Grade: Grade 10 Subject: SAT/ACT Skills Unit: Timed Modules SAT: ProblemSolving+DataAnalysis ACT: Math

Question Types Overview

Learn

Understanding the different question types you'll encounter on the SAT and ACT is essential for effective time management. Each question type requires a specific approach, and knowing what to expect helps you allocate your time wisely.

SAT Math Question Types

  • Multiple Choice: Four answer choices; use process of elimination
  • Student-Produced Response (Grid-In): No answer choices; calculate and enter your answer
  • Data Analysis Questions: Interpret graphs, tables, and charts
  • Word Problems: Translate real-world scenarios into mathematical expressions

ACT Math Question Types

  • Pre-Algebra: Basic operations, fractions, decimals, percentages
  • Elementary Algebra: Variables, expressions, equations
  • Intermediate Algebra: Quadratics, systems, inequalities
  • Coordinate Geometry: Graphing, slopes, distances
  • Plane Geometry: Angles, triangles, circles, area, perimeter
  • Trigonometry: Basic trig functions and identities

Time Allocation Strategy

Different question types require different amounts of time. Quick-solve questions (basic algebra, simple calculations) should take 30-60 seconds. Medium-complexity questions (word problems, data interpretation) typically need 60-90 seconds. Complex questions (multi-step problems, proofs) may require 2+ minutes.

Examples

Let's identify question types and estimate time needed for each.

Example 1: Quick-Solve (30-45 seconds)

Question: If 3x + 7 = 22, what is the value of x?

Type: Basic algebra / Multiple choice

Strategy: Direct solve - subtract 7, divide by 3

Solution: 3x = 15, so x = 5

Example 2: Medium Complexity (60-90 seconds)

Question: A store increases prices by 20%, then offers a 20% discount. What is the final price as a percentage of the original?

Type: Word problem / Percent change

Strategy: Work through systematically with a starting value

Solution: Start with $100. After 20% increase: $120. After 20% discount: $120 x 0.80 = $96. Final = 96% of original.

Example 3: Complex (2+ minutes)

Question: The table shows data for 200 students. If a student is selected at random from those who play a sport, what is the probability they also play an instrument?

Type: Data analysis / Conditional probability

Strategy: Read table carefully, identify the subset, calculate probability

Practice

Categorize each question by type and estimate the time you would spend on it. Then solve.

1. What is 15% of 80?

Hint: Identify type first, then solve.

2. If f(x) = 2x² - 3x + 1, what is f(4)?

Hint: Function evaluation - substitute and calculate.

3. A rectangle has a perimeter of 28 and a length that is 3 more than its width. What is the area?

Hint: Set up equations from the given relationships.

4. The graph shows monthly sales for two products. In which month was the difference between Product A and Product B sales the greatest?

Hint: Data interpretation - compare values at each point.

5. Simplify: (3x² + 2x - 5) - (x² - 4x + 2)

Hint: Combine like terms carefully with signs.

6. A car travels 180 miles in 3 hours. At this rate, how long will it take to travel 300 miles?

Hint: Find the rate first, then use it.

7. If the mean of 5 numbers is 12, and four of the numbers are 8, 10, 14, and 15, what is the fifth number?

Hint: Use the definition of mean to find the sum.

8. In a right triangle, one leg is 6 and the hypotenuse is 10. What is the area of the triangle?

Hint: Find the other leg using Pythagorean theorem.

9. Which of the following is equivalent to (x + 3)(x - 3)?

Hint: Recognize the special product pattern.

10. A survey of 100 students found that 60 like pizza, 45 like burgers, and 20 like both. How many like neither?

Hint: Use the inclusion-exclusion principle.

Check Your Understanding

Answer these reflection questions to solidify your learning.

  1. What are the main differences between SAT and ACT math question formats?
  2. How much time should you typically spend on a "quick-solve" question?
  3. What strategy helps you when you don't immediately know how to solve a multiple choice question?
  4. Why is it important to identify question types before solving?

Next Steps

  • Practice categorizing questions before solving them
  • Time yourself on individual questions to build awareness
  • Move on to the Timed Drill lesson to practice under pressure
  • Create a personal reference sheet of question types you find challenging