|
|
Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IB Analysis and Approaches |
Consider the expansion of:
$$ (3x^4+\frac{1}{5x})^n $$where \( n \in \mathbb{Z}^+\)
Determine all possible values of \(n\) for which the expansion has a non-zero constant term.
2. | IB Analysis and Approaches |
Nine cats squeeze through a gap in a fence to get to a fish pond. There is only enough room for one cat at a time to squeeze through the gap.
Seefer and Sushi are two of the nine cats attracted to the fish pond.
Find the total number of possible ways in which the nine cats can squeeze through the gap if Seefer passes through
(a) in the position immediately after Sushi;
(b) in any position after Sushi.
3. | IB Analysis and Approaches |
A fund-raising activity involves people choosing three balls from a jar containing balls numbered 1 to 30. A prize of £5 is awarded if the three numbers chosen sum to a multiple of three. It costs £2 to have a go.
(a) How many ways are there of choosing three numbers from the integers 1 to 30 that sum to a multiple of 3?
(b) What is the probability of person winning a prize?
(c) What is the expected profit made for the fund after 300 people have had a go?
4. | IB Analysis and Approaches |
Fifty years ago there was a zoo where animals were housed in cages. There were eight animal cages in a line on the northern perimeter of the zoo. Only four cages were being used: one to hold the gorilla, one for the chimpanzees, one for the gibbons and one for the macaques.
(a) Find the number of ways the four cages can be assigned to the animals so that the cages are next to each other.
It was decided that the gorilla should have at least one empty cage between its cage and the next occupied cage. The other animal cages do not have to be next to each other.
(b) Find the number of ways the four cages can be assigned now.
If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
