E is the number of edges.
(a)A regular octahedron has 8 faces and 6 vertices. Use Euler's formula (F + V - E = 2) to calculate the number of edges it must have.(2)
(b)A different solid has 9 faces and 16 edges. Calculate the number of vertices it must have.(2)
(Total for Question 18 is 4 marks)
19
A 3D shape has exactly one curved face, no edges and no vertices. What is this shape?
  • A) Cone
  • B) Cylinder
  • C) Sphere
  • D) Hemisphere
(Total for Question 19 is 1 mark)
20
Triangle J has vertices at (2, 1), (5, 1) and (2, 4). Triangle J is rotated 180 degrees about the origin to give triangle J'.
(a)Write down the coordinates of the image of (2, 1) after this rotation.(1)
(b)Write down the coordinates of the image of (5, 1) after this rotation.(1)
(c)Write down the coordinates of the image of (2, 4) after this rotation.(1)
(Total for Question 20 is 3 marks)
21
A point W has coordinates (-6, -1). In which quadrant of the coordinate grid does W lie?
(Total for Question 21 is 1 mark)
22
State the number of lines of symmetry of each capital letter.
(a)The capital letter T.(1)
(b)The capital letter S.(1)
(c)The capital letter X.(1)
(Total for Question 22 is 3 marks)
23
Explain, using a calculation, why a regular pentagon cannot tessellate (tile a flat surface with no gaps or overlaps) on its own.
(Total for Question 23 is 3 marks)
24
A quadrilateral has four angles: (x + 10) degrees, 2x degrees, (x + 30) degrees and (2x - 10) degrees.
Diagram NOT accurately drawn
(x + 10)° 2x° (x + 30)° (2x - 10)° (not to scale)
(a)Form an equation using the fact that the angles of a quadrilateral sum to 360 degrees, and solve it to find the value of x.(2)
(b)Hence calculate the size of all four angles.(2)
(Total for Question 24 is 4 marks)
25
Triangle DEF is isosceles with DE = DF. The apex angle D = (4x - 20) degrees and each base angle (angle DEF and angle DFE) = (x + 10) degrees. Side EF is extended beyond F to a point G.
Diagram NOT accurately drawn
D E F G (4x - 20)° (x + 10)° (x + 10)° Not to scale
(a)Form an equation using the fact that the angles in a triangle sum to 180 degrees, and solve it to find the value of x.(2)
(b)Hence calculate the size of angle D and each base angle.(2)
(c)Calculate the size of the exterior angle DFG.(2)
(Total for Question 25 is 6 marks)
26
The number of diagonals in a polygon can be found using a formula.
(a)The number of diagonals in a polygon with n sides is given by d = n(n - 3) / 2. A nonagon has 9 sides. Calculate the number of diagonals in a nonagon.(2)
(b)A different polygon has exactly 20 diagonals. By trying different values of n in the formula, determine how many sides this polygon has.(2)
(Total for Question 26 is 4 marks)
Mark scheme · EP.M80 Geometry and Shape: Practice Set 4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26