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Last week's blog article provided an extensive overview and look into Heart of Algebra, a major section of the SAT Math test (it constitutes for 33% of the examination's questions!).
If you have not yet taken a read of that piece yet, go ahead and do so before moving on with today's blog. We will be moving forward to the next section that is covered on the SAT Math, Problem Solving and Data Analysis.
The Problem Solving and Data Analysis section of SAT Math accounts for the second-largest area of the college entrance examination, roughly 29% to be exact.
As an introductory refresher, these sub-categories of SAT Math is used by the College Board in order to help break down your math score into useful subscores on your comprehensive results.
What Is Tested On The SAT Math Section?
Within the SAT Math section, you will find the format is structured by multiple-choice questions and "grid-ins." While the majority of SAT math is multiple-choice, 22% of the math examination portion will constitute grid-ins.
Grid-ins are student-produced, meaning that they require you to first solve the mathematical problem and then enter your answer into the grid provided on the answer sheet.
In total there are 58 questions, with 45 being multiple-choice and 13 as grid-ins.
The SAT Math exam is separated into four main component areas:
Heart of Algebra (19 questions)
Problem Solving and Data Analysis (17 questions)
Passport to Advanced Math (16 questions)
Additional Topics in Math (6 questions)
Need help building a study plan? Look no further, click here to read our previous blog!
Last week, we went over the first domain, Heart of Algebra. Now we will proceed towards the second-largest component of the SAT Math portion.
What Is Problem Solving And Data Analysis?
Students can anticipate working on a total of 17 Problem Solving and Data Analysis questions on the SAT Math exam. You will never be told by the College Board what type of question you are working on from the four major component areas, but you can identify them if you understand what to look for.
Problem Solving and Data Analysis problems revolve around applying your mathematical understanding beside realistic scenarios and analyzing the data rather than working through conceptual situations.
TIP: An important thing to remember for this category of SAT Math is that there will be no Problem Solving and Data Analysis questions on the no-calculator portion. This means that for every Problem Solving and Data Analysis problem you encounter, you will always be allowed to utilize an approved calculator in order to solve the question. You may not always require the aid of a calculator, but it will be permitted if you choose to use it for any Problem Solving and Data Analysis question.
Straight from the College Board, the Problem Solving and Data Analysis section test students' abilities to:
"Create a representation of a problem, consider the units involved, attend to the meaning of quantities, and know and use different properties of operations and objects. Problems in this category will require significant quantitative reasoning about ratios, rates, and proportional relationships and will place a premium on understanding and applying unit rate."
In broad terms, this category is used to illustrate a student's math comprehension and capability to solve problems that they could potentially encounter in real-life.
Struggling with reading? Get some insights on what the ACT 4 core reading passages are with our recent blog article!
You should expect that the majority of these problems will be set in either academic or career contexts and are more than likely to reference the sciences and social science.
What Will Problem Solving And Data Analysis Questions Look Like?
According to the official College Board, you can expect this sub-category to inquire about 10 major types of questions:
Use of ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.
Solve single- and multistep problems involving percentages
Solve single- and multistep problems involving measurement quantities, units, and unit conversion
Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related.
Use the relationship between two variables to investigate key features of the graph
Compare linear growth with exponential growth
Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability.
Make inferences about population parameters based on sample data.
Use statistics to investigate measures of center of data and analyze shape, center, and spread.
Evaluate reports to make inferences, justify conclusions, and determine the appropriateness of data collection methods.
To condense the areas above, we will provide an overview of Problem Solving and Data Analysis three major concepts:
Ratios, units, and percentages
Relationships in Scatterplots, Graphs, Tables, and Equations
Data and Statistics Relationships
We will reference the Official College Board SAT Study Guide, Chapter 17, Problem Solving and Data Analysis.
Ratios, Units, and Percentages
A ratio is a numerical comparison that illustrates some sort of relationship between two or more values. In order to complete ratio calculations, you should increase your comfort level when it comes to multiplying and dividing fractions.
A ratio can be expressed in any of the following formats on SAT Math:
X to Y
X:Y
X/Y
X (when Y is equal to 1)
You may see something like this:
This means that there were 5 adults for every 1 child. Of every 6 people who attended the show, 5 were adults and 1 was a child. Turning this problem into fractions, 5/6 of the 240 people that attended were adults and 1/6 were kids. 1/6 * 240 would equal 40 children attended the show, leaving you with the answer choice A.
You will encounter units in terms of oƒ unit conversion and unit rates. Unit rates express one quantity compared to another ("miles per hour", "dollars per year", etc.) Look for terms like "per" or "each." More often than not, they will require that you convert from one unit to another.
You may see something like this:
You are given that 1 mile = 1.6 kilometers. Using that information, you solve for the distance in miles. Take 1,060 kilometers and multiply it by (1 mile/1.6 kilometers) and you are left with 664.5 miles, roughly around 663 miles. The correct answer choice is C.
TIP: The College Board usually draws on both the English system of feet and inches as well as the metric system of kilometers and meters. As such, you should be well-versed and familiar with the common units for both. Practice with everyday concepts such as changing your height from inches to centimeters or concerting a car's speed from kilometers to miles.
As for percentages, students should always remember that these are relative to the number 100 and that they are a form of proportions. Given that, these questions involve usually the concepts of percentage increase and percentage decrease.
You may see something like this:
The sale price of the table is $299. Consider x as the cost from the wholesaler. Your sale price of the table is equal to the cost from the wholesaler plus 15%. Therefore, you will have $299 = 1.15x. Solve for this and the cost from the wholesaler will be $299/1.15 which equals to $260. You are told that the usual price is the cost from the wholesale (which we now know is $260) plus a percentage increase of 75%. The usual price the store charges for the table will be 1.75 * $260, which equals $455. Your answer choice is B.
TIP: In order to do well on Problem Solving and Data Analysis percentage problems, you can brush up on your practice with cross-multiplication when solving for missing values in a formula. Also, remember to work through the problems step-by-step. In the previous example, we had to solve for the cost from the wholesaler first before finally solving for the usual store price with its percentage increase.
Here is a handy list of all the important formulas given on the SAT!
Scatterplots, Graphs, Tables, and Equations
You can anticipate that questions in the Problem Solving and Data Analysis will concentrate on linear, quadratic, and exponential relationships. These are usually depicted by scatterplots, graphs, tables, or tables.
TIP: You can differentiate between linear and exponential as such,
A model is linear if the difference in quantity is constant.
A model is exponential if the ratio in the quantity is constant
The first thing you should think of when you see either a scatterplot, graph, table, or chart is how you can analyze and draw a relational conclusion between its variables.
Be knowledgable about the foundational equations and its components such as for lines (y = mx + b), quadratic equations (ax² + bx + c = 0).
You may see something like this:
TIP: If you are unsure whether it is linear or exponential, try to follow this type of thinking.
If a quantity is increasing linearly over time, then the difference in the quantity between each time period should be the same.
If a quantity is increasing exponentially over time, then the ratio in the quantity between each time period should be the same.
Using this logic for the problem above, you see that after each hour the number of bacteria in the culture is 4 times as great as it was the prior hour. We see a constant ratio between each time period that increases the number of bacteria over time so answer choice D is the correct answer.
Data and Statistics Relationships
For the Problem Solving and Data Analysis category of SAT Math, you will most likely run into data that involves the measures of the center (the mean, average, median).
If the problem you are given does not provide enough information to calculate the for the measures of center, you may still be asked to pull a conclusion about them.
For a beginner refresher:
Mean - the average
Median - the number exactly in the middle when values are placed in order
Mode - the value that appears the most often
Range - the difference between the highest value and the lowest
If you have a strong grasp on these concepts, then it will be much easier for you to make sense and move forward with more challenging statistical concepts on the SAT Math.
The more complicated ideas revolve around terms like population parameter, standard deviation, or how far apart points in a data set are from the mean.
Let's take a look at the concept of standard deviation. It is the measure of spread and generally, the College Board will ask that you compare two sets of data to define which has a more spread out distribution (a greater standard deviation). In these particular cases, do not worry about calculating the exact value. You will need to know the foundational theory and comprehension in order to solve this type of problem.
You may see something like this:
You see that Class A has a mean score between 3 and 4. The bulk of the scores are 3 and 4, with a very few landing in 0, 1, 2, and 5. As for Class B, the mean score is 2.5 with all scores being equally distributed across all possible scores. Not many of these quiz scores are close to the mean score. Since Class A has quiz scores that are grouped closely together around the mean, the spread (or standard deviation) of the scores in Class A is smaller. The correct answer choice is A.
Conclusion
Covering approximately 29% of the concepts found on the SAT Math test, Problem Solving and Data Analysis assesses a student's math ability alongside real-world scenarios. You will be expected to pull information from the concepts and apply reasoning that is more practical for your future professional careers.
As for any portion of SAT Math, we recommend our students to take each step at a time to ensure that they do not make minor mistakes. One little, but crucial, error when working through a mathematical problem can result in the wrong answer choice.
Be sure to brush up on foundational concepts and equations that you should be aware of for this domain of SAT Math and start practice problems or exercises that can help you prepare.
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