Changes in quantities over time are also known as rates of change and may be calculated from;
Rate of change
Under this topic we shall consider the rates of change of
1. Distance with time
2. Velocity with time.
The rates of change may also be obtained from gradients of graphs, so we shall specifically consider
1. Distance – time graphs
2. Velocity – time graphs
A VIDEO BELOW ABOUT RATE OF CHANGE
1. DISTANCE – TIME GRAPHS
1. Tony walks 3 km at a constant speed, taking 50 minutes. He then runs 5 km at a constant speed, taking 25 minutes. Draw a distance time graphs of Tony Journey. Using a scale of 2 cm = 1 km and 1 m a scale of 2 cm = 1 km and 1 cm = 10 minutes. Use the graph to find his average speed for the whole journey in m/s.
2. Mary travels by car. At constant speed, from her home to London which is 70 km a way. She leaves home at 2.00 pm and arrives at 2.45 pm. She stays in London for 2 hours, then return homes , taking 50 minutes. Draw a distance – time graph showing Mary’s journey to and from London. Use a scale of 1 cm= 20 minutes and 2 cm = 10 km. Use the graph to find her velocity.
2. VELOCITY- TIME GRAPHS
From the velocity – time graphs we may obtain the distance covered by the body and the acceleration of the body.
Distance covered – Area under the curve.
Acceleration at a point – gradient of graph.
THE VIDEO BELOW IS ABOUT DISTANCE TIME GRAPHS
A UNIT CIRCLE
This is a circle whose radius is 1 unit.
Note ; The x- coordinate gives the cosine of the angle and the y- coordinate gives the sine of the angle , the coordinate can therefore be given in the form p(cosθ,Sin θ)
Where θ is the angle , the radius makes with the x-axis.
If the radius is multiplied by a scale 2, 3…..(Unit circle enlarged) then the coordinates are given in form of p(rcosθ,r sinθ)where r is 1,2,3…….
Example . Write down the coordinates of a point
For grouped data the median is obtained from the formula.
- Find the matrix that maps the final image back onto its object.
- b) i) Single matrix that maps segment AB onto A”B”
Solve the following equations by completing squares;
A video about Factoring Quadratic Expressions
Find the maximum or minimum value of each of each of the expression and when they occur;
To investigate whether -2 is the maximum or maximum value of the expression. we find that -2 ,8 the minimum vale.
For what value of x does this occur.
Find the maximum value of the following expressions.