S-Cool Revision Summary
S-Cool Revision Summary
Linear functions can be written in the form y = mx + c where y and x are variables and m and c are constants (numbers).
If you write them like this then m is the gradient and c is the y-intercept (point where it crosses the y-axis). The graphs of linear functions are straight lines.
To find m:
Pick any two points.
To find c:
c is the point where the graph crosses the y-axis.
Quadratic functions can be written in the form:
y = ax2 + bx + c
where a, b and c are constants and 'a' doesn't equal zero.
Quadratic graphs are always parabolas ('U' shapes).
The really important bits of a quadratic are:
Where it turns (the bottom of the 'U')
Where it crosses the x-axis (if it does!)
The solutions of a quadratic are where the graph crosses the x-axis!
Cubic and reciprocal graphs
You need to be able to:
- Plot and draw these.
- Recognise the shapes.
- Read the solutions from the graph (cubics only).
Cubics can be written in the form:
y = ax3 + bx2 + cx + d
Reciprocals are where the x is on the bottom of a fraction.
Drawing their graphs - Table - Axes - Plot - Draw - Label
The solutions of a cubic are where it crosses the x-axis and it can have up to 3.
Graphs of simultaneous equations
As simultaneous equations at GCSE are linear (can both eb written in the form y = mx + c) their graphs will be straight lines.
The solution (x-value and y-value) is where the straight lines intersect (cross one another).
Inequalities - regions on a graph
To draw a graph:
- Change the inequality sign to an '=' sign.
- By choosing 4 or 5 different values for x, make a table of co-ordinates.
- Draw and label the line (make it dotted if the inequality sign is < or >).
- Choose a test point (not on the line!).
- Put the x and y values of the test point into the inequality.
- If it works, shade and label that side of the line with the inequality.
- If it doesn't work, shade and label the other side.
If you show a graph of a journey showing distance travelled (on the y-axis) against time (on the x-axis):
- The gradient (or slope) of the graph represents the speed.
- A horizontal section indicates that you have stopped.
- A section sloping up means that you are going away.
- A section sloping down means you are coming back.
- The steeper the line, the faster you are going.
- The gradient (or slope) of the graph represents the acceleration.
- The area under the graph (for any section) is the distance travelled (in that section).
- A horizontal section indicates constant speed (no acceleration).
- A section sloping up means accelerating.
- A section sloping down means slowing down.
- The steeper the line, the quicker the acceleration.