2018 Mathematical Methods Written examination 1 - Pages

Victorian Certificate of Education 2018

STUDENT NUMBER

SUPERVISOR TO ATTACH PROCESSING LABEL HERE

Letter

MATHEMATICAL METHODS

Written examination 1

Wednesday 7 November 2018

Reading time: 9.00 am to 9.15 am (15 minutes) Writing time: 9.15 am to 10.15 am (1 hour)

QUESTION AND ANSWER BOOK

Number of questions

9

Structure of book

Number of questions to be answered

9

Number of marks

40

? Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners and rulers.

? Students are NOT permitted to bring into the examination room: any technology (calculators or software), notes of any kind, blank sheets of paper and/or correction fluid/tape.

Materials supplied ? Question and answer book of 14 pages ? Formula sheet ? Working space is provided throughout the book.

Instructions ? Write your student number in the space provided above on this page. ? Unless otherwise indicated, the diagrams in this book are not drawn to scale. ? All written responses must be in English.

At the end of the examination ? You may keep the formula sheet.

Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

? VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2018

2018 MATHMETH EXAM 1

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2018 MATHMETH EXAM 1

Instructions

Answer all questions in the spaces provided. In all questions where a numerical answer is required, an exact value must be given, unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown. Unless otherwise indicated, the diagrams in this book are not drawn to scale.

Question 1 (3 marks) a. If y = (-3x3 + x2 - 64)3, find dy .

dx

1 mark

b. Let f ( x) = ex .

cos( x) Evaluate f ().

2 marks

TURN OVER

2018 MATHMETH EXAM 1

4

Question 2 (3 marks)

The derivative with respect to x of the function f : (1, ) R has the rule

f (x)=

1- 1

2 (2x - 2)

Given that f (2) = 0, find f (x) in terms of x.

Question 3 (5 marks) Let f : [0, 2] R, f (x) = 2cos(x) + 1.

a. Solve the equation 2cos(x) + 1 = 0 for 0 x 2.

2 marks

Question 3 ? continued

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2018 MATHMETH EXAM 1

b. Sketch the graph of the function fon the axes below. Label the endpoints and local minimum

point with their coordinates.

3 marks

y 4

3

2

1

0

2

4

5

2

x

3

3

3

3

?1

?2

TURN OVER

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