2013 MATHEMATICS TEAM CHALLENGE
SENIOR SECONDARY
TEAMS CONTEST
Time: 45 minutes
Calculators may be used
Each question is worth 10 points
Total of 100 points
T1 (10 points)
The picture shows 25 dots evenly spaced in a five by five grid arrangement.
How many squares can be drawn using the dots as vertices? One example is drawn below.
T2 (10 points)
The coefficients (a, b and c) for the quadratic expression below are obtained by rolling a standard six
sided die.
ax2+ bx + c
Some of the quadratic expressions can be factorised. For example 1x2 + 5x + 6 = (x + 2)(x + 3)
What is the probability of obtaining a quadratic expression which can be factorised?
An example of a factorised quadratic is: 4x2 + 6x + 4 = 2(2x2 + 3x + 2)
Note: Putting a 1 outside the brackets is not a factorised quadratic. eg 1(x2 + x + 1)
T3 (10 points)
Binary uses only 0’s and 1’s.
Powers of 2
Binary decimal
25
1
24
0
23
1
22
0
21
0
20
1
2-1
0
2-2
1
2-3
0
2-4
0
The binary decimal (101001.0100)2 = 1 × 25 + 1 × 23 + 1 × 20 + 1 × 2-2 = 41.25
What is the binary representation of 3.1415?
This is π to four decimal places.
T4 (10 points)
Permutable primes remain prime when their digits are jumbled. For example 13 is a permutable
prime. Find one three-digit permutable prime.
T5 (10 points)
A packaging firm makes cardboard boxes according to the following specifications.
Length + width + height = 24 cm and each box has integral side lengths. How many different box sizes
can the packaging firm provide for customers? The size in this case refers to the volume of the box.
[Note: a box with length 5 cm, width 9 cm and height 10 cm has the same volume as a box with length
10 cm, width 5 cm and height 9 cm]
T6 (10 points)
The equation 91 = 12 + 22 + 32 + 42 + 52 + 62 shows that 91 is the sum of the first six squares, so 91 is a
square pyramidal number. It is also a triangular number since.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 91
Fifty-five is another two-digit number that is both a square pyramidal number and a triangular
number. To date, there is one other number that is both a square pyramidal number and a triangular
number. This number has six digits. What is this number?
T7 (10 points)
Five two metre diameter spheres are stacked as shown below. What is the distance between the
centres of the top and bottom spheres?
T8 (10 points)
The crescent moon is made of two circles. A is the centre of the bigger circle. The width of the crescent
between points B and C is 18 cm. The width between points D and E is 10 cm. What is the radius of the
bigger circle?
T9 (10 points)
A certain type of screw comes in packs of 6, 9 or 20. Determine the largest number of screws that you
cannot buy when combining various packets.
T10 (10 points)
For what value of “n” is the following equation correct?
1
1+√
+
3
1
√3+√
+
5
1
√5+√7
+
1
√7+√
+ ⋯…+
9
1
√2𝑛−1 + √2𝑛+1
= 1,000
School Name:________________________ Team 1:
Team 2:
2013 MATHS TEAM CHALLENGE
SENIOR SECONDARY
TEAM EVENT
ANSWER SHEET
Question
T1. (10 points)
Answers
Points
T2. (10 points)
T3. (10 points)
T4. (10 points)
T5. (10 points)
T6. (10 points)
T7. (10 points)
T8. (10 points)
T9. (10points)
T10. (10 points)
Total
/100
2013 MATHS TEAM CHALLENGE
SENIOR SECONDARY
TEAM EVENT
ANSWER SHEET
Question
T1. (10 points)
T2. (10 points)
Answers
52 13
,
216 54
T3. (10 points)
T4. (10 points)
50
or 0.24074
11.001001000011
113, 199, or 337
T5. (10 points)
48
T6. (10 points)
208,335
T7. (10 points)
4√
2
3
cm or 3.266 m
T8. (10 points)
50 cm
T9. (10 points)
43
T10. (10 points)
n = 2,002,000
Points