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
2
THIS PAGE IS BLANK
3
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
5
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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