ENGL5013EF University English III

/ Student Name: ______
Student Number:______

Redo Coursework

Course Title:Foundations in Mathematics

Course Code:MATH2002EF

Intake:2011/S1AS

Submission: / 5 March 2012, Monday
Please submit IN-PERSON toMs. Hui
Full-time Programme Office
3/F Lai King Learning Centre (OCLC)
This assignment has 12pages (including this page).
Instructions to candidates :
  1. Please write down your name, student number and class in the spaces provided above.
  2. The total mark is 100.
  3. You are required to answer ALLthe questions in the space provided.
  4. All answers to questions must be in English.
  5. You should clearly show your steps. In general, round your answer in 2 decimal places.
  6. Write clearly; illegible answers will not be marked.
  7. Submit your answers in person to Ms. Hui at 3/F of Lai King Learning Centre, 201-203 Lai King Hill Road, Kwai Chung, N.T.

Total: / /100

MATH2002EF (Re-do coursework) 2011/S1A

MATH2002EF Foundations in Mathematics (Re-do Coursework)

Answer ALL questions in this paper. You should clearly show your steps.
In general, round your answer in 2 d.p..

Question 1

Calculate the following, giving your answers, in the simplest fraction terms.

a.b.

c.d.

Question 2

The figure shown below represents a cylindrical water tank, with radius of 2 m and a height of 5 m.

A B

C D

a.Find the volume of the water tank

b.Find the total external surface area of the tank

c.CD is a diameter of the base and B is just vertically above D. A curve is drawn on the surface of the tank from C to B. Find its shortest possible length of arc BC

Question 3

Mr. Chan plans to buy a flat in Kwun Tong. The flat costs HK$1,600,000. Mr. Chan finds a local bank ABC where he can borrow up to 70% of the flat price at 3.5% p.a. over 15 years.

  1. What is the monthly installment on that mortgage?
  2. What would the total repayments be over 15 years?
  3. If Mr. Chan want to extend the period to 20 years,

i.how much would be save each month by comparing with case (a)

ii.howmuch interest would be pay extra over the whole mortgage by comparing with case (b)

Monthly Installment Table (per $10,000）

/ 5 years / 10 years / 15 years / 20 years / 25 years / 30 years
3.00% / $179.69 / $96.56 / $69.06 / $55.46 / $47.42 / $42.16
3.25% / $180.80 / $97.72 / $70.27 / $56.72 / $48.73 / $43.52
3.50% / $181.92 / $98.89 / $71.49 / $58.00 / $50.06 / $44.90
3.75% / $183.04 / $100.06 / $72.72 / $59.29 / $51.41 / $46.31
4.00% / $184.17 / $101.25 / $73.97 / $60.60 / $52.78 / $47.74

Question 4

The list price of a product in Hong Kong Sogo is ￥$2,500. During the sales period, this product is 10% off. If a customer buys 10 units or more, further 5% off. If Mary prepares to buy 25 units, what should she pay in HKD? (Given:￥$1,000 = HKD96.5)

Question 5

If

Prove

Question 6

Given △ABC as shown, find

  1. the length of AC
  2. ∠BAC and ∠BCA
  3. area of △ABC

Question 7

Find θ where 0o≦θ≦90o.

  1. sin θ = 0.5
  2. 2cos 2θ = 0.8
  3. tan 6θ = 5
  4. cos2 θ + 7 cos θ = 5sin2 θ

Question 8

A rectangular box 8 cm  4 cm  3 cm

  1. Find the lengths of AH, AC, AG and CH.
  2. Calculate the angles of ∠CAH, ∠GAH. (correct to nearest degree)

Question 9

A party conducted a survey on the hourly rates of pay at 20 car parks in Hong Kong side. The rates were (in HK$):

15 / 15 / 14 / 12 / 20 / 15 / 12 / 14 / 15 / 20
30 / 25 / 12 / 18 / 20 / 20 / 18 / 16 / 25 / 15

a.Find

  1. the modal rate
  2. the median rate
  3. the mean rate
  4. the range
  5. the standard deviation

b.Draw a frequency distribution table for the interval 10–14.9, 15–19.9,....

c.By using the result of part (b), draw a pie chart to show the distribution of hourly rates of car parks.

Question 10

A box contains 2 red, 3 black and 4 white balls. One ball is drawn randomly from the box. After putting the ball back into the box, one ball is again drawn randomly. Find the probability that:

  1. the two balls drawn are both red;
  2. the two balls drawn are of the same colours;
  3. the two balls drawn are of different colours.

[End of Paper]

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