Year 12 graphs and transformations test to download as PDF

This Year 12 graphs and transformations 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 – Sketching a cubic
Sketch \(y=(x-1)^2(x+2)\) showing the coordinates of all intercepts and say where the curve touches the axis.
Question 2 – Transformations of a curve
The point \(P(3,-2)\) lies on \(y=f(x)\). Write down the coordinates of its image on each curve.
1. \(y=f(x+1)\) (1 mark)
2. \(y=3f(x)\) (1 mark)
3. \(y=f(x/3)\) (1 mark)
4. \(y=-f(x)+2\) (1 mark)
Question 3 – Reciprocal graph
Sketch \(y=\dfrac1{x+2}-3\). Give the equations of the asymptotes and the coordinates where it crosses the axes.
Question 4 – Describing transformations
Describe the transformation that maps \(y=f(x)\) to (a) \(y=f(x-5)+1\) and (b) \(y=f(2x)\).
Question 5 – Problem: number of solutions
The curve \(y=x^2(x-3)\) has a local maximum at \((0,0)\) and a local minimum at \((2,-4)\).
1. Sketch the curve. (2 marks)
2. Write down the number of solutions of \(x^2(x-3)=k\) for \(k=-2\) and for \(k=-4\). (2 marks)
3. Show that \(x^3-3x^2+4=(x+1)(x-2)^2\). (1 mark)

How to use this Year 12 graphs and transformations test

First, revise with the graphs and transformations 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 graphs and transformations test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 graphs and transformations 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.