HSC Maths Advanced free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper HSC Maths Advanced set, then download the 3-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
A taxi company charges a flat fee of $8 plus $3 for each kilometre travelled. A passenger paid $35. How many kilometres did the passenger travel?
A 17
B 27
C
D 9
Correct answer: D — 9
- Write the cost as an equation: cost = 8 + 3 × kilometres.
- $35 = 8 + 3 × m, so 3 × m = 35 - 8 = 27.
- m = 27 ÷ 3 = 9 kilometres.
- Why the other options are wrong:
- A (17): This is the correct answer (9) plus 8: an extra 8 was added at the end of the calculation (an off-by-8 error).
- B (27): That is the cost of the kilometres, not the number of kilometres.
- C (
A flat fee plus a rate per unit gives y = (rate)x + (fee): subtract the fee before dividing by the rate.
Your sample is downloading. Liked it? HSC Maths Advanced Paper 1 is the full paper: a full practice examination with Section I 10 multiple-choice, Section II 90 marks, 100 marks in all, 3 hours working time plus 10 minutes reading time, with a worked solution for every question.
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Questions about this sample
What is in the HSC Maths Advanced 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 HSC Maths Advanced papers are there?
20 original papers for Year 12 students preparing for the NSW HSC. Each is a full practice examination with Section I 10 multiple-choice, Section II 90 marks, 100 marks in all, 3 hours working time plus 10 minutes reading time, 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.