Improve Competency with MyMathsHero
Special relations where every x-value (input) corresponds to exactly one y-value (output) are called functions. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph.
In this topic, we cover the following: Linear graphs, linear programming, quadratic graphs, sketch graphs and relations & functions. At the end of this topic, students should understand the following among other things:
- How to solve quadratic equations using factorization, completing the square, the quadratic formula, and graphical methods,
- Transform word problems into quadratic and linear equations that may be solved algebraically,
- Use algebraic and graphical methods to solve simultaneous linear and quadratic equations.
- Be able to use various expressions for the gradient of a straight line,
- Able to find the intercepts that a line makes with the x- and y- axes and use them to draw the line,
- Find the distance between two points and also find the coordinates of the midpoint of a straight line joining two points on the Cartesians plane,
- Calculate the angle between two lines on the Cartesian plane and be able to use the conditions for two lines to be ‘a ‘parallel, ‘b’ perpendicular.
- Show on a graph the region which contains the solutions of the simultaneous inequalities,
- Represent various inequalities on a separate number line and draw the graphs of various linear equations on separate axis