2013 MATHEMATICS TEAMS CHALLENGE
Primary Relay
Time: 60 min
Calculators Allowed
100 points
-------------------------------------------------------------------------------------------------------------------------------------R1. (4 points)
Find the sum of the 10th and 14th terms of the following sequence.
[96 points remaining]
1, 3, 6, 10, 15,……
R2. (4 points)
[92 points remaining]
What is the number?
 It is a prime number less than 40 (primes only have two factors; 1 and the number itself)
 The sum of its digits is 4
 When squared, the last digit is 1.
R3. (6 points)
Determine the sum of all of the positive integers less than 100 that are divisible by 5.
[86 points remaining]
R4. (2 points)
What is the 15th term in the sequence below?
[84 points remaining]
0, 2, 4, 6, 12, 14, 28, 30, ………
R 5. (4 points)
[80 points remaining]
Seven consecutive integers sum to 14 and have a product of 0. What is the sum of the largest and smallest
integers? (intergers are positive or negative whole numbers, eg …-3, -2, -1, 0, 1, 2, 3,…)
R 6. (8 points)
[72 points remaining]
A relay race involves running to a baton, picking up the baton then returning to the start. There are 10 batons
evenly spaced 10 metres apart in a straight line and the first baton is 10 metres from the start. Only one baton
can be picked up at a time and the batons can be picked up in any order. If Mark can run at 10 metres/second,
how long will it take him to pick up all of the batons and return to the start?
R 7. (4 points)
What is the smallest counting number “n” that would make 12 × n a perfect square?
[68 points remaining]
R 8. (8 points)
[60 points remaining]
What is the sum of all of the positive integers less than 100 that are divisible by 3 but not divisible by 2.
R 9. (6 points)
[54 points remaining]
Two numbers are relatively prime if the only common factor they have is 1. For example 12 and 17 are
relatively prime. How many numbers less than 50 are relatively prime to 15?
R 10. (4 points)
[50 points remaining]
Alex and Jeff cut a piece of wire into two pieces. Alex makes a square with an area of 25 cm2, while Jeff’s
square has an area of 81 cm2. How long was the wire before it was cut into two pieces?
R 11. (6 points)
[44 points remaining]
The train tunnel under the English channel is approximately 50 km in length. How long would it take a 5
kilometer long coal train travelling at 110 km/hour to completely pass through the tunnel?
R12. (6 points)
[38 points remaining]
A rabbit is 200 paces ahead of a pursuing dingo. If the dingo covers 10 paces each time the rabbit covers 2
paces, how many paces will it take for the dingo to catch up to the rabbit?
R 13. (6 points)
A single digit number d is multiplied by a three-digit number abc to get 2013.
What is the three-digit number abc?
[32 points remaining]
R 14. (8 points)
[24 points remaining]
Two six-sided dice are rolled. What is the probability that the numbers are consecutive?
R 15. (2 points)
[22 points remaining]
At the Toowoomba show, a show-bag costs $4 plus half the cost. How much does a show-bag cost?
R 16. (4 points)
[18 points remaining]
120 students sit down to do their exam. 10% of them have one pen. Of the remaining 90%, half of them have
two pens, while the other half have none at all. How many pens do the students have between them?
R 17. (4 points)
[14 points remaining]
The array of numbers below is known as Pascal’s triangle. The first six rows are shown.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
What is the sum of all the numbers in the row which begins 1, 10,…….?
R 18. (4 points)
[10 points remaining]
A bakery is commissioned to make three cakes, but can only bake two cakes at a time in the oven. Also, each
cake needs to be baked for 4 minutes on each side. What is the minimum amount of time required to bake all 3
cakes?
R 19. (6 points)
[4 points remaining]
1
1
Erin earned $75,000 per year two years ago. Her salary increased by 4 last year, then fell by 5 this year. How
much does she earn now?
R 20. (4 points)
How many squares are there in this geometric diagram?
[0 points remaining]
Problem
R 1 (4 points)
R 2 (4 points)
R 3 (6 points)
R 4 (2 points)
Change
R 5 (4 points)
R 6 (8 points)
R 7 (4 points)
R 8 (8 points)
Change
R 9 (6 points)
R 10 (4 points)
R 11 (6 points)
R 12 (6 points)
Change
R 13 (6 points)
R 14 (8 points)
R 15 (2 points)
R 16 (4 points)
Change
R 17 (4 points)
R 18 (4 points)
R 19 (6 points)
R 20 (4 points)
MATHS TEAM CHALLENGE (2013)
Relay Answer Sheet
PRIMARY
Answer
Attempts √ or ×
Score Progressive
8 7 6 5 4 3 2 1
Score
160
31
950
508
Change
Change
4
110 seconds
n=3
867
Change
Change
27
56 cm
30 min or
0.5 hours
250 paces
Change
Change
671
5
10
𝑜𝑟
or
18
36
0.2777..
$8
120
Change
Change
1024
12 minutes
$75,000
31
Total
School:___________________________________
Team 1:
Team 2: