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Year 11 Mathematics Extension 1 Practice Questions

Question 01 of 05|Further work with functions
Question 014 marks

The daily cost, in dollars, of running a small workshop is modelled by C(x)=x2−6x+13C(x)=x^2-6x+13, where xx is the number of hours it operates, for 0≤x≤80\le x\le 8. The diagram shows the graph of y=C(x)y=C(x), which has a minimum turning point at (3,4)(3,4). A manager studies the function R(x)=1C(x)R(x)=\dfrac{1}{C(x)}.

(a)Explain why the graph of y=R(x)y=R(x) has no vertical asymptotes.1 mark
(b)Find the maximum value of R(x)R(x) and the value of xx at which it occurs.2 marks
(c)State the range of R(x)R(x) for 0≤x≤80\le x\le 8.1 mark

Random year 11 mathematics extension 1 exam practice, one question at a time

Each set on this page is a random selection of Year 11 Mathematics Extension 1 questions from across the course, so no two attempts cover the same ground. Random practice is how you find the gaps a topic-by-topic revision guide hides: you cannot predict what is coming, so you have to recall the method rather than recognise it. That is the same condition you face in a final exam, and it is why this page is built for revision in the weeks before trials and the HSC rather than for learning a topic for the first time.

Every question carries its own marking criteria, with the marks shown beside each line, in the wording an examiner uses, so you award yourself the marks your working actually earns instead of a right-or-wrong tick. Use it to check your fundamentals are secure across further work with functions, permutations and combinations, polynomials and the rest of the syllabus, then reload for a fresh set. A free account removes the five-question limit and marks photos of your handwritten working automatically, with a band breakdown per topic.

Topics in this course
  • Further work with functions
  • Permutations and combinations
  • Polynomials
  • Further trigonometry
  • The binomial theorem
Common questions

Is this the real Year 11 Mathematics Extension 1 question bank?

The five questions you see are drawn at random from a larger sample of it, so a reload gives you a different set. The bank behind an account covers every topic and dot point in the course, and it generates fresh questions rather than reusing a fixed set.

Why are the marking criteria hidden until you reveal them?

Because reading the marking criteria before attempting the question teaches you almost nothing. Attempt it first, then reveal the criteria and mark your own working against them.

Do I need an account to use this page?

No. The demo runs entirely in the page and nothing is saved. An account adds unlimited questions, automatic marking of handwritten working, and progress tracking.

How is the marking decided?

Against the same criteria list you see here. Each line shows the marks it is worth and is judged on the working you show, so partial credit behaves the way it does in a real exam.

Other subjects
Mathematics AdvancedMathematics Extension 1Mathematics Extension 2Year 11 Mathematics Standard
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