Grade: Grade 11 Subject: SAT/ACT Skills Unit: Strategy Playbook SAT: ProblemSolving+DataAnalysis ACT: Math

Question Types Mastery

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Success on standardized tests requires recognizing question types quickly and applying the right strategy for each. This lesson teaches you to categorize questions and match them with optimal approaches.

SAT Math Question Categories

  • Heart of Algebra: Linear equations, systems, inequalities, and word problems involving linear relationships
  • Problem Solving and Data Analysis: Ratios, percentages, proportions, data interpretation, and statistical concepts
  • Passport to Advanced Math: Quadratics, polynomials, exponential functions, and complex equations
  • Additional Topics: Geometry, trigonometry, and complex numbers

ACT Math Question Categories

  • Pre-Algebra (20-25%): Basic operations, fractions, decimals, integers, and number properties
  • Elementary Algebra (15-20%): Variables, expressions, equations, and inequalities
  • Intermediate Algebra (15-20%): Quadratics, systems, functions, matrices, and roots
  • Coordinate Geometry (15-20%): Graphs, slopes, distance, midpoint, and conic sections
  • Plane Geometry (20-25%): Shapes, angles, area, perimeter, and proofs
  • Trigonometry (5-10%): Trig ratios, identities, and graphing

Recognition Strategies

Train yourself to identify question types within 5-10 seconds by looking for:

  • Key vocabulary (e.g., "proportion," "rate," "system")
  • Mathematical symbols and structures
  • Graph or table presence
  • Word problem context clues

Examples

Practice identifying these question types:

Example 1: Type Identification

"If 3x + 5 = 17, what is the value of x + 2?"

Type: Heart of Algebra / Elementary Algebra

Strategy: Solve for x first, then add 2. Or recognize you can solve for (x + 2) directly.

Example 2: Data Analysis

"A survey of 200 students found that 35% prefer online learning. Based on this sample, how many students in a school of 1,400 would be expected to prefer online learning?"

Type: Problem Solving and Data Analysis

Strategy: Apply the percentage to the larger population: 0.35 x 1400 = 490

Example 3: Advanced Math

"If f(x) = x^2 - 4x + 3, for what value of x does f(x) = 0?"

Type: Passport to Advanced Math / Intermediate Algebra

Strategy: Factor or use quadratic formula: (x-1)(x-3) = 0, so x = 1 or x = 3

Practice

Identify the question type and write down your strategy before solving each problem.

1. A car travels 240 miles in 4 hours. At this rate, how many miles will it travel in 7 hours?

2. Solve the system: 2x + y = 10 and x - y = 2

3. The function g(x) = 2^x passes through which of the following points?

4. In a right triangle with legs of 5 and 12, what is the length of the hypotenuse?

5. If the average of 5 numbers is 24, what is their sum?

6. A store reduces prices by 20%. If an item originally cost $45, what is the sale price?

7. What is the slope of a line perpendicular to y = 3x - 7?

8. Simplify: (x^2 - 9)/(x + 3)

Check Your Understanding

  1. What are the four main SAT Math content areas?
  2. Which ACT category typically has the highest percentage of questions?
  3. What visual cues help you identify a data analysis problem?
  4. How do word problem contexts differ between algebra and geometry questions?
  5. Why is quick type recognition important for pacing?

Next Steps

  • Create flashcards for each question type with key identifiers
  • Practice type identification with 20 random problems (focus on speed)
  • Track which question types you find most challenging
  • Move on to Timed Drill Techniques to practice under time pressure