VCE Mathematical Methods Units 3-4 - Written Examination 1 - Trial Examination 2019

Sep 20, 2026

Trial Examination 2019 for VCE Mathematical Methods Units 3&4, Written Examination 1, with specified reading and writing times and a total structure of 8 questions worth 40 marks. The booklet states permitted and prohibited items, includes a supplied formula sheet and working space, and requires all responses in English. Questions cover logarithms and differentiation, function rules, tangents, trigonometric equation solving, logarithmic equations, function sketching and area, probability density functions and means, and probability calculations with complements and independence, plus a hyperbola graph interpretation.

LanguageEnglish

CategoryExam

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Structure of booklet

Instructions

Answering rules and allowed items

Questions 1-8

Trial Examination 2019 VCE Mathematical Methods Units 3&4 Written Examination 1 Question and Answer Booklet Reading time: 15 minutes Writing time: 1 hour Student’s Name: Teacher’s Name: Structure of booklet | Number of | Number of questions | Number of | | --- | --- | --- | | questions | to be answered | marks | | 8 | 8 | 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 booklet of 9 pages Formula sheet Working space is provided throughout the booklet. Instructions Write your name and your teacher’s name in the space provided above on this page. Unless otherwise indicated, the diagrams in this booklet 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 anyother unauthorised electronic devices into the examination room. Students are advised that this is a trial examination only and cannot in any way guarantee the content or the format of the 2019 VCE Mathematical Methods Units 3&4 Written Examination 1. Neap Trial Exams are licensed to be photocopied or placed on the school intranet and used only within the confines of the school purchasing them, for the purpose of examining that school’s students only. They may not be otherwise reproduced or distributed. The copyright of Neap Trial Exams remains with Neap. No Neap Trial Exam or any part thereof is to be issued or passed on by any person to any party inclusive of other schools, non-practising teachers, coaching colleges, tutors, parents, students, publishing agencies or websites without the express written consent of Neap. Copyright © 2019 Neap ABN 49910906643 58 Pelham St Carlton VIC 3053 Tel: (03) 9639 4318 Fax: (03) 8610 0090 MMU34EX1 _QA_2019.FM 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 booklet are not drawn to scale. Question 1 (4 marks) a. Let y = 􀀋3loge􀀋x􀀌􀀌 2 . dy Find -----dx. 1 mark | | | --- | | | | | b. Let f􀀋x􀀌 = ---􀀋--2- . x Find f 􀁣 2---- . 3 marks | | | --- | | | | | | | | | | | Question 2 (4 marks) Let f 􀁣􀀋x􀀌 = 1 + -2-- . e a. Given f􀀋0􀀌 = 4, find the rule for f􀀋x􀀌 . 2 marks | | | --- | | | | | | | b. Find the equation of the tangent to y = f􀀋x􀀌 at the y-intercept. 2 marks | | | --- | | | | | | | Question 3 (2 marks) Solve tan2 􀀋2x􀀌 – 1 = 0 for x, where x 􀂏 􀀾0􀀏 􀁓 􀁀 . | | | --- | | | | | | | | | | | Question 4 (5 marks) a. Solve the equation 5 – 2loge􀀋x􀀌 = loge􀀋 x 􀀌 for x. 2 marks | | | --- | | | | | | | | | b. Find the value(s) of k for which the equation 5x = 125k – x2 has no solutions for x. 3 marks | | | --- | | | | | | | | | | | | | | | | | | | | | Question 5 (6 marks) Let f : 􀀋–2􀀏 4 􀁀 􀁯 R􀀏 f􀀋x􀀌 = 4 – x – 1. a. Sketch the graph of on the axes below. Label the axis intercepts and endpoints with their coordinates. y = f􀀋x􀀌 | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | O | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 21.51 0.5
| | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | –2 | –1 | –0.5
–1
–1.5 | | 1 | 2 | 3 | 4 | x y b. Find the area bounded by the graph of y = f􀀋x􀀌 , the x-axis and the y-axis. 3 m

FAQs

What are the allowed and prohibited items for the trial examination?

Allowed items include pens, pencils, highlighters, erasers, sharpeners and rulers. Prohibited items include any technology such as calculators or software, notes of any kind, blank sheets of paper, correction fluid/tape, and mobile phones or other unauthorised electronic devices.

What rules apply to answering the questions?

Write your name and teacher’s name in the spaces provided. Answer all questions in the provided spaces, give exact values for numerical answers when required, and show appropriate working when more than one mark is available. Responses must be in English.

What topics are covered across the 8 questions?

The exam covers logarithmic differentiation, function rules and tangents, solving trigonometric and logarithmic equations, sketching a function and finding a bounded area, probability density functions (including finding parameters, mean, and derived density mean), probability with complements and independence, and analysis of a hyperbola graph.

Sep 20, 2026

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