IB Mathematics AA HL - Mock Exams
Mock Exam Set 1 - Paper 3
Trial Examinations for IB Mathematics AA HL
Paper 3
2 Questions
60 mins
55 marks
Paper
Difficulty
View
Question 1
[Maximum mark: 24]
This question asks you to investigate some properties of hexagonal numbers.
Hexagonal numbers can be represented by dots as shown below where denotes the th hexagonal number, .
Note that points are required to create the regular hexagon with side of length , while points are required to create the next hexagon with side of length , and so on.
-
Write down the value of .[1]
-
By examining the pattern, show that , . [3]
-
By expressing as a series, show that , .[3]
-
Hence, determine whether is a hexagonal number.[3]
-
Find the least hexagonal number which is greater than .[5]
-
Consider the statement:
is the only hexagonal number which is divisible by .
Show that this statement is false.[2]
Matt claims that given and , , then
- Show, by mathematical induction, that Matt's claim is true
for all .[7]
Mark Scheme
Video (a)
Video (b)
Video (c)
Video (d)
Video (e)
Video (f)
Video (g)
Revisit
Check with RV Newton
Mark Scheme
Solutions
Revisit
Ask Newton
Question 2
[Maximum mark: 31]
This question ask you to investigate the relationship between the number of sides and the area of an enclosure with a given perimeter.
A farmer wants to create an enclosure for his chickens, so he has purchased meters of chicken coop wire mesh.
-
Initially the farmer considers making a rectangular enclosure.
-
Complete the following table to show all the possible rectangular enclosures with sides of at least m he can make with the m of mesh. The sides of the enclosure are always a whole number of metres.[3]
-
What is the name of the shape that gives the maximum area?[1]
-
The farmer wonders what the area will be if instead of a rectangular enclosure he uses an equilateral triangular enclosure.
- Show that the area of the triangular enclosure will be
.[3]
Next, the farmer considers what the area will be if the enclosure has the form of a regular pentagon.
The following diagram shows a regular pentagon.
Let O be the centre of the regular pentagon. The pentagon is divided into five congruent isosceles triangles and angle is equal to radians.
-
-
Express in terms of .
-
Show that the length of OA is m.
-
Show that the area of the regular pentagon is m.[6]
-
Now, the farmer considers the case of a regular hexagon.
- Using the method in part (c), show that the area of the regular hexagon is [5]
The farmer notices that the hexagonal enclosure has a larger area than the pentagonal enclosure. He considers now the general case of an -sided regular polygon. Let be the area of the -sided regular polygon with perimeter of m.
-
Show that [5]
-
Hence, find the area of an enclosure that is a regular 14-sided polygon with a perimeter of m. Give your answer correct to one decimal place.[2]
-
-
Evaluate
-
Interpret the meaning of the result of part (g) (i). [6]
-
Mark Scheme
Video (a)
Video (b)
Video (c)
Video (d)
Video (e)
Video (f)
Video (g)
Revisit
Check with RV Newton
Mark Scheme
Solutions
Revisit
Ask Newton
Thank you Revision Village Members
#1 IB Math Resource
Revision Village is ranked the #1 IB Math Resources by IB Students & Teachers.
34% Grade Increase
Revision Village students scored 34% greater than the IB Global Average in their exams (2021).
80% of IB Students
More and more IB students are using Revision Village to prepare for their IB Math Exams.