SAT MATH: GRAPH
The SAT is going to test your graph skills. SAT math and SAT reading both will be comprising of graph questions.
There are various types of
graphs asked in SAT exam staring from bar graph to line graph but before discussing them let's discuss the basis for understanding graphs.
CARTESIAN PLANE
Cartesian plane is a 2D plane comprising of 2 axes X - axis and Y - axis. X - axis is the horizontal axis while the Y - axis is the perpendicular one. both the Axes are perpendicular to each other and intersect each other at 1 point that is known as origin.
The line which goes towards right side of origin is + X - axis while the one towards left is - X - axis it comprises of all the negative numbers.
Similarly the line which goes towards top from origin is considered as + Y - axis while the one which goes towards bottom is - Y - axis.
Most of the data collected in the real world comprises of positive values only thus quadrant 1 the one in which both X and Y are positive is used the most.
QUADRANTS
There are 4 quadrants
Quadrant 1 - both X and Y are positive
Quadrant 1 - X is negative but Y is positive
Quadrant 3 - both X and Y are negative
Quadrant 4 - X is positive but Y is negative
IMPORTANT TERMS
1) ABSCISSA - distance from Y - axis
2) ORDINATE - distance from X - axis
the plotting of linear graphs is explained in HEART OF ALGEBRA SECTION
now coming to other graphs
1)BAR GRAPH
So let's understand bar graph in it generally the X- axis comprises of different groups whose values are given in Y - axis with the help of which we can easily compare them.
let's take an example, let there be a school having 4 sections of class 8 and a person wants to compare which section scored the highest marks so he takes out the average and compare the marks.
without even calculating anything you can see that the bar of section 1 is highest. Thus it has the highest average percentage.
In this bar graph in the X - axis there are 4 different groups Section - 1, section - 2, section - 3, section - 4. each of them corresponds to certain values in Y - axis which is the average percentage scored by students of that section. here you cansee that the average percentage of :-
2) HISTOGRAM
Unlike Bar graph the histogram doesn't have the spaces between the different groups. This is because in it the X - axis has values which are compared against the values of Y.
For example, you and I went out together in a park to play badminton.
There we came up with a peculiar thought to make a chart between the height of trees in the park versus the number of trees with that height. we planned to make a histogram for it. So let's write the data for that
Here height of the trees is written in cm. To plot the histogram, we have to understand that there is no space between the bars so we will draw it in the same way as the bar graph but with no spaces in between. It will be something like this.
There is a special instruction given about histograms in SAT and that is in SAT, all histograms have the same type of boundary condition. That is, the values represented by a bar include the left point but not the right end point. What it means is that in the section 300 -350 which we plotted above the section contain 300 but not 350. 350 comes under the next section 350 - 400.
PIE CHART
It's one of the easiest chart it involves different groups with different shares. the Pie chart is made when there are 2 or more groups having different amount of shares in one thing. It can be different shareholders of a company with percentage of their shares or different daily tasks you do with number of hours you invest in them.
Now let's take an example of a pie chart comprising numbers of hours a person studied a subject in a week.
Math - 8 hrs
Physics - 2 hrs
Chemistry - 1 hr
English - 3 hrs
History - 2 hrs
So it's pie chart will look something like this
You can see exactly half of it is blue it's because time for which the person studied math is 8 hrs and the total time is 16 hrs. Just by a glance you can see that math has the maximum portion while chemistry has the minimum portion that's the beauty of Pie chart. This data can help the student to adjust the number of hours of his time to be given to a subject.
LINE GRAPHS
In these, graphs line/lines are drawn into a Cartesian plane representing the relation between X and Y. Here X can be age and Y can be height of a person. Thus, lines drawn between them represents the change of height of a person with respect to their age.
Plotting line graphs has already been done in Heart of Algebra. So let's discuss about the other operations.
SLOPE
The slope of a line could be directly asked in SAT.
Slope = Rise/Run = Change in Y/ Change in X
Slope = tanš³ can be used in questions with trigonometry.
SCATTER PLOT
In this, type of graph points are plotted and we see their density to interpret data. Then there is a line of best fit which passes through the maximum number of points. It's sometime also referred as trend. It is used to predict the trend of the graph.
You can be asked to find the equation of the best fit and to find it's slope.
EX) let's see this scatter plot and try to find it's line of best fit.
On noticing it, you will find it's trend. Here, the value of Y = X for most of the points. Thus the line Y = X is the line of best fit.
When you will be doing this in SAT you will have to plug in the answers to find the line of best fit.
Now let's find the slope of Y = X
Now to calculate the slope take any 2 random points in the line and put them in the formula. Suppose the points are A(1,1) and B(2,2)
slope = change in Y/change in X = (Y2 - Y1)/(X2 - X1)
= (2-1)/(2-1)
=1
Now let's discuss the method we have to do.
Equation of a line is
Y = MX + C
where M is it's slope
for Y = X
M = 1
so slope = 1
BONNE CHANCE !
SAT HOMEPAGE
SAT EXAM FORMAT
SAT READING
SAT WRITING
SAT MATH
SAT MATH: HEART OF ALGEBRA
SAT MATH: PROBLEM SOLVING AND DATA ANALYSIS
SAT MATH: ADDITIONAL TOPIC IN MATH
SAT MATH: PASSPORT TO ADVANCE MATH
SAT MATH:GRAPH
SAT ESSAY
There are various types of
graphs asked in SAT exam staring from bar graph to line graph but before discussing them let's discuss the basis for understanding graphs.
CARTESIAN PLANE
Cartesian plane is a 2D plane comprising of 2 axes X - axis and Y - axis. X - axis is the horizontal axis while the Y - axis is the perpendicular one. both the Axes are perpendicular to each other and intersect each other at 1 point that is known as origin.
The line which goes towards right side of origin is + X - axis while the one towards left is - X - axis it comprises of all the negative numbers.
Similarly the line which goes towards top from origin is considered as + Y - axis while the one which goes towards bottom is - Y - axis.
Most of the data collected in the real world comprises of positive values only thus quadrant 1 the one in which both X and Y are positive is used the most.
QUADRANTS
There are 4 quadrants
Quadrant 1 - both X and Y are positive
Quadrant 1 - X is negative but Y is positive
Quadrant 3 - both X and Y are negative
Quadrant 4 - X is positive but Y is negative
IMPORTANT TERMS
1) ABSCISSA - distance from Y - axis
2) ORDINATE - distance from X - axis
the plotting of linear graphs is explained in HEART OF ALGEBRA SECTION
now coming to other graphs
1)BAR GRAPH
So let's understand bar graph in it generally the X- axis comprises of different groups whose values are given in Y - axis with the help of which we can easily compare them.
let's take an example, let there be a school having 4 sections of class 8 and a person wants to compare which section scored the highest marks so he takes out the average and compare the marks.
without even calculating anything you can see that the bar of section 1 is highest. Thus it has the highest average percentage.
In this bar graph in the X - axis there are 4 different groups Section - 1, section - 2, section - 3, section - 4. each of them corresponds to certain values in Y - axis which is the average percentage scored by students of that section. here you cansee that the average percentage of :-
| SECTION-1 | 85% | ||
SECTION-2 |
65% | ||
SECTION- 3 |
75% | ||
SECTION- 4 |
70% |
2) HISTOGRAM
Unlike Bar graph the histogram doesn't have the spaces between the different groups. This is because in it the X - axis has values which are compared against the values of Y.
For example, you and I went out together in a park to play badminton.
There we came up with a peculiar thought to make a chart between the height of trees in the park versus the number of trees with that height. we planned to make a histogram for it. So let's write the data for that
Here height of the trees is written in cm. To plot the histogram, we have to understand that there is no space between the bars so we will draw it in the same way as the bar graph but with no spaces in between. It will be something like this.
There is a special instruction given about histograms in SAT and that is in SAT, all histograms have the same type of boundary condition. That is, the values represented by a bar include the left point but not the right end point. What it means is that in the section 300 -350 which we plotted above the section contain 300 but not 350. 350 comes under the next section 350 - 400.
PIE CHART
It's one of the easiest chart it involves different groups with different shares. the Pie chart is made when there are 2 or more groups having different amount of shares in one thing. It can be different shareholders of a company with percentage of their shares or different daily tasks you do with number of hours you invest in them.
Now let's take an example of a pie chart comprising numbers of hours a person studied a subject in a week.
Math - 8 hrs
Physics - 2 hrs
Chemistry - 1 hr
English - 3 hrs
History - 2 hrs
So it's pie chart will look something like this
You can see exactly half of it is blue it's because time for which the person studied math is 8 hrs and the total time is 16 hrs. Just by a glance you can see that math has the maximum portion while chemistry has the minimum portion that's the beauty of Pie chart. This data can help the student to adjust the number of hours of his time to be given to a subject.
LINE GRAPHS
In these, graphs line/lines are drawn into a Cartesian plane representing the relation between X and Y. Here X can be age and Y can be height of a person. Thus, lines drawn between them represents the change of height of a person with respect to their age.
Plotting line graphs has already been done in Heart of Algebra. So let's discuss about the other operations.
SLOPE
The slope of a line could be directly asked in SAT.
Slope = Rise/Run = Change in Y/ Change in X
Slope = tanš³ can be used in questions with trigonometry.
SCATTER PLOT
In this, type of graph points are plotted and we see their density to interpret data. Then there is a line of best fit which passes through the maximum number of points. It's sometime also referred as trend. It is used to predict the trend of the graph.
You can be asked to find the equation of the best fit and to find it's slope.
EX) let's see this scatter plot and try to find it's line of best fit.
On noticing it, you will find it's trend. Here, the value of Y = X for most of the points. Thus the line Y = X is the line of best fit.
When you will be doing this in SAT you will have to plug in the answers to find the line of best fit.
Now let's find the slope of Y = X
Now to calculate the slope take any 2 random points in the line and put them in the formula. Suppose the points are A(1,1) and B(2,2)
slope = change in Y/change in X = (Y2 - Y1)/(X2 - X1)
= (2-1)/(2-1)
=1
Now let's discuss the method we have to do.
Equation of a line is
Y = MX + C
where M is it's slope
for Y = X
M = 1
so slope = 1
BONNE CHANCE !
SAT HOMEPAGE
SAT EXAM FORMAT
SAT READING
SAT WRITING
SAT MATH
SAT MATH: HEART OF ALGEBRA
SAT MATH: PROBLEM SOLVING AND DATA ANALYSIS
SAT MATH: ADDITIONAL TOPIC IN MATH
SAT MATH: PASSPORT TO ADVANCE MATH
SAT MATH:GRAPH
SAT ESSAY
Comments