Learn smart - Learn online. Upto 88% off on courses for a limited time. View Courses

Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!
Add File

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

Guaranteed Higher Grade!

MAT9004 Practice Exam

tag 1 Download 4 Pages / 867 Words tag 13-11-2020
  • Course Code: MAT9004
  • University: Monash University
    icon is not sponsored or endorsed by this college or university

  • Country: Australia


where x ∈ [−2, 3]. (a) What is f 0 (x)? [1] (b) What is f 00(x)? [1] (c) Find all the stationary points of f. Find the value of f(x) at each stationary point. [2] (d) For each stationary point of f, find whether it is a local minimum, a local maximum or neither. [2] (e) Find all the global minima and maxima of f in the interval [−2, 3]. [2] 2. Let M =  1 6 1 0  (a) Find the eigenvalues of M. [3] (b) Find one eigenvector of M with respect to each eigenvalue. [3]
(c) Diagonalize M, i.e., write M in the form M = NDN −1 , where D is a diagonal matrix. [2] 3. X is a continuous random variable with density f where f(x) = x + x 2 + x 5 for x ∈ [0, 1] and f(x) = 0 elsewhere. What is the probability of the event {X > 1/2}? [6] 4. Suppose you want to launch your startup in some innovative area. Currently, there exist two enterprises A and B competing for this market. You want to find out their investment strategies (which are given by real numbers a, b) prior to commiting into the competition.
A friend who works in A told you that their profit is given by p(a, b) = ab2 − a 2 + b 2 + 6b − 9a + 10, but unfortunately he does not know the values of a, b. He also mentioned that both enterprises are apparently not very good in keeping secrets, so the function f(x) = p(x, b) achieves the maximum value at point x = a, while x = b minimises g(x) = p(a, x). Use this information to find a and b [8] 5. A positive integer is called prime-like if it is not divisible by 2 and not divisible by 5.
(a) How many prime-like numbers with 4 digits (from 1000 to 9999)? [2] (b) How many prime-like numbers with 4 digits have at least one even digit? [3]
(c) How many prime-like numbers with 4 digits are not divisible by 3? [4] 6. Let Y be a random variable uniformly distributed on the set {−1, 0, 1, 2}. Let U1, U2 be the random variables defined by U1 = Y 2 − Y and U2 = Y 2−1 Y 3−2 . (a) Find the expected values of U1 and U2. [2] (b) Find variances of U1 and U2. [2] (c) Is U1 independent of U2? Justify your answer. [2] 7. A fair 6-sided die is rolled three times. (a) Find the probability that the sum of all three outcomes equals 8.
[4] (b) Find the probability that the first roll was 1 given that the sum of outcomes equals 8. [3] 8. Eight students Alice, Bob, Casey, Drew, Eva, Francis, Glen, Hunter entered Monash University this year. Alice, Bob and Casey are from Canberra and Drew, Eva, Francis are from Newcastle.
Glen and Hunter are international students from different countries. Alice, Casey and Hunter practice tennis, while Drew, Francis, Glen and Hunter practice soccer. Any two students from the same city or practicing the same sport know each other. (a) Draw a graph corresponding to the student acquaintances. Find its number of edges.
[2] (b) Write down the adjacency matrix for this graph. Does it contain a spanning tree? [3] (c) Is it possible to seat all eight students at a round table in such a way that any of them knows both neighbours. Justify your answer. [3]
Download Sample Now

Earn back the money you have spent on the downloaded sample by uploading a unique assignment/study material/research material you have. After we assess the authenticity of the uploaded content, you will get 100% money back in your wallet within 7 days.

Unique Document

Under Evaluation

Get Money
into Your Wallet

Total 4 pages

Cite This Work

To export a reference to this article please select a referencing stye below:

My Assignment Help. (2020). Practice Exam. Retrieved from

My Assignment Help (2020) Practice Exam [Online]. Available from:
[Accessed 10 August 2022].

My Assignment Help. 'Practice Exam' (My Assignment Help, 2020) <> accessed 10 August 2022.

My Assignment Help. Practice Exam [Internet]. My Assignment Help. 2020 [cited 10 August 2022]. Available from:

We Can Help!

Get top notch assistance from our best tutors !
Excel in your academics & career in one easy click!


Other Samples

Content Removal Request

If you are the original writer of this content and no longer wish to have your work published on then please raise the content removal request.


5% Cashback

On APP - grab it while it lasts!

Download app now (or) Scan the QR code

*Offer eligible for first 3 orders ordered through app!

callback request mobile
Have any Query?