Plotting cubic, reciprocal and exponential graphs

Sample Plotting cubic, reciprocal and exponential graphs questions

A few of the 6 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 13 marksGrade 6
   (a) Complete the table of values for $y = x^3 + x - 4$, then plot the points on the grid and join them with a smooth curve. [2] (b) Use your graph to solve $x^3 + x - 4 = 0$. Give your answer correct to 1 decimal place. [1]

   On the practice page you draw or plot the answer on screen.

   Show the worked solution

   (a) $y = x^3 + x - 4$: when $x = -2$, $y = -14$
2. Question 23 marksGrade 7
   (a) The mass, $y$ mg, of a radioactive sample after $x$ hours is given by $y = 16 \times \left(\dfrac{1}{2}\right)^x$

Common mistakes in Plotting cubic, reciprocal and exponential graphs

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Counts only one crossing

  Counted only one crossing. The curve turns and crosses the x-axis three times between x = −2 and x = 2.

• Gives y value not x value

  Subtracted 1 from 12 and stopped. The question asks for x, read across from y = 12 to the curve and down to the x-axis.

• Reads root not intersection with line

  Gave the x-value where the curve crosses the x-axis. For x³ − 4x = 2 you need where the curve meets the line y = 2.