Paper Paer
and 8cm. How many possibilities are there for the length of the third side of the triangle?
A1
B2
C3
D4
21. The square ABCD has an area of 196. It contains two overlapping
E more than 4
A
B
squares; the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1. What is the total area of the shaded regions?
A 44
B 72
E more information is needed
C 80
MT
UK
UK
MT
20. Jack's teacher asked him to draw a triangle of area 7cm2. Two sides are to be of length 6cm
UKMT
UK INTERMEDIATE MATHEMATICAL CHALLENGE
THURSDAY 7TH FEBRUARY 2013
D 152
D
C
Organised by the United Kingdom Mathematics Trust and supported by
22. The diagrams show squares placed inside two identical semicircles.
In the lower diagram the two squares are identical.
What is the ratio of the areas of the two shaded regions?
A 1:2
B 2:3
C 3:4
D 4:5
E 5:6
RULES AND GUIDELINES (to be read before starting)
1. Do not open the paper until the Invigilator tells you to do so.
23. Four brothers are discussing the order in which they were born. Two are lying and two are telling the truth. Which two are telling the truth?
2. Time allowed: 1 hour.
No answers, or personal details, may be entered after the allowed hour is over.
Alfred: “Bernard is the youngest.” Horatio: “Bernard is the oldest and I am the youngest.”
Inigo: “I was born last.”
Bernard: “I'm neither the youngest nor the oldest.”
3. The use of rough paper is allowed; calculators and measuring instruments are forbidden.
A Bernard and Inigo
B Horatio and Bernard
C Alfred and Horatio
D Alfred and Bernard
E Inigo and Horatio
24. The diagram shows a shaded shape bounded by circular arcs with
5. Use B or HB pencil only. Mark at most one of the options A, B, C, D, E on the
Answer Sheet for each question. Do not mark more than one option.
the same radius. The centres of three arcs are the vertices of an
equilateral
A1
B2
C3
D4
21. The square ABCD has an area of 196. It contains two overlapping
E more than 4
A
B
squares; the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1. What is the total area of the shaded regions?
A 44
B 72
E more information is needed
C 80
MT
UK
UK
MT
20. Jack's teacher asked him to draw a triangle of area 7cm2. Two sides are to be of length 6cm
UKMT
UK INTERMEDIATE MATHEMATICAL CHALLENGE
THURSDAY 7TH FEBRUARY 2013
D 152
D
C
Organised by the United Kingdom Mathematics Trust and supported by
22. The diagrams show squares placed inside two identical semicircles.
In the lower diagram the two squares are identical.
What is the ratio of the areas of the two shaded regions?
A 1:2
B 2:3
C 3:4
D 4:5
E 5:6
RULES AND GUIDELINES (to be read before starting)
1. Do not open the paper until the Invigilator tells you to do so.
23. Four brothers are discussing the order in which they were born. Two are lying and two are telling the truth. Which two are telling the truth?
2. Time allowed: 1 hour.
No answers, or personal details, may be entered after the allowed hour is over.
Alfred: “Bernard is the youngest.” Horatio: “Bernard is the oldest and I am the youngest.”
Inigo: “I was born last.”
Bernard: “I'm neither the youngest nor the oldest.”
3. The use of rough paper is allowed; calculators and measuring instruments are forbidden.
A Bernard and Inigo
B Horatio and Bernard
C Alfred and Horatio
D Alfred and Bernard
E Inigo and Horatio
24. The diagram shows a shaded shape bounded by circular arcs with
5. Use B or HB pencil only. Mark at most one of the options A, B, C, D, E on the
Answer Sheet for each question. Do not mark more than one option.
the same radius. The centres of three arcs are the vertices of an
equilateral