WACEhub

Rossmoyne Senior High School

Year 12 Trial WACE Examination, 2014

Question/Answer Booklet

If required by your examination administrator, please place your student identification label in this box

MATHEMATICS 3A/3B

Section One:

Calculator-free

In words

Your name

Time allowed for this section

Reading time before commencing work: five minutes

Working time for this section: fifty minutes

Materials required/recommended for this section

To be provided by the supervisor

This Question/Answer Booklet

Formula Sheet

To be provided by the candidate

Standard items: pens, pencils, pencil sharpener, eraser, correction fluid/tape, ruler, highlighters

Special items: nil

Important note to candidates

No other items may be used in this section of the examination. 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.

Structure of this paper

Instructions to candidates

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.

Write your answers in the spaces provided in this Question/Answer Booklet. 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.

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.

Section One: Calculator-free (50 Marks)

This section has six (6) questions. Answer all questions. Write your answers in the spaces provided.

Working time for this section is 50 minutes.

Question 1 (7 marks)

(a) Use the laws of indices to simplify

(i) . (2 marks)

(ii) . (2 marks)

(b) Solve . (3 marks)

Question 2 (8 marks)

(a) Factorise . (1 mark)

(b) Solve the following equations.

(i) . (1 mark)

(ii) . (2 marks)

(c) The time, in seconds, for a suitcase to travel along a particular conveyor belt is inversely proportional to the speed, in metres per second, of the conveyor belt.

(i) Describe the effect on if is halved. (1 mark)

(ii) Write an equation, using as the constant of proportionality, to represent the relationship between and . (1 mark)

(iii) Given that s when m/s determine when m/s. (2 marks)

Question 3 (9 marks)

The graph of the function is shown below.

(a) Determine the coordinates of the -intercept. (2 marks)

(b) For this function, state the number of

(i) stationary points. (1 mark)

(ii) local minima. (1 mark)

(iii) points of inflection. (1 mark)

(c) Circle all of the intervals below in which the graph is always concave down. (2 marks)

(d) Calculate the global minimum for the function over the domain . (2 marks)

Question 4 (9 marks)

(a) A animal researcher described the association between several variables measured in an experiment using the following statements:

A. There was a weak positive association between exercise time and sleep time.

B. There was no association between weight of food consumed and exercise time.

C. There was a strong negative association between sleep time and task errors.

Mark each of these three expressions of association on the scale below, labelling each mark with its letter. (3 marks)

(b) The scatterplot and regression line for a set of bivariate data with correlation coefficient 0.9 is shown.

(i) Describe the effect on the correlation coefficient if the point labelled P was removed from the dataset. (1 mark)

(ii) Describe the effect on the regression line if data points with were cropped from the dataset. (2 marks)

(iii) Construct a residual plot for the dataset on the axes below. (3 marks)

Question 5 (9 marks)

(a) Calculate the gradient of at the point (2, 5). (2 marks)

(b) Show use of the product rule to determine .

Give your answer in the form . (3 marks)

(c) A function is given by . Given that and , write down two equations and solve them simultaneously to determine the values of and .

(4 marks)

Question 6 (8 marks)

The function is shown below.

(a) State the equation of in the form , where the constants and are both integers. (2 marks)

(b) State the domain and range of . (2 marks)

Another function is given by .

(c) Describe the transformations required to produce from . (2 marks)

(d) Draw the graph of on the axes above. (2 marks)

Additional working space

Question number: _________

Additional working space

Question number: _________

This examination paper may be freely copied, or communicated on an intranet, for non-commercial purposes within educational institutes that have purchased the paper from WA Examination Papers provided that WA Examination Papers is acknowledged as the copyright owner. Teachers within Rossmoyne Senior High School may change the paper provided that WA Examination Paper's moral rights are not infringed.

Copying or communication for any other purposes can only be done within the terms of the Copyright Act or with prior written permission of WA Examination papers.

Published by WA Examination Papers

PO Box 445 Claremont WA 6910