Chapter 1: Types of Relationships Notes

Sections

1. 1A Simultaneous equations graphically Mastered

   Solving a pair of linear equations by graphing both lines and reading the point of intersection, checking the answer, and recognising parallel and identical lines.

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2. 1B Simultaneous equations algebraically Mastered

   Solving simultaneous linear equations exactly by substitution and by elimination, and setting up a pair of equations from a worded problem.

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3. 1C Break-even, profit and loss Mastered

   Cost and revenue as a pair of simultaneous equations, the profit equation, break-even by algebra and by graph, target profit, how changes to price and costs move the break-even point, and a spreadsheet model.

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4. 1D Exponential growth and decay Mastered

   The graphs of y = a^x and y = a^(−x), exponential models y = k·a^x for growth and decay, what k and a mean in context, finding when an amount doubles or halves, and the limits of exponential models.

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5. 1E Quadratic models Mastered

   The parabola y = ax² + bx + c, its intercepts, axis of symmetry and vertex found from the midpoint of the x-intercepts, and quadratic models of projectiles, areas and profit with a sensible domain.

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6. 1F Reciprocal models and inverse variation Mastered

   Inverse variation y = k/x, the shape of the hyperbola and its asymptotes, finding k from one pair of values, using reciprocal models for shared work, speed and time, and their limitations.

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