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Stage 1 · Mixed

10 problems · · mathsolympiadprep.com

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1. The value of $10^2+10+1$ is

   1. A$101$
   2. B$1035$
   3. C$1011$
   4. D$111$
   5. E$31$

   Algebra Solution and answer checking →

2. 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$\frac 18$

   Geometry Solution and answer checking →

3. The number 10 101 is equal to

   (A) $1000+100+1$ (B) $1000+10+1$ (C) $10\,000+10+1$ (D) $10\,000+100+1$ (E) $100\,000+100+1$

   Number theory Solution and answer checking →

4. In the diagram, how many of the shapes are triangles?

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

   Combinatorics Solution and answer checking →

5. What is the value of $\dfrac{10^2 + 6^2}{2}$?

   1. A$16$
   2. B$86$
   3. C$34$
   4. D$68$
   5. E$128$

   Algebra Solution and answer checking →

6. When the four digits of $2024$
   are added, the result is

   1. A$10$
   2. B$8$
   3. C$224$
   4. D$44$
   5. E$16$

   Number theory Solution and answer checking →

7. 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$10 \text{ cm}$

   Geometry Solution and answer checking →

8. In the diagram, how many of the $24$ circles are shaded?

   1. A$10$
   2. B$12$
   3. C$14$
   4. D$16$
   5. E$18$

   Combinatorics Solution and answer checking →

9. What is the remainder when 14 is divided by 5?

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

   Number theory Solution and answer checking →

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

    The area of the rectangle is

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

    Geometry Solution and answer checking →

Answer key — Stage 1 · Mixed

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

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

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