18.1- Introduction
Work with coordinates in all four quadrants
Question 1 : Solve graphically the following simultaneous equations
y=4-x and y=2x-5 ?
18.2 Cubic and Reciprocal Functions
A cubic equation contains only terms up to and including x^{3}. Here are some examples of cubic equations:
y=x^{3}
y=x^{3}+5
Cubic graphs are curved but can have more than one change of direction.
A graph of the form y=\(\frac{1}{x}\) is known as a reciprocal graph
18.3- Exponential and Trigonometric functions
Exponential graphs are graphs in the form y=k^{x}. These graphs increase rapidly in the y direction and will never fall below the x-axis.
18.4-Real life graphs
Real life graphs are graphs representing real things, these can be straight line graphs and curved graphs.
For many real life graphs the gradient will represent the rate of change.
18.5 Gradients and areas under graphs
We calculate the instantaneous rate of change by drawing a tangent to the curve (a straight line just touching the curve) at the desired point, and then calculating the gradient of this tangent (which can be worked out using standard straight line methods).
This will correspond to the gradient of the curve at that individual point.
Question 1 : Calculate the area under the line y=3x+4 between x= 0 and x=4 ?
18.6- Equation of a circle
Question 1 : A circle, centre O, passes through (5, 0). What is the equation of the circle?
Question 2 : A circle, centre (5, 4) and radius 4. What is the equation of the circle?
18.7- Summary and Review
Question 1 : 6 The straight line L has the equation 3y = 4x + 7 . The point A has coordinates (3,-5). Find an equation of the straight line that is perpendicular to L and passes through A ?
18.8- Assessment 18
Question 1 : The equation x^{3} – x^{2}= 30 has a solution between 3 and 4. Use a trial and improvement method to calculate this solution ?
18.9 Revision exercise 3
Question 1 : The points A, B and C lie in order on a straight line.
The coordinates of A are (2, 5)
The coordinates of B are (4, p)
The coordinates of C are (q, 17)
Given that AC = 4AB, Calculate the values of p and q?
Question 2 : Liquid A has a density of 0.7 g cm^{-3} . Liquid B has a density of 1.6 g cm^{-3} . 140 g of liquid A and 128 g of liquid B are mixed to make liquid C. Calculate the density of liquid C?