Download MATH 151 Class Test 3: Mathematics Exam with Short Answer Questions and Calculator Use and more Exercises Mathematics in PDF only on Docsity!
Family Name First Name Student Number Tutorial Day and Time
University of Wollongong
School of Mathematics and Applied Statistics
MATH 151 — GENERAL MATHEMATICS 1A
Autumn Session
Class Test 3
Time Allowed: 50 minutes
This test consists of two parts.
Part A: 9 Questions. These questions are worth a total of 10 marks.
Part B : 6 Questions. These questions are worth a total of 10 marks.
Directions to Candidates
- Answer questions in Part A and Part B in the space provided, showing full working.
Examination Materials/Aids Allowed
Non-alphanumeric, non-programmable, calculators are permitted. A one-page, double-sided, A4 size summary sheet is permitted.
This test paper is NOT to leave this room.
Part A: Short Answer Questions
Show full working to the following problems in the space provided. Questions 1–8 are worth one mark each. Question 9 is worth two marks.
- Sketch the graph of y = x^2. Use this graph to sketch y =
x^2
- A culture of a certain bacteria initially weighs 1 gram and doubles in size every 12 hours. What will be the weight of the sample after 2 days?
- The formula for the radioactive decay of Polonium is given by p (t) = e−^0.^005 t^ (t in days). A certain substance has
of its original amount of polonium when tested. Find the approximate age of the substance (in days).
- A logistic model p (t) is given by p (t) =
1 + Ce−t^
. If p (0) = 1, then find the value of C.
- Sketch the graph of the function y = f (x) = −1 + 3 cos 2x, noting its period.
(This question is worth two marks)
Part B
Show full working to the following problems in the space provided. The number of marks for each question is shown.
- Find the exponential function which best describes the following data. [2]
t 0 0.5 1 2 ln y 0 -1 -2 -
- When cancer cells are subjected to radiation treatment, the proportion of cells that survive the treatment (P ) is given by P = e−kr^ , where r is the radiation level (in Roentgens) and k a constant. It is found that 30% of the cancer cells survive when r = 400 Roentgens. What should the radiation level be in order to allow 2% to survive? [2]
- Are the following calculations correct? For each incorrect answer explain where the error is. [1]
Q. The definition of pH is pH = − log
[
H+
]
where
[
H+
]
is the concentration of hydrogen ions measured in units of mol dm−^3. The pH of a solution of trifluoroethanoic acid is 4.5. What is the concentration of hydrogen ions? A
4 .5 = − log
[
H+
]
⇒ 104.^5 =
[
H+
]
A
4 .5 = − log
[
H+
]
⇒ log 4.5 =
[
H+
]
[
H+
]
- A culture of bacteria initially weighs 0.15 g and its weight doubles every 45 minutes. What will be the weight have 100 minutes? [2]
