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Sketch graphs, with labelled but unscaled axes, to qualitatively describe trends.
Construct and interpret graphs using logarithmic scales.
Draw lines or curves of best fit.
Extrapolate and interpolate graphs.
Linearize graphs (only where appropriate).
Interpret features of graphs including gradient, changes in gradient, intercepts, maxima and minima, and areas under the graph.
Understand direct and inverse proportionality, as well as positive and negative relationships or correlations between variables.
No relationship
No relationship
When you change the IV there is no consistent pattern to the dependent variable.
No effect
No effect
When you change the IV the DV stays the same.
There is a pattern, but the pattern is that the IV does not affect the DV.
Directly proportional (y = ax)
Directly proportional (y = ax)
When you change the IV, the DV changes proportionally, or the slope is constant and passes through the origin.
For example, F = ma, where F is the DV and a is the IV, yields F ∝ a, when m is constant.
Directly proportional relationships can increase or decrease. That is the slope can be positive or negative.
When the slope is positive, there is a positive correlation. When the slope is negative, there is a negative correlation.
Linear (y = mx + b)
Linear (y = mx + b)
When you change the IV, the DV changes linearly, or the slope is constant, and there is a y intercept.
Linear relationships can increase or decrease. That is the slope can be positive or negative.
When the slope is positive, there is a positive correlation. When the slope is negative, there is a negative correlation.
For example, v = u + at, where t is the IV and v is DV, yields a linear relationship when a is constant.
Inverse (y = a/x)
Inverse (y = a/x)
When you change the IV, the DV changes such that if you plot the DV variable versus the inverse of the IV, the graph becomes a straight line.
For example, m = F/a yields m ∝ 1/a, when F is constant.
Inverse-squared (y = a/x^2)
Inverse-squared (y = a/x^2)
When you change the IV, the DV changes such that if you plot the DV variable versus the square of inverse of the IV, the graph becomes a straight line.
For example, F = GmM/r^2 yields F ∝ 1/r^2, when G, m, and M are constant.
Quadratic (y = ax^2 + bx + c)
Quadratic (y = ax^2 + bx + c)
When you change the IV, the DV changes such that if you plot the DV variable versus the square of the IV, the graph becomes a straight line.
For example, s = ut + 1/2at^2 yields s ∝ t^2, when a is constant.
Exponential (y = e^ax)
Exponential (y = e^ax)
When you change the IV, the DV changes such that if you plot the DV variable versus natural log of the IV, the graph becomes a straight line.
For example, N = No e^λt yields N ∝ e^t, when No and λ are constant.
Video Lectures
Video Lectures
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