Rate of Change Worksheets
The concept of rate of change is when we are track at least two quantities and see how their values get modified over time. The independent variable is variable that stands alone and the cause for this distortion. We normally define the independent variable as x. The variable that it has a direct effect on is referred to as the dependent variable. The dependent variable is normally stated as y. The rate of change is quantifiable by determining the quotient of these two variables in context of the equation: rate of change = difference in y (dependent variable) ÷ difference in x (independent variable). This is a wonderful selection of worksheets and lessons that show you how to predict the possible rate of change of various functions.
Aligned Standard: HSF-IF.B.6
- Starting with Slope Step-by-step Lesson- This is more of a basic reminder of the skills that will be required for the other sections.
- Guided Lesson - I know that it is a pretty lame scenario with the potatoes. I was running low on creativity that day.
- Guided Lesson Explanation - I always like to encourage students to draw a graph even if all they needed was to calculate the slope.
- Practice Worksheet - Some of the word problems might stump kids. That is why it gets them into a set routine to adapt to the problem.
- Matching Worksheet - Many people will trip up between choices d and e.
- Answer Keys - These are for all the unlocked materials above.
Finding the slope on the first two leads us to finding an average trend on the third homework.
- Homework 1 - Slope is basically a measure of how fast a line ascends or descends.
- Homework 2 - The formula of slope is: y2 - y1 / x2 - x1
- Homework 3 - Mack had 4 kg Onions. He peeled 3 kg of them in 1 hour. Now he has 1 kg Onions left. The graph below shows Mack's situation.
Now we have students start to interpret the meaning of the slope of the line.
- Practice 1 - Find the average rate of change of y with respect to x over the interval [11, 12].
- Practice 2 - To find the average rate of change put the interval values in equation and solve them.
- Practice 3 - Mary had 6 liters of milk in his jug. She was making milk shake at the rate of 3 liters of milk shake in 2 hours. He had 3 liters of milk left. The graph shows Mary's situation.
Math Skill Quizzes
We start with some simple word problems to target the concept of slope.
- Quiz 1 - A wall is 7 feet tall. After 2 years it was 9 feet tall. What does the slope tell us about the tree's growth situation is this negative or positive?
- Quiz 2 - A building was 100 feet tall. After 4 days construction was done and it was 150 feet tall. What does the slope tell us about the building growth situation is this negative or positive?
- Quiz 3 - Maria has 16 kg fresh fruits. After 2 hours she left with 8 kg fresh fruits. If an equation were written to represent this situation, what does the slope tell us about the growth of Maria's fresh flower is this negative or positive?
What Are the Degrees of Rates of Change?
Rates of change can be determined to be positive or negative. A positive rate of change is indicated by the upward trajectory of x and y on a graph. A negative rate of change is indicated by x and y values being in conflict, as the x value increase the y value decreases on a graph. These degrees vary by the elevation or decline in y-value. There are also situations where there is no or zero rate of change, this results in a flat horizontal line when it is graphed.
How to Predict the Rate of Change of Functions
Functions have extensive usage in advanced mathematics and calculus. Calculus is used extensively in other aspects of science. By definition, a function is a procedure in which every input gets associated with only one output. One of the implementations of the function is finding out its rate of change. What this does is describe the transformation in one quantity about the other. In other words, if y is the independent variable and x is the dependent one then: rate of change= (change in x )/(change in y).
There are numerous parameters in which the rate of change of functions can be used comprehensively. Such as finding out the acceleration of a vehicle. The acceleration deals with the change in velocity concerning time. In general, the change in the rate of a function can be denoted as: f(x) = (f(x + h) - f(a)) / (b - a ).