1. Essential Math For Economics
Dianna DaSilva-Glasgow
Department of Economics
University of Guyana
September 7, 2017

2. Basic Algebra and percentages
Wk Lecture
Basic Algebra and percentages

3. Equation of a linear relationship
If we know the intercept and slope we can describe the line succinctly in equation form. In its general form the equation of a straight line is
Where b = intercept
m = slope
y = dependent variable
x = independent variable

4. Helpful Hint
There are several different ways to describe the variables of a function.
Independent
Variable
Dependent
Variable
x-values
y-values
Domain
Range
Input
Output x
f(x)

5. The input of a function is the independent variable
The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

6. Exercise: Equation of a linear relationship
 Interpreting the Slope
Given the equation y= 2x + 6
What is the slope of the line?
What is the value of y, when x = 1
Interpret the slope;

7. Exercise: Equation of a linear relationship
 Since y = mx + c
Y = 2(1) +6
What is the slope?
Y = 2+6
It is m = 2.
Y = 8
What is the value of y, when x = 1
Y = 2x + 6

8. Exercise: Equation of a linear relationship
Interpreting the slope of the line ( Y = 2x +6)
This value tells us that, for every increase of 1 unit in the input variable of Y or (x in this case), the value of the output variable Y will increase by 2.

9. Equation of a linear relationship
Solving simultaneous equations
2x+3y= x -2y = solve for x and y

10. Percentages

11. What does % mean?
per
for every
cent
100

12. Percentages
A percentage is a fraction converted to a decimal, and then multiplied by 100 and add percent sign (%).
For example,

13. (move all digits 2 places to the right)
To find 1% of a number ÷ by 100
Find 1% of 225
225.
225 ÷ 100
(move all digits 2 places to the right) 2 . 2 5
1% of 225 =
2.25

14. (move all digits 1 place to the right)
To find 10% of a number ÷ by 10
Find 10% of 376
376.
376 ÷ 10
(move all digits 1 place to the right) 3 7 . 6
10% of 376 =
37.6

15. How to change percentages, into fractions and decimals
A percentage is a special fraction.
The % says, “per hundred.”
For example, 47%, is simply another way of writing the fraction 47/100

16. You can almost see the 100 in the percentage sign%
The noughts
The 1
Percentage
Fraction 7%
7/100
19%
19/100
83%
83/100
Etc.

17. So to write a percentage as a fraction, you simply put it over 100 like this:
24% = 24/100
Yes, but remember to try to write the fraction in its simplest terms
24% = 24/ / /25

18. To change decimal into a percentage
To change a decimal into a percentage, you X by 100
X 100 %

19. Percentage Change
When an original value is changed to a new value, the percentage change of the value can be measured in the following way.  

20. Percentage Change Example
Peter’s weight decreases from 60 kg to 48 kg. Find the percentage change of his weight.

21. Percentage Change Example
Solution :
 Percentage decrease of weight is 20%.

22. Lecture
Basic calculus

23. Basic Differentiation Rules
Lesson 3.2A

24. Basic Derivatives Constant function Then f’(x) = 0 Power Function Then
Given f(x) = k
Then f’(x) = 0
Power Function
Given f(x) = x n
Then

25. Exercises
Use combinations of the two techniques to take derivatives of the following

26. Basic Rules
Constant multiple
Sum Rule
Difference Rule

27. Exercises
Determine the following

28. Lecture
Presentation of Data

29. The Presentation of Scientific Data: Results, Tables and Graphs

30. Data Individual facts, statistics, or items of information.
Generated from experiment, observation or research.
How do we convey Data to others?
Data Table (Visual/Organizer).
Graphs (Visual).

31. Data Tables
A Data Table is a mode of visual communication and means of arranging data (organization).
Age Table:
First Name
Last Name
Age (yrs)
Bill
Davolio 33
Nancy
Klondike 43
Sarah
Obesanjo 23
Justin
Saunders 37
Mike
Timberlake 26
Paulo
Ilustre 11
Variable “B” or “Y”
Variable “A” or “X”
Independent Variable
Dependent Variable

32. Graphs
A diagram (visual) showing the relationship between sets of numbers, or topics, that represents how one set depends or changes with another.
Different graphs can show different things.
Examples…...

33. Bar Graph
Used to show relationships between variables that may be “fixed” in time or space.
A “snap shot”.
Bars can help to give a sense of quantity.

34. Line Graph Used to show relationships, such as rates.
Changes over time or given variable.

35. Scatter Plot Points “plotted” between to axis (the variables).
Add trendlines to see correlations in the data.
Trendlines or lines of best fit. Part of linear regressions for statistical analysis.

36. Pie Chart (Circle Graph)
A circular chart that illustrates relative magnitudes or frequencies (Example Percentages)
Pie chart of populations of English native speakers

37. How do you draw a graph?
Important skill, to draw it means you can read a graph.
Remember, it’s a visual expression, or picture, of data.

38. 1st - A graph – Basic Terms
Number Line “Y”
“Y” Axis
Plot/Data Area
Number Line “X”
“X” Axis

39. Using Microsoft Excel Steps In excel file, highlight data
Go to ‘Insert’
Select chart type
Edit chart