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Stage 1 · Geometry

10 problems · · mathsolympiadprep.com

Print or save as PDF The answer key prints on its own page at the end.

1. The points $O(0, 0)$, $P(0,3)$, $Q$, and $R(5,0)$ form a rectangle, as shown.

   

   The coordinates of $Q$ are

   $(5,5)$
   $(5,3)$
   $(3,3)$
   $(2.5,1.5)$
   $(0,5)$

   CEMC Fermat 2020

   Geometry Solution and answer checking →

2. The regular pentagon shown has a side length of 2 cm.

   

   The perimeter of the pentagon is

   1. A$2 \text{ cm}$
   2. B$4 \text{ cm}$
   3. C$6 \text{ cm}$
   4. D$8 \text{ cm}$
   5. E$10 \text{ cm}$

   CEMC Gauss (Grade 8) 2022

   Geometry Solution and answer checking →

3. In the triangle shown, the value of $x$ is

   

   1. A$30$
   2. B$60$
   3. C$45$
   4. D$90$
   5. E$55$

   CEMC Gauss (Grade 8) 2019

   Geometry Solution and answer checking →

4. In the diagram, each of the five squares is $1 \times 1$.

   

   What percentage of the total area of the five squares is shaded?

   1. A$25\%$
   2. B$30\%$
   3. C$35\%$
   4. D$40\%$
   5. E$45\%$

   CEMC Pascal 2016

   Geometry Solution and answer checking →

5. The base of a rectangular box measures 2 cm by 5 cm. The volume of the box is $\text{30 cm 3}$. What is the height of the box?

   1. A$\text{1 cm}$
   2. B$\text{2 cm}$
   3. C$\text{3 cm}$
   4. D$\text{4 cm}$
   5. E$\text{5 cm}$

   CEMC Cayley 2015

   Geometry Solution and answer checking →

6. How many solid $1\times 1\times 1$ cubes are required to make a solid $2\times 2\times 2$ cube?

   1. A$4$
   2. B$7$
   3. C$6$
   4. D$5$
   5. E$8$

   CEMC Fermat 2024

   Geometry Solution and answer checking →

7. In the diagram, square $PQRS$ is divided into four identical squares.

   

   What percentage of square $PQRS$ is shaded?

   1. A$33\%$
   2. B$40\%$
   3. C$25\%$
   4. D$50\%$
   5. E$15\%$

   CEMC Gauss (Grade 7) 2019

   Geometry Solution and answer checking →

8. In the diagram, squares of side length 1 meet each other at their vertices.

   

   The perimeter of the figure is

   1. A$14$
   2. B$20$
   3. C$24$
   4. D$28$
   5. E$32$

   CEMC Pascal 2021

   Geometry Solution and answer checking →

9. A square has an area of 144$\text{cm 2}$. The side length of the square is

   1. A$\text{288 cm}$
   2. B$\text{72 cm}$
   3. C$\text{48 cm}$
   4. D$\text{12 cm}$
   5. E$\text{36 cm}$

   CEMC Gauss (Grade 7) 2018

   Geometry Solution and answer checking →

10. A square with side length $5$
    has an area of

    1. A$5$
    2. B$10$
    3. C$15$
    4. D$16$
    5. E$25$

    CEMC Gauss (Grade 7) 2024

    Geometry Solution and answer checking →

Answer key — Stage 1 · Geometry

Worked solutions for every problem are on the site, one page per problem.

1. $B$ open
2. $C$ open
3. $D$ open
4. $D$ open
5. $C$ open
6. $E$ open
7. $C$ open
8. $D$ open
9. $D$ open
10. $E$ open

Problems belong to the competitions that set them. Each question on this sheet names the competition it came from, and the licences the material is used under are listed below. Free to copy for classroom use.

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