Autumn Main Exam SEAT NUMBER: STUDENT NUMBER: SURNAME: (FAMILY NAME) OTHER NAMES:

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1 Autumn Main Exam SEAT NUMBER: ~UTS UNIVERSITY OF TECHNOLOGY SYDNEY STUDENT NUMBER: SURNAME: (FAMILY NAME) OTHER NAMES: This paper and all materials issued must be returned at the end of the examination. They are not to be removed from the exam centre. Examination Conditions: It is your responsibility to fill out and complete your details in the space provided on all the examination material provided to you. Use the time before your examination to do so as you will not be allowed any extra time once the exam has ended. You are not permitted to have on your desk or on your person any unauthorised material. This includes but not limited to: Mobile phones Smart watches and bands Electronic devices Draft paper (unless provided) Textbooks (unless specified) Notes (unless specified) Foundation Mathematics Time Allowed: 2 hours and 10 mi Includes 10 minutes of reading time. Reading time is for reading only. You are n paper in any way during reading time. You are not permitted to obtain assistance by improper means or ask for help from or give help to any other person. If you wish to leave and be re-admitted (including to use the toilet), you have to wait until90 mins has elapsed. If you wish to leave the exam roo permanently, you have to wait u mins has elaps During seek pe from a sup Leav1 Using t Accessing ach question MUST be attempted in a separate booklet. Marks may be lost due to the failure to do so. You MUST indicate the question number on the cover of each booklet. Show all working. Marks may be lost if sufficient working is not shown, or if working is untidy and difficult to read. An answer with no working may be given a mark of zero. Disciplinary action will be taken against you if you infringe university rules. Do not open your exam paper until instructed.... Page 1 of 7

2 35010 Foundation Mathematics- Main Exam Rough work space Do not write your answers on this page. P~9;2 ~r-7_.....

3 Foundation Mathematics- Main Exam Question 1 ( = 12 marks) BEGIN A NEW BOOKLET AND WRITE 01 ON THE COVER a) Find (algebraically) where the following lines intersect: { Sx- y = 10 4y + 3x = 6 b) Find the domain and range of the following functimi: y =.Jzx c) A car starts moving up a hill along a straight road from ground level - see the diagram on th The height of the hill is 80 m and the elevation from the ground level to the top of is 15. What is the distance the car ha order to reach the top of the hill? G. two decimal places Give the answer to two decimal places Page 3 of 7

4 Foundation Mathematics- Main Exam Question 2 (4+4+4= 12 marks) BEGIN A NEW BOOKLET AND WRITE 02 ON THE COVER a) When a player kicks a football, the football's trajectory can be modelled by the equation h = d d + 1.9, where dis the horizontal distance (in meters) travelled by the football after the kick, and his the height of the ball at the distance d after the kick. 1. Find the longest distance travelled by the football after the kick; ii. Find the maximum height achieved by the football after the kick Give the answers to one decimal place. b) for () ~ x ~ 2rr. Where it is possible, give ~ rr, here a and b are integers. lation N(t), introduced to a new nutrient, grows according to the 25000t N(t) = tz' where timet is measured in hours. Use calculus to determine: 1. when the bacteria population will achieve its maximum size; 11. the maximum size of the bacteria population. P~9~ 4-~i"7.....

5 35010 Foundation Mathematics- Main Exam... Question 3 (4+4+4= 12 marks) BEGIN A NEW BOOKLET AND WRITE 03 ON THE COVER a) Differentiate each of the following, showing all working. Simplify your answer as much as possible: b) During hot and wet summers the population of mosquitoes N (in thousan growth in a lake resort area. The population size grows according to N(t) = l6ekt, where t is number of weeks from the beginning of the summe of mosquitoes increased between the 5 1 h and the ih wee weeks of the summer the number of mosqui trst two c) Consider the curve y = 2x 4 - x 3-9x values of x within this interval the erval -1.5 :S; x :S; 1.5. For what... Page 5 of?

6 Foundation Mathematics- Main Exam Question 4 (4+4+4= 12 marks) BEGIN A NEW BOOKLET AND WRITE 04 ON THE COVER a) Find the following the following, showing all working: ' Vi X 1. f ( e-sx -.2_ + ~ ) dx ; 11. J sinx dx (5-cosx) ' b) A car's displacement s(t) at timet is given by the equation: s(t) = ~ at 2 + v 0 t + s 0, where s 0 is initial displacement, v 0 is initial velocity, and a and the car's velocity v(t) at timet is given by the equation: 2 The car was travelling at 70 km/h, When th constant deceleration should be applied to th eters ahead. What c) The diagram below shows gr (i) Find x-coordinate of each of the two points where the graphs intersect; (ii) Find the exact value of the shaded area. P~9~ 5 ~; 7

7 35010 Foundation Mathematics- Main Exam TABLE OF INTEGRALS AND FORMULAE J n+l xn dx =! +C, n+l I cos x dx = sin x + C I sin x dx = -cos x + C I 2. sec x dx = tan x + C... Page 7 of 7