Question Types
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Understanding the different question types you will encounter on the SAT and ACT is essential for developing effective strategies. Each question type requires a slightly different approach, and recognizing them quickly will help you manage your time efficiently.
SAT Problem Solving and Data Analysis Question Types
- Ratio and Proportion Problems: Questions that ask you to set up and solve proportional relationships or compare quantities.
- Percentage Problems: Calculate percent increase, decrease, or find the original value given a percentage.
- Unit Conversion: Convert between different units of measurement within a problem context.
- Data Interpretation: Read and analyze information from tables, graphs, charts, and diagrams.
- Statistics: Calculate or interpret mean, median, mode, range, and standard deviation.
- Probability: Determine the likelihood of events occurring based on given data.
- Scatterplots and Lines of Best Fit: Analyze trends and make predictions using linear models.
ACT Math Question Types
- Pre-Algebra: Basic operations, fractions, decimals, and number properties.
- Elementary Algebra: Solving linear equations and inequalities.
- Intermediate Algebra: Quadratics, systems of equations, and functions.
- Coordinate Geometry: Graphing, slope, distance, and midpoint formulas.
- Plane Geometry: Properties of shapes, angles, area, and perimeter.
- Trigonometry: Basic trig ratios and identities.
Identifying Question Types Quickly
Before solving any problem, take 5-10 seconds to identify:
- What type of problem is this?
- What information is given?
- What am I being asked to find?
- What strategy or formula applies?
Examples
Example 1: Identifying a Ratio Problem
Question: In a class of 30 students, the ratio of boys to girls is 2:3. How many girls are in the class?
Type Identification: This is a ratio problem because it involves a comparison between two groups using a ratio.
Solution: Total parts = 2 + 3 = 5. Each part = 30/5 = 6. Girls = 3 x 6 = 18.
Example 2: Identifying a Data Interpretation Problem
Question: According to the bar graph, which month had the highest sales?
Type Identification: This is a data interpretation problem because you must read and analyze visual data.
Strategy: Scan the graph for the tallest bar and identify its label.
Example 3: Identifying a Percentage Problem
Question: A shirt originally costs $40. If it is on sale for 25% off, what is the sale price?
Type Identification: This is a percentage decrease problem.
Solution: Discount = 40 x 0.25 = $10. Sale price = $40 - $10 = $30.
Practice
For each problem below, first identify the question type, then solve.
1. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 9 cups of sugar, how many cups of flour do you need?
Hint: What type of relationship is described?
2. The mean of five numbers is 12. If four of the numbers are 10, 11, 13, and 15, what is the fifth number?
Hint: This involves a statistical measure.
3. A store increases the price of an item from $80 to $100. What is the percent increase?
Hint: Calculate the change relative to the original.
4. Convert 5 kilometers to meters.
Hint: This is a unit conversion problem.
5. A bag contains 4 red marbles and 6 blue marbles. If one marble is drawn at random, what is the probability it is red?
Hint: This asks about likelihood.
6. The scatterplot shows a positive correlation between hours studied and test scores. If a student studies for 5 hours, and the line of best fit suggests a score of 85, what does this represent?
Hint: This involves trend analysis.
7. Solve for x: 3x + 7 = 22
Hint: Identify the algebra type.
8. What is the median of the data set: 3, 7, 9, 12, 15?
Hint: This is a statistics problem.
9. A map uses a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, how far apart are they in reality?
Hint: Scale problems are a type of proportion.
10. The table shows the number of books read by students in a class. What is the range of books read?
| Student | Books Read |
|---|---|
| A | 5 |
| B | 8 |
| C | 3 |
| D | 12 |
| E | 7 |
Hint: Range is a measure of spread.
Check Your Understanding
Q1: What should you do before solving any problem?
Show Answer
Take 5-10 seconds to identify the question type, given information, what you need to find, and which strategy or formula applies.
Q2: Name three question types in the SAT Problem Solving and Data Analysis domain.
Show Answer
Possible answers: Ratio/proportion, percentage, unit conversion, data interpretation, statistics, probability, scatterplots/lines of best fit.
Q3: How do you recognize a data interpretation problem?
Show Answer
A data interpretation problem typically includes a visual element like a table, graph, chart, or diagram that you must analyze to answer the question.
Next Steps
- Practice identifying question types before solving - this builds speed
- Create flashcards for each question type with example problems
- Move on to the Timed Drill lesson to practice under time pressure
- Keep a log of which question types you find most challenging