3cdmat semester one examination 2013 calc free

Semester One Examination 2013Question/Answer Booklet

MATHEMATICS 3C/3D

Section OneCalculator-free

Student number: In figures

In words

Time allowed for this section

Reading time before commencing work: 5 minutes Working time for paper: 50 minutes

Material required/recommended for this section

To be provided by the supervisorQuestion/answer booklet for Section One.Formula sheet. To be provided by the candidateStandard items: pens, pencils, pencil sharpener, highlighter, eraser, ruler.

Important note to candidates

Semester One Examination Calculator-Free 3CD MAT 2013 Murdoch College

No other items may be taken into the examination room. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the examination room. If you have any unauthorised material with you, hand it to the supervisor before reading any further

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Structure of this examination

Number of questions Working time (minutes) Marks available

This Section (Section 1)Calculator-free 10 50 50

Section TwoCalculator-assumed 15 100 100

Total marks 150

Instructions to candidates

1. The rules for the conduct of Western Australian external examinations are detailed in the Year 12 Information Handbook 2013. Sitting this examination implies that you agree to abide by these rules.

2. Answer the questions according to the following instructions.

Section One: Write answers in this Question/Answer Booklet. All questions should be answered.

Show all your working clearly. Your working should be in sufficient detail to allow your answers to be checked readily and for marks to be awarded for reasoning. Incorrect answers given without supporting reasoning cannot be allocated any marks. For any question or part question worth more than two marks, valid working or justification is required to receive full marks. If you repeat an answer to any question, ensure that you cancel the answer you do not wish to have marked.

It is recommended that you do not use pencil except in diagrams.

3. You must be careful to confine your responses to the specific questions asked and to follow any instructions that are specific to a particular question.

4. Spare pages are included at the end of this booklet. They can be used for planning your responses and/or as additional space if required to continue an answer. Planning: If you use the spare pages for planning, indicate this clearly at the top of the page. Continuing an answer: If you need to use the space to continue an answer, indicate in the original

answer space where the answer is continued, i.e. give the page number. Fill in the number of the question(s) that you are continuing to answer at the top of the page.


Section One: Calculator-free (50 marks)

This section has ten (10) questions. Answer all questions. Write your answers in the space provided.

Spare pages are included at the end of this booklet. They can be used for planning your responses and/or as additional space if required to continue an answer. Planning: If you use the spare pages for planning, indicate this clearly at the top of the page. Continuing an answer: If you need to use the space to continue an answer, indicate in the original answer

space where the answer is continued, i.e. give the page number. Fill in the number of the question(s) that you are continuing to answer at the top of the page.

Suggested working time for this section is 50 minutes.

Question 1 (5 marks)

Simplify the following:

(a) (2)

(b) (3)

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See next pageQuestion 2 (7 marks)

Differentiate each of the following with respect to x. Do not simplify after the first line of your solution.

(a) (2)

(b) (2)

(c) (3)

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A curve contains the point (1, 9) and the gradient of the curve at any point is given by:

.

Find the equation of the curve.


a, b, c and d represent the x values of the 4 points marked on the graph above.Express the shaded area in terms of definite integrals.

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Study the graph of shown below.

Given that (1, 0) is a point of inflection, evaluate the constants a, b and c.


Given that , and ,

(a) Calculate (2)

(b) Are events A and B independent? Justify your answer. (2)

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Find the following:

(a) (1)

(b) (1)

(c) (2)

(d) (3)

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Let A, B, C, D, E, F and G be points on the graph of a continuous function .The table below contains information about the sign of at these points.

Point A B C D E F G- 4 - 3 - 1 0 1 2 4+ 0 - 0 + + +- - 0 + + 0 ++ + + 0 - 0 +

There are no other points at which are equal to zero.

(a) Which point is a local minimum? (1)

(b) Describe the nature of the graph at point F. (2)

(c) Sketch the function on the axes below. (4)

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W is a Binomial variable with parameters n and p = . Find in terms of n, P(W > 1). Do not simplify your

answer.


A certain type of computer password is 8 characters long. Six of the characters are lower-case letters from the English alphabet, i.e. members of the 26-element set

. The other 2 characters are decimal digits. However, the decimal digits must occur

consecutively. So are possible passwords, but is not.How many possible passwords are there? Give your answer as an arithmetical expression, without evaluating.

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3cdmat semester one examination 2013 calc free

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