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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. In the diagram, the fraction of the circle that is shaded is equal to

   1. A$\frac 12$
   2. B$\frac 13$
   3. C$\frac 14$
   4. D$\frac 16$
   5. E$\frac 18$

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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$10 \text{ cm}$

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3. A rectangle has width 2 cm and length 3 cm.

   The area of the rectangle is

   $\text{2 cm 2}$
   $\text{9 cm 2}$
   $\text{5 cm 2}$
   $\text{36 cm 2}$
   $\text{6 cm 2}$

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4. A cube has 12 edges, as shown.
   How many edges does a square-based pyramid have?

   1. A$6$
   2. B$12$
   3. C$8$
   4. D$4$
   5. E$10$

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5. In the diagram shown, what are the coordinates
   of point $P$?

   1. A$(4,0)$
   2. B$(2,2)$
   3. C$(2,0)$
   4. D$(4,4)$
   5. E$(2,4)$

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6. In the diagram, point $F$ has coordinates $(5,5)$.

   
   Hide/Reveal Description of Points

   The point F is 5 units right and 5 units up from the origin.
   The point A is 1 unit right and 2 units up from the origin.
   The point B is 2 units up from the origin.
   The point C is 4 units right and 4 units up from the origin.
   The point D is 2 units right and 4 units up from the origin.
   The point E is 4 units right from the origin.

   The point with coordinates $(2,4)$ is located at

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

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7. 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$\text{5 cm}$

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8. 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$8$

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9. A triangle has side lengths $3~\text{cm}$, $5~\text{cm}$, and $x~\text{cm}$, as shown.

   If the perimeter of the triangle is $12~\text{cm}$, the value of $x$ is

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

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10. Points $P$, $Q$, $R$ lie in a straight line.

    The value of $x$ is

    1. A$69$
    2. B$138$
    3. C$75$
    4. D$64$
    5. E$54$

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Answer key — Stage 1 · Geometry

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

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

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