Mathematics (Core)Exam code: 0580
Further Graphs
Coordinate Geometry and Graphs
Reading the answers off
- The solutions of an equation are the x values where two graphs meet
- Where the equation is set equal to zero, the answers are where the curve crosses the x-axis
- Where it is set equal to a number, draw that horizontal line and read across
- Where two curves are given, the meeting points solve them simultaneously, and there the y values are wanted too
- Read to within half of the smallest square, the accuracy the syllabus sets, and give the x values only, unless the question asks to solve simultaneously
When the equation is not the one plotted
- A question often asks you to solve an equation that is not the one drawn
- Rearrange the new equation until one side is exactly the expression that was plotted
- Whatever is left on the other side is the line you must draw on the grid
- Then read off the x values where that line cuts the curve
Exam tip
Each crossing point is a separate mark
Each solution read off the graph is a separate mark, and it is checked against the curve you drew, so a slip earlier in the question does not cost it. Give an x value for every point where the line meets your curve, even when your curve looks wrong.
Worked example
Choosing the line to draw
The graph of y = x² − 3x + 1 is drawn on a grid. Explain how to use it to solve x² − 3x − 2 = 0.
Solution:
- The plotted expression is x² − 3x + 1, so make that appear on one side of the new equation
- Start from x² − 3x − 2 = 0
- Add 3 to both sides: x² − 3x + 1 = 3
- The left side is now exactly the plotted curve
- The line to add to the grid is therefore y = 3
- The solutions are the x values where that line meets the curve
