VCE Methods Mathematics free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper VCE Methods Mathematics set, then download the 3-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
(2 marks)
(a) Differentiate y = ln(x² + 4) with respect to x. [1 mark]
(b) Hence find the gradient of the curve at x = 0. [1 mark]
Question 1 (2 marks) [Chain rule]
(a) Answer: dy/dx = 2x/(x² + 4)
- Chain rule: the derivative of ln g is g'/g.
- g = x² + 4, g' = 2x.
- f'(x) = 2x/(x² + 4).
(b) Answer: 0
- Substitute x = 0 into dy/dx.
- Gradient = 0. d/dx ln g(x) = g'(x)/g(x).
Your sample is downloading. Liked it? VCE Methods Mathematics Paper 1 is the full paper: Exam 1 with 10 short-answer questions (40 marks) and Exam 2 with 20 multiple-choice plus 5 extended-response questions (80 marks), 120 marks in all, with a worked solution for every question.
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Questions about this sample
What is in the VCE Methods Mathematics free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 3-page PDF; this page shows question 1 with its answer.
How many full VCE Methods Mathematics papers are there?
20 original papers for Victorian Year 12 students (VCE Units 3 and 4). Each is Exam 1 with 10 short-answer questions (40 marks) and Exam 2 with 20 multiple-choice plus 5 extended-response questions (80 marks), 120 marks in all, with a worked solution for every question. Papers start at A$15.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.