SAT (Scholastic Assessment Test) Math: Problem-Solving and Data Analysis Syllabus

Math: Problem-Solving and Data Analysis syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Math: Problem-Solving and Data Analysis in SAT (Scholastic Assessment Test), not a summary of it.

1. 1

   Ratios, Rates, and Proportions

   3 topics

   • Ratios and proportional relationships
     • Setting up proportions
     • Constant of proportionality
   • Unit rates and unit conversion
     • Dimensional analysis
   • Scale and similar figures
2. 2

   Percentages

   3 topics

   • Percent of a quantity
   • Percent increase and decrease
     • Successive percent changes
   • Percent word problems in context
3. 3

   Statistics and Data Distributions

   4 topics

   • Measures of center and spread
     • Mean, median, mode
     • Range and standard deviation concepts
   • Effects of outliers and data changes
   • Interpreting graphical data displays
     • Histograms, dot plots, box plots
     • Scatterplots and lines of best fit
   • Comparing two data sets
4. 4

   Probability and Inference

   3 topics

   • Probability of single and compound events
     • Two-way frequency tables
     • Conditional probability
   • Sample statistics and population inference
     • Random sampling and bias
     • Margin of error and confidence intervals
   • Evaluating statistical claims and study design
     • Observational studies vs. experiments

Math: Problem-Solving and Data Analysis flashcards for SAT (Scholastic Assessment Test)

18 of 50 cards from the Math: Problem-Solving and Data Analysis deck — real questions with worked answers.

1. What is a ratio, and what are the two common ways to write the ratio of a to b?

   A ratio compares two quantities by division. It can be written as a:b or as the fraction a/b.

2. What is a proportion, and how do you solve one?

   A proportion is an equation stating two ratios are equal (a/b = c/d). Solve it by cross-multiplying: a·d = b·c, then isolate the unknown.

3. In a proportional relationship y = kx, what does the constant k represent and what is its graph?

   k is the constant of proportionality (the unit rate y/x). The graph is a straight line through the origin (0,0) with slope k.

4. How can you tell if two quantities are directly proportional from a table?

   They are directly proportional if the ratio y/x is the same constant for every pair of values.

5. What is the difference between a direct proportion and an inverse proportion?

   Direct: y = kx, so y increases as x increases and y/x is constant. Inverse: y = k/x, so y decreases as x increases and the product xy is constant.

6. What is a unit rate?

   A unit rate is a rate expressed as a quantity per one unit of another quantity (denominator of 1), e.g., 60 miles per 1 hour = 60 mph.

7. How do you find a unit rate from a rate like 150 words in 3 minutes?

   Divide the numerator by the denominator: 150 ÷ 3 = 50 words per minute.

8. What is the dimensional-analysis (factor-label) method for unit conversion?

   Multiply the quantity by conversion factors written as fractions equal to 1, arranged so unwanted units cancel and the desired units remain.

9. To convert 5 feet to inches using a conversion factor, what setup do you use?

   5 ft × (12 in / 1 ft) = 60 in. The 'ft' units cancel, leaving inches.

10. When converting a rate such as 90 km/h to m/s, how do you handle both units?

    Multiply by conversion factors for each unit: 90 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 25 m/s.

11. What is a scale factor between two similar figures?

    The scale factor is the ratio of any pair of corresponding lengths in the two figures; it is the same for all corresponding side pairs.

12. For similar figures with scale factor k, how do the areas and volumes compare?

    Corresponding lengths scale by k, areas scale by k², and volumes scale by k³.

13. What conditions make two figures similar?

    Corresponding angles are equal (congruent) and corresponding side lengths are in the same proportion.

14. How do you use a map scale of 1 inch = 25 miles to find actual distance for 4 inches?

    Multiply by the scale: 4 in × 25 miles/in = 100 miles.

15. How do you find percent of a quantity, e.g., 30% of 80?

    Convert the percent to a decimal and multiply: 0.30 × 80 = 24.

16. How do you convert a percent to a decimal and a decimal to a percent?

    Percent to decimal: divide by 100 (move decimal two places left). Decimal to percent: multiply by 100 (move decimal two places right).

17. What is the formula for percent change (increase or decrease)?

    Percent change = (new value − original value) / original value × 100%. A positive result is an increase; a negative result is a decrease.

18. How do you compute the result of a percent increase of p% on a value V in one step?

    Multiply by (1 + p/100). For a 20% increase: V × 1.20.

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