Questions:

1. Which of the following does not represent a situation that involves an average rate of change? Explain your answer.

a) A child grows 7 cm in 6 months.

b) A jogger ran 25 km in 2 hours.

c) A plane travelled 550 km in 3 hours.

d) The average height of the basketball players is 1.9 m.

e) The room temperature decreased by 3⁰C over one week.

2. The height, h, in metres, of a ball above the ground after t seconds can be modeled by the function h(t) = -3.8t² + 10t.

a) What does the average rate of change represent for this situation?

b) Determine the average rate of change of the height of the ball for each time interval.

i) (1, 3)

ii) (1, 1.2)

iii) (1, 1.5)

iv) (1, 1.01)

v) (1, 1.001)

c) Compare the values in part b). Describe their relationship.

3. A soccer ball is kicked into the air such that its height, h, in metres after t seconds can be modeled by the function h(t) = -2.8t² + 10t + 0.5.

a) Determine the average rate of change of the height of the ball from 1s to 2s.

b) Estimate the instantaneous rate of change of the height of the ball after 1s.

c) Sketch the curve and the tangent.

d) Explain the average rate of change and the instantaneous rate of change in this situation.

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1.5 Slopes of Secants and Average Rate of Change

- Slope is a measure of the steepness of a line

                          

- Rate of change is a measure of the change in one quantity (dependent variable) with respect to a change in another quantity (independent variable)

- 2 types of rates of change

a) Average rate of change - a change that happens over an interval

b) Instantaneous rate of change - a change that happens in an instant

- Secant is a line that connects 2 points on a curve

Average rate of change
- can be represented using secant lines

- methods to determine average rate of change:

a) Calculate the slope between 2 points in a table of values

b) Calculate the slope by using an equation

1.6 Slopes of Tangents and Instantaneous Rate of Change

- Tangent to a curve at a given point is a line that intersects the curve at that point

Instantaneous rate of change

- can be represented using tangent lines

- methods to determine instantaneous rate of change:

a) Graph - estimate the slope of a secant passing through that point

               - use 2 points on an approximate tangent line

b) Table of values - estimate the slope between the point and a nearby point in the table

c) Equation - estimate the slope using a short interval between the tangent point and a 2^nd point found using the equation

Ms Foo had taught us everything in chapter 1 last week. I'm sure some of you might have difficulties in certain subtopics. So I decided to do a journal about chapter 1.5 and 1.6 only. For the other subtopics, my group members, Meng Chong, Sharan and Maya will be doing them. So no worries.
Basically, I'll be posting my journal bout slopes of secants and average rate of change, then slopes of tangents and instantaneous rate of change. Anyway, I also have a bit difficulty in those subtopics. However, after Ms Foo had taught us many times in class bout those subtopics, I'm sure that we all have better understanding now. We all really appreciate it so much. Thank you, Ms Foo.

Hello everyone, i'm Robin. This is my first time that I ever create a blog. In the beginning, I thought it was hard to create it because I'd no experience in creating blogs before. It was actually easy and fun indeed to make a blog. Finally, I managed to create it with Meng Chong's help. Hooray!!! This blog is about Advanced Functions.
Hope you guys have fun learning Advanced Functions as our teacher is Ms Foo. She's a very nice and caring teacher.
Besides that, she also likes to give a lot of homework to us because "practice makes perfect". She always makes things easier for us to remember especially the math concepts. Sometimes, her teaching is so funny until we laugh because she wants to make the class interesting and alive. That's why we all like her so much.