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Stage 1 · Mixed

10 problems · · mathsolympiadprep.com

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1. 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) $100\,000+100+1$

   CEMC Gauss (Grade 8) 2014

   Number theory Solution and answer checking →

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

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

   CEMC Gauss (Grade 8) 2013

   Algebra Solution and answer checking →

3. 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$16$

   CEMC Gauss (Grade 7) 2024

   Number theory Solution and answer checking →

4. 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$128$

   CEMC Fermat 2013

   Algebra Solution and answer checking →

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

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

   CEMC Fermat 2019

   Number theory Solution and answer checking →

6. Which of the following has the largest value?

   1. A$4^2$
   2. B$4\times 2$
   3. C$4-2$
   4. D$\dfrac{4}{2}$
   5. E$4+2$

   CEMC Pascal 2016

   Algebra Solution and answer checking →

7. The integer 2014 is between

   (A) $\text{10 0 and 10 1}$ (B) $\text{10 1 and 10 2}$ (C) $\text{10 2 and 10 3}$ (D) $\text{10 3 and 10 4}$ (E) $\text{10 4 and 10 5}$

   CEMC Fermat 2014

   Number theory Solution and answer checking →

8. What is the value of $13+15+17$?

   1. A$35$
   2. B$45$
   3. C$55$
   4. D$39$
   5. E$51$

   CEMC Cayley 2026

   Algebra Solution and answer checking →

9. The ones (units) digit of 542 is 2. When 542 is multiplied by 3, the ones (units) digit of the result is

   1. A$9$
   2. B$3$
   3. C$5$
   4. D$4$
   5. E$6$

   CEMC Cayley 2021

   Number theory Solution and answer checking →

10. 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 →

Answer key — Stage 1 · Mixed

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

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