GeometryIB MYP Maths Standard: Topic test

1. 1
   A regular polygon has an interior angle of $156^{\circ}$.

   (a)

   What is the size of one exterior angle of the polygon?

   [1 mark]

   • A$12^{\circ}$
   • B$156^{\circ}$
   • C$24^{\circ}$
   • D$204^{\circ}$

   (b)

   How many sides does the polygon have?

   [1 mark]

   • A$15$
   • B$13$
   • C$24$
   • D$7.5$

   (c)

   Calculate the sum of the interior angles of the polygon.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A storage hall is a cuboid that is $12$ m long, $4$ m wide and $3$ m high.

   (a)

   What is the length of the diagonal of the floor of the hall, to $3$ significant figures?

   [1 mark]

   • A$16$ m
   • B$160$ m
   • C$8$ m
   • D$12.6$ m

   (b)

   What is the length of the longest straight line that can be drawn from one corner of the hall to the opposite corner, through the inside of the hall?

   [1 mark]

   • A$12.6$ m
   • B$13$ m
   • C$169$ m
   • D$19$ m

   (c)

   A straight cable is $13.5$ m long. Can it be stored in the hall without bending? Show your working and explain your answer.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A souvenir in Athens is a scale model of a marble column. The real column is $6$ m tall and the model is $15$ cm tall.

   (a)

   The top of the model has an area of $20$ cm$^2$. Find the area of the top of the real column in m$^2$.

   [3 marks]

   (b)

   The model has a volume of $250$ cm$^3$. Find the volume of the real column in m$^3$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A café in Vienna serves soup in hemispherical bowls of internal radius $6$ cm. The soup is kept in a cylindrical pot of radius $10$ cm. The volume of a sphere is $\frac{4}{3}\pi r^{3}$ and the volume of a cylinder is $\pi r^{2}h$.

   (a)

   (i) Show that the volume of one bowl is $144\pi$ cm$^3$. (ii) Write the volume of one bowl in litres, correct to $2$ decimal places. (iii) How many complete bowls can be filled from $5$ litres of soup?

   [6 marks]

   (b)

   (i) $12$ bowls of soup are served from the pot. Find by how much the depth of soup in the pot falls. (ii) The pot is filled to a depth of $25$ cm. Find the depth of soup left after the $12$ bowls are served, and state whether there is enough soup for them.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   Triangle $T$ has vertices $(2,\ 1)$, $(5,\ 1)$ and $(5,\ 3)$ on a coordinate grid.

   (a)

   $T$ is reflected in the line $x=1$. What are the coordinates of the image of the vertex $(5,\ 3)$?

   [1 mark]

   • A$(-5,\ 3)$
   • B$(-3,\ 3)$
   • C$(-4,\ 3)$
   • D$(5,\ -1)$

   (b)

   $T$ is rotated $90^{\circ}$ clockwise about the origin. What are the coordinates of the image of the vertex $(5,\ 3)$?

   [1 mark]

   • A$(-3,\ 5)$
   • B$(-5,\ -3)$
   • C$(5,\ -3)$
   • D$(3,\ -5)$

   (c)

   A single transformation maps $T$ onto a triangle with vertices $(6,\ 3)$, $(9,\ 3)$ and $(9,\ 5)$. Describe the transformation fully.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   $A$, $B$ and $C$ are points on a circle with centre $O$. $AB$ is a diameter of the circle and angle $BAC=28^{\circ}$.

   (a)

   What is the size of angle $ACB$?

   [1 mark]

   • A$90^{\circ}$
   • B$28^{\circ}$
   • C$62^{\circ}$
   • D$56^{\circ}$

   (b)

   What is the size of angle $ABC$?

   [1 mark]

   • A$90^{\circ}$
   • B$28^{\circ}$
   • C$62^{\circ}$
   • D$56^{\circ}$

   (c)

   Find the size of angle $AOC$ and give a reason for each step.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A pizza in Naples has a diameter of $30$ cm and is cut into $8$ equal slices. Each slice is a sector of the circle.

   (a)

   Find the angle of each slice and the area of one slice, correct to $3$ significant figures.

   [3 marks]

   (b)

   (i) Find the perimeter of one slice, correct to $3$ significant figures. (ii) The topping covers a circle of radius $13$ cm at the centre of the whole pizza. Find the area of the pizza with no topping, correct to $3$ significant figures.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A designer in Marrakech is planning a floor pattern using regular polygons: octagons, squares, pentagons, hexagons and equilateral triangles.

   (a)

   (i) Calculate the size of one interior angle of a regular octagon. (ii) Show that two regular octagons and one square fit together exactly around a point. (iii) State the order of rotational symmetry and the number of lines of symmetry of a regular octagon.

   [6 marks]

   (b)

   (i) Calculate the size of one interior angle of a regular pentagon. (ii) Explain why regular pentagons cannot tessellate on their own. (iii) Show that two regular hexagons and two equilateral triangles can fit together around a point.

   [6 marks]

   Total for question 8: 12 marks

End of questions