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Revision notes
Read line and quadratic graphs, distinguish power and exponential functions, and estimate a curve's gradient using a tangent.
Key ideas
- Coordinates, lines and gradients
Plot ordered pairs and read a straight line’s gradient from changes in the labelled coordinates.
- Quadratic graphs and turning points
Use tables and symmetry to locate a quadratic curve’s roots and extremum.
- Power and exponential graphs
Use domains, tables and asymptotes to distinguish power functions from exponential growth.
- Estimate a curve’s gradient
Draw a tangent at the specified point and use two separated points on that tangent.
From the G2 Mathematics 2027 syllabus
- Cartesian coordinates in two dimensions
- Graph of a set of ordered pairs as a representation of a relationship between two variables
- Linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c)
- Graphs of linear functions
- The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- Graphs of quadratic functions and their properties: ∗ positive or negative coefficient of x^2 ∗ maximum and minimum points ∗ symmetry
- Graphs of power functions of the form y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these
- Graphs of exponential functions y = ka^x, where a is a positive integer
- Estimation of the gradient of a curve by drawing a tangent