MATH1720 2019 Exam PDF

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DESK No.

FAMILY NAME: GIVEN NAMES: SIGNATURE: STUDENT NUMBER:

SEMESTER 1, 2019 EXAMINATIONS

MATH1720

Physics, Mathematics & Computing

Mathematics Fundamentals

Faculty of Eng, Computing and Maths

.

This paper contains: 13 Pages (including title page)

Time Allowed: 2:00 hours

INSTRUCTIONS: This examination constitutes 60 % of the total assessment for MATH1720. There are 15 questions in this examination, worth a total of 50 marks. Marks for each part of each question are shown in square brackets. No calculators are permitted. The MATH1720 Formula Sheet is attached to the end of the examination paper. No other notes are permitted. All answers should be supported by adequate working. Marks are given for clarity and correctness of method, not just for correct answers. Write your answers in the blank spaces provided after each question. The blank pages at the end of the examination paper may be used for rough working. Your answers must be written in pen { do not use pencil.

THIS IS A CLOSED BOOK EXAMINATION SUPPLIED STATIONERY No Supplied Stationery required.

ALLOWABLE ITEMS No Allowable Items.

PLEASE NOTE Examination candidates may only bring authorised materials into the examination room. If a supervisor finds, during the examination, that you have unauthorised material, in whatever form, in the vicinity of your desk or on your person, whether in the examination room or the toilets or en route to/from the toilets, the matter will be reported to the head of school and disciplinary action will normally be taken against you. This action may result in your being deprived of any credit for this examination or even, in some cases, for the whole unit. This will apply regardless of whether the material has been used at the time it is found. Therefore, any candidate who has brought any unauthorised material whatsoever into the examination room should declare it to the supervisor immediately. Candidates who are uncertain whether any material is authorised should ask the supervisor for clarification. Candidates must comply with the Examination Rules of the University and with the directions of supervisors. No electronic devices are permitted during the examination. All question papers and answer booklets are the property of the University and remain so at all times.

MATH1720 FIRST SEMESTER EXAMINATION 2019

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MATH1720 FIRST SEMESTER EXAMINATION 2019

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1. Evaluate the following expression. 1 − 2



3 5 − 4 6



×

7 8 [2 marks]

2. Solve the following equation for x. 5 − 4 {3 + 2 [1 − 2 (3x + 4)]} = 5 [3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019

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3. Solve the following pair of simultaneous equations. 2x + y = −1

(1)

3x + 5y = 9

(2) [3 marks]

4. Formulate the following problem as a pair of simultaneous equations. Do not solve the resulting pair of simultaneous equations. A farmer grows two kinds of vegetables - carrots and bananas. If two bags of carrots and five bags of bananas cost $51 in total, and three bags of carrots and four bags of bananas cost $64 in total, what is the cost of each bag of vegetables? [3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019

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5. Factorise the following quadratic without using the quadratic formula. x2 − 10x + 16 [3 marks]

6. Sketch the following parabola, clearly showing the intercepts and the vertex. y = 4x2 − 2x − 2 [3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019

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7. Expand the brackets and simplify the following expression.    4 √x 4 √x −√ +√ 2 2 3 3 [3 marks]

8. Simplify the following expression. 3

2 4 · x−1 · x5 √ 12 · x−6

[3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019

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9. Write the following expression as the logarithm of a numerical expression. log2 3 − 4 log 2 5 + log2 6 [3 marks]

10. Solve the following equation for x.   4 log 3 x2 − 7 log 3 x = 2 log3 3

[3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019 11. Solve the following equation for x. 

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4 √ A − B 3x − C = D [3 marks]

12. Solve the following equation for t.   B A ln + eC = D t [3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019 13. (a) Find the x-intercept of the straight line y = 2x − 3.

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[2 marks]

(b) Sketch the graph of the straight line y = 2x − 3, clearly showing the intercepts. [3 marks]

(c) Find the equation of the straight line passing through the point (−2, 1) which has the same x-intercept as the straight line y = 2x − 3. [3 marks]

MATH1720 FIRST SEMESTER EXAMINATION 2019

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14. An animal population numbered 300 at the start of a study (time t = 0) and after six years numbered 3, 600. Assuming the population law P (t) = P0 ekt , find the values of N0 and k and predict when the population will exceed 9, 000. [4 marks]

15. Solve the following equation for x by considering it as a quadratic in ln(2x). [ln(2x)]2 − ln(2x) − 2 = 0 [3 marks]

[END OF EXAMINATION]

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The University of Western Australia Department of Mathematics and Statistics MATH1720 Mathematics Fundamentals Formula Sheet

The laws of indices km “ k m´n kn

k m k n “ k m`n 0

1

k “1

´1

k “k

k

pjkqn “ j n ˆ k n k ´n “

1 kn

1

kn “

? n

pk m qn “ k mn ˆ ˙´1 j k “ k j

1 “ k ˆ ˙n j jn “ n k k 1

k2 “

k

?

k

The laws of logarithms ˆ ˙ x “ logb x ´ log b y logb pxyq “ log b x ` logb y log b y logb pxr q “ r log b x

logb b “ 1

logb 1 “ 0

e and the natural logarithm es “ es´t et

es et “ es`t

e0 “ 1

lnpstq “ ln s ` ln t

ln

ln 1 “ 0

pes qt “ est ´ s¯ t

e´s “

e1 “ e

ln psr q “ r ln s

“ ln s ´ ln t

ln e “ 1

The quadratic formula If

2

ax ` bx ` c “ 0

then

x“

´b ˘

1 es

?

b2 ´ 4ac 2a...