Do charts and graphs make problem-solving difficult? Complex problems with visual representations can drain your brain during a test. In this lesson, learn three simple rules for solving problems with charts and graphs. We’ll try them out as we walk through two sample problems.

## Solving Problems with Charts and Graphs

Have you ever been in the middle of a test, happily going along question-by-question, trying to pace yourself, and all of a sudden – wham – they smack you with a huge, scary graph and a whole page of questions about it? It takes you five minutes just to read the questions through and another five minutes to try and interpret the graph. Complex chart problems are just as stressful as table problems during an exam. But, just like you learned in our lesson on table problems, there are certain tactics that can help you get by.

In this lesson, we’ll walk through two chart problems and learn three simple rules for solving them efficiently.

## Three Rules for Chart Problems

Our first chart problem describes a situation with enzymes. Let’s see what it says.

‘The graph below illustrates the percentage of maximum activity for three different enzymes over a range of pH levels. Use the graph to answer the following three questions.’

x-axis here is titled ‘pH.’ We can see that the graph covers the full range of pH levels, from 0 to 14. The y-axis measures enzyme activity in terms of percentages. When one of the lines reaches the height of the graph, that means that the enzyme represented by that line reaches the highest activity level at that pH.
Now that we’ve oriented ourselves to the axes, we need to Enzyme B peaks at a pH of 7, and enzyme C looks like it peaks around pH 11 or 12. The three lines cross over one another at intermediate pH levels. So at the pHs of 5 and 9, none of the enzymes are all that active.Alright, so we have a good understanding of what this graph is about. Now, we can go ahead and look at the questions. Our first question asks, ‘Which enzyme does best at pH 3?’ So, looking at our graph, we’ll find pH 3 along the x-axis. Move straight up to follow the y-axis, and we intersect with the line that corresponds to enzyme A. That was easy! We’ll pick enzyme A. The next question asks us to do the same thing, only backwards. Instead of finding the enzyme that peaks at a certain pH, we need to find the pH at which a certain enzyme peaks. Our question reads, ‘What is the optimum pH for enzyme C?’ You know that the optimum pH for an enzyme is the pH level at which it reaches maximum activity. So let’s find the graph for enzyme C, locate the highest point, and then move vertically downward to see where we end up on the x-axis. We end up right around pH 11. So, we’ll choose pH 11 from our list of choices. Did you notice that in both questions, we found our own answer before looking at any of the choices? It’s usually best to If you come up with the right answer before you look at the other choices, you’ll save yourself from becoming distracted, or even swayed, by the other options available. Let’s try this tactic with our third question. It reads, ‘What is the order of enzyme activity, from greatest to least, at a pH of 8?’ Let’s look at what’s going on at pH 8 in our graph. If we go up from the x-axis, we first cross the line for enzyme A, then C, then B. So that means at a pH level of 8, enzyme B is the most active, enzyme C is less active and enzyme A is the least active. Our answer to this question, without looking at any of the choices, would be enzyme B, then C, then A. Now, is that answer listed as one of our choices? Yup, it’s right here. So, we circle that answer and now we’ve done the problem! ## Same Rules, Harder ProblemNext, we’ll try a chart problem that’s a little bit harder. Here’s what it says: ‘The following chart illustrates how many families of species exist in the fossil record as a function of geologic time. Use the chart to answer the next four questions.’This problem may look like it’s going to take a lot of work. But, remember that before you read through any of the questions, you should first orient yourself to the x- and y-axes. The x-axis here reads ‘Geologic Time in Millions of Years Ago.’ That word ‘ago’ should tell you something important. Notice that the numbers down here run backwards, with the zero at the right-hand side of the graph. Instead of counting up the years from left to right, we’re counting back the years from right to left. This chart sort of functions as a timeline. And look, down here we have the different periods of geologic history labeled and sectioned off for us. The y-axis here reads ‘Number of Families.’ They must be talking about families in a phylogenic sense. Rather than tracking the number of species that existed through time, they’ve tracked organisms in larger groups – families. Now that we know what the axes represent, it’s time to identify the trends of the chart. This line moves generally upward from left to right, meaning that over time, the number of families increased. That makes sense with what we know about the history of life on Earth. We started with just a few kinds of organisms, which diversified greatly over time. But, we see five points where the line dips down. These must represent times when the number of families suddenly decreased – in other words, major extinction events. We can probably assume that the questions we’re asked in this problem will relate to these five extinction events that are evident in the fossil record.It’s finally time to read the first question. Remember to try and answer the question on your own before you go looking at any of the choices. Our first question asks us to identify which period had the largest number of families. Number of families is our y-axis, so we just need to find the highest point on our graph. This corresponds to the Tertiary Period on the x-axis. So, that’s our answer.The next question asks at which point the largest extinction occurred. This one’s going to take a bit of thought. We can recognize the five extinction events, but how do we know which is the largest? It must be the one with the largest dip, the region in which the line plummets the furthest distance from top to bottom. We can eyeball each of the extinction events and see that the one in the middle is the largest. This event happened right at the end of the Permian Period. So, we’ll pick this one as our answer. Finally, our last question wants us to identify the extinction event that made the smallest impact on the number of families. Notice that they didn’t say, ‘Which is the smallest extinction?’ If they had, we would compare the heights of the valleys of each extinction event, just like when we were trying to find the largest dip. Sometimes, the wording of a test question can lead you to believe it’s asking something it’s not. So, pay close attention to the phrases they use, especially words like ‘always,’ ‘never,’ ‘only,’ ‘every’ and ‘except.’ When you’re asked to identify the ‘highest’ or ‘lowest’ of something, be careful to note exactly what it is you’re looking for.In this question, they’re asking about how the extinctions affected the number of families at the time of the extinction. So, we need to compare the size of the dips with the total number of families at each time point. We need the dip that accounts for the smallest percentage of existing families. It looks to me like the Triassic-Jurassic event and the Cretaceous-Tertiary event are the smallest extinctions. But, the first one makes up about one-sixth of the total, while the other extinction only knocks out about one-tenth of the number of families. This has got to be the extinction with the smallest total impact. It occurred at the end of the Cretaceous Period, right before the Tertiary. The best answer choice for our conclusion is the ‘Cretaceous-Tertiary extinction event.’ ## Lesson SummaryThe next time you get smacked in the face with a complex chart problem on an exam, don’t panic. Just try to follow the three rules we talked about. **Orient yourself to the x- and y-axes**. Read the headings and units and make sure you know what they mean.**Identify the trends of the chart**.Be sure you understand where the lines are going in a line graph and what it means for them to be shaped the way they are. - When you’re ready to read through the questions, try to
**answer the questions on your own**. Reading through all of the choices might distract you from drawing your own conclusions from your chart interpretation.
Take your time with problems involving graphs and charts, and you can solve them pretty easily. They’re not nearly as scary as you might think! ## Learning OutcomeAt the conclusion of this video, you’ll be able to describe three tips that will help you answer complex graph and chart problems on exams. |