Understanding the 2003 Australian Mathematics Competition Problem

Understanding the 2003 Australian Mathematics Competition Problem

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

CCSS
HSF.IF.A.2, HSF.IF.A.3, 8.F.A.1

+5

Standards-aligned

Created by

Emma Peterson

Used 3+ times

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
,
CCSS.HSF.IF.A.3
,
CCSS.8.F.A.1
CCSS.HSN.RN.A.2
,
CCSS.HSF.BF.A.2
,
CCSS.4.NBT.B.6
,
CCSS.4.OA.B.4
,
CCSS.HSF.IF.A.1
,
The video tutorial presents a challenging math problem from the 2003 Australian Mathematics Competition, where only 3% of students answered correctly. The problem involves a recursive function, f(n), with given conditions. The instructor demonstrates an approach to solve for f(2003) by identifying a repeating pattern in the function values. The solution involves calculating the number of times 3 is added to 11 to reach 2003, and determining the position in the repeating sequence. The instructor verifies the solution by applying the same process to a known value, ensuring accuracy. The video concludes with an invitation for viewers to engage and a preview of the next topic.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial condition given for the function f in the problem?

f(11) = 11

f(11) = 0

f(11) = 1

f(11) = -11

Tags

CCSS.HSF.IF.A.3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula used to find f(n+3) in terms of f(n)?

f(n+3) = f(n) - 1

f(n+3) = f(n) + 1

f(n+3) = (f(n) + 1) / (f(n) - 1)

f(n+3) = (f(n) - 1) / (f(n) + 1)

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of f(14) after applying the formula to f(11)?

1/2

11

5/6

2/3

Tags

CCSS.HSN.RN.A.2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you simplify the expression when dealing with fractions within a fraction?

Subtract the fractions

Divide the fractions

Add the fractions

Multiply top and bottom by the same number

Tags

CCSS.HSF.IF.A.2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of f(17) after simplification?

11

-11

-1/11

1/11

Tags

CCSS.HSF.BF.A.2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What pattern is observed in the function values as n increases?

The values decrease exponentially

The values remain constant

The values form a repeating cycle

The values increase linearly

Tags

CCSS.4.NBT.B.6

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many 3s are added to 11 to reach 2003?

664

500

1000

200

Tags

CCSS.4.OA.B.4

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