For teachers / Printable sets /Stage 2 · Geometry

Stage 2 · Geometry

10 problems · · mathsolympiadprep.com

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

1. Two identical smaller cubes are stacked next to a larger cube. Each of the two smaller cubes has a volume of 8. What is the volume of the larger cube?

   CEMC Cayley

   Geometry Solution and answer checking →

2. In the diagram, what is the value of $x$?

   

   1. A$65$
   2. B$75$
   3. C$85$
   4. D$95$
   5. E$105$

   CEMC Pascal 2014

   Geometry Solution and answer checking →

3. The entire exterior of a solid $6 \times 6 \times 3$ rectangular prism is painted. Then, the prism is cut into $1 \times 1 \times 1$ cubes. How many of these cubes have no painted faces?

   CEMC Pascal

   Geometry Solution and answer checking →

4. The minute hand on a clock points at the 12. After rotating $120^{\circ}$ clockwise, which number will it point at?

   CEMC Cayley

   Geometry Solution and answer checking →

5. In $\triangle PQR, \angle RPQ=90^{\circ}$ and $S$ is on $PQ$. If $SQ=14, SP=18$, and $SR=30$, what is the area of $\triangle QRS$?

   CEMC Pascal

   Geometry Solution and answer checking →

6. Points $A, B, C$, and $D$ are on a line in that order. The distance from $A$ to $D$ is 24. The distance from $B$ to $D$ is 3 times the distance from $A$ to $B$. Point $C$ is halfway between $B$ and $D$. What is the distance from $A$ to $C$?

   CEMC Cayley

   Geometry Solution and answer checking →

7. In the diagram, rectangle $PQRS$ has $PQ=30$ and rectangle $WXYZ$ has $ZY=15$.

   
   If $S$ is on $WX$ and $X$ is on $SR$ so that $SX=10$, then $WR$ equals

   1. A$20$
   2. B$25$
   3. C$55$
   4. D$45$
   5. E$35$

   CEMC Fermat 2013

   Geometry Solution and answer checking →

8. Square $P Q R S$ has an area of 900. $M$ is the midpoint of $P Q$ and $N$ is the midpoint of $P S$. What is the area of triangle $P M N$?

   CEMC Cayley

   Geometry Solution and answer checking →

9. What is the measure of the largest angle in $\triangle P Q R$?

   CEMC Cayley

   Geometry Solution and answer checking →

10. In the diagram, $\angle ABC=90\degree$.

    

    The value of $x$ is

    1. A$68$
    2. B$23$
    3. C$56$
    4. D$28$
    5. E$26$

    CEMC Gauss (Grade 8) 2022

    Geometry Solution and answer checking →

Answer key — Stage 2 · Geometry

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

1. $64$ open
2. $C$ open
3. $16$ open
4. $4$ open
5. $168$ open
6. $15$ open
7. $E$ open
8. $112.5$ open
9. $108^{\\circ}$ open
10. $A$ 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.

Apache-2.0 · CC-BY-NC-4.0