2.4 Coordinates and graphs
Coordinates and graphs
Everything on coordinates and graphs that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise coordinates and graphs free
A worked example
Gradient · [2 marks]
Work out the gradient of the straight line through (0, 1) and (1, 2).
- M1(2 − 1) ÷ (1 − 0)
- A11
The exam skills (10)
Gradient
- Gradient = change in y ÷ change in x.
- Subtract in the same order on the top and bottom.
- Simplify the fraction.
Watch out: Doing change in x ÷ change in y.
Straight-line graphs
- Find where the line crosses the y-axis: that is c.
- Pick two clear points and find the gradient: up ÷ across.
- Write y = mx + c.
Watch out: Missing the minus sign on a line that slopes down.
Equation of a line
- Find the gradient from the two points.
- Substitute one point into y = mx + c to find c.
- Write the equation with your m and c.
Watch out: Stopping after the gradient.
Parallel lines
- Parallel lines have the same gradient.
- Perpendicular gradient = −1 ÷ the gradient (flip it and change the sign).
- Put the point into y = mx + c to find c.
Watch out: Flipping without changing the sign (or the other way round).
Quadratic graphs
- The solutions of ... = 0 are where the curve crosses the x-axis.
- Read off the x values.
- A quadratic usually has two.
Watch out: Giving the y-intercept.
Simultaneous equations with graphs
- The solution is where the two lines cross.
- Read the x-coordinate (across) and the y-coordinate (up).
- Write both: x = …, y = ….
Watch out: Giving the coordinates the wrong way round.
Turning points
- Complete the square: x² + bx + c = (x + b/2)² − (b/2)² + c.
- The turning point is (−b/2, the number at the end).
- Watch the sign: (x + 6)² has its turning point at x = −6.
Watch out: Getting the x-coordinate sign wrong.
Recognising graphs
- Straight line: linear. U or ∩ shape: quadratic (x²).
- S shape: cubic (x³).
- Two curves in opposite corners that never touch the axes: reciprocal (1/x).
Watch out: Calling a cubic a quadratic. A cubic changes direction twice.
Trig graphs
- Draw (or imagine) a horizontal line at the value you want.
- Your calculator gives the first answer: sin⁻¹.
- Use the symmetry of the graph for the second: for sine, 180° − the first.
Watch out: Only giving one answer when the range has two.
Solving with graphs
- Rearrange the equation so one side matches the curve that is drawn.
- Whatever is on the other side is the straight line to draw.
- The solutions are the x-values where the line crosses the curve.
Watch out: Changing a sign when moving terms across. Check by substituting back.
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