Question Types
Learn
Understanding question types is the foundation of effective SAT/ACT review cycles. When you can quickly identify what a question is testing, you can apply the right strategy and manage your time more efficiently.
SAT Math Question Categories
- Heart of Algebra: Linear equations, systems, and inequalities
- Problem Solving and Data Analysis: Ratios, percentages, data interpretation, and statistics
- Passport to Advanced Math: Quadratics, polynomials, and complex equations
- Additional Topics: Geometry, trigonometry, and complex numbers
ACT Math Question Categories
- Pre-Algebra (20-25%): Basic operations, fractions, decimals, integers
- Elementary Algebra (15-20%): Variables, expressions, basic equations
- Intermediate Algebra (15-20%): Quadratics, systems, functions
- Coordinate Geometry (15-20%): Graphing, slopes, distances, midpoints
- Plane Geometry (20-25%): Shapes, angles, area, perimeter
- Trigonometry (5-10%): Trig ratios, identities, equations
Why Categorization Matters
By tagging each practice question with its type, you can:
- Identify patterns in your mistakes
- Focus review time on weak areas
- Build confidence in strong areas
- Predict question difficulty before solving
Examples
Practice identifying question types before solving:
Example 1: Category Identification
Question: If 3x + 7 = 22, what is the value of 6x + 14?
Type: Heart of Algebra / Elementary Algebra
Why: This is a linear equation problem with a twist - recognizing that 6x + 14 = 2(3x + 7) = 2(22) = 44
Example 2: Category Identification
Question: A store increases prices by 20%, then offers a 20% discount. What is the net change?
Type: Problem Solving and Data Analysis / Pre-Algebra
Why: This tests percentage reasoning and requires understanding that percent changes don't simply add/subtract
Example 3: Category Identification
Question: If f(x) = x^2 - 4x + 3, for what values of x does f(x) = 0?
Type: Passport to Advanced Math / Intermediate Algebra
Why: This requires factoring or using the quadratic formula
Practice
For each question below, identify the category BEFORE attempting to solve:
1. The ratio of boys to girls in a class is 3:5. If there are 24 students total, how many are girls?
Category: _____________
2. What is the slope of the line perpendicular to y = -2x + 5?
Category: _____________
3. If |2x - 3| = 7, what are the possible values of x?
Category: _____________
4. A circle has center (3, -2) and passes through (7, 1). What is the radius?
Category: _____________
5. The mean of 5 numbers is 12. If one number is removed, the mean becomes 10. What number was removed?
Category: _____________
6. Simplify: (x^2 - 9)/(x + 3)
Category: _____________
7. In triangle ABC, angle A = 30 degrees and side a = 5. If angle B = 60 degrees, find side b.
Category: _____________
8. A table shows the frequency distribution of test scores. What is the median?
Category: _____________
9. If f(x) = 3x - 2 and g(x) = x^2, what is f(g(2))?
Category: _____________
10. Two trains leave stations 300 miles apart traveling toward each other. One travels 60 mph, the other 40 mph. When do they meet?
Category: _____________
Check Your Understanding
Q1: What is the primary benefit of identifying question types before solving?
Q2: Which SAT domain covers linear equations and inequalities?
Q3: On the ACT, approximately what percentage of questions are geometry-related?
Q4: How does categorizing questions help with time management during the test?
Next Steps
- Create a personal "question type cheat sheet" with examples from each category
- Practice categorizing questions for 5 minutes before each study session
- Track which categories appear most frequently in your practice tests
- Move on to the Timed Drill lesson to practice under pressure