Year 12 simultaneous equations, inequalities and polynomials test to download as PDF

This Year 12 simultaneous equations, inequalities and polynomials test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-17, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Simultaneous equations
Solve the simultaneous equations \(x-y=2\) and \(xy=15\).
Question 2 – Inequalities
Solve \(2x^2-7x-4\ge0\).
Also solve \(3(x-2)<2x+5\) and hence find the values of \(x\) that satisfy both inequalities.
Question 3 – Factor theorem
\(f(x)=x^3-4x^2+x+6\).
1. Show that \((x-2)\) is a factor of \(f(x)\). (1 mark)
2. Factorise \(f(x)\) completely. (3 marks)
Question 4 – Remainder theorem
When \(p(x)=2x^3+ax-5\) is divided by \((x-2)\) the remainder is 7. Find \(a\).
Question 5 – Problem: a rectangular lawn
The length of a rectangular lawn is 3 m more than its width \(w\) m. The area is 54 m\(^2\).
1. Show that \(w^2+3w-54=0\). (1 mark)
2. Find the dimensions of the lawn. (2 marks)
3. Edging costs £4.50 per metre. Find the cost of edging the whole perimeter. (1 mark)

How to use this Year 12 simultaneous equations, inequalities and polynomials test

First, revise with the simultaneous equations, inequalities and polynomials lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the simultaneous equations, inequalities and polynomials test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 simultaneous equations, inequalities and polynomials test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Simultaneous equations, inequalities and polynomials – Year 12 A level maths test to download as PDF

Question 1 – Simultaneous equations

Question 2 – Inequalities

Question 3 – Factor theorem

Question 4 – Remainder theorem

Question 5 – Problem: a rectangular lawn

How to use this Year 12 simultaneous equations, inequalities and polynomials test

Similar pages

More on this chapter

Other chapters in this level