Math — Problem Solving & Data Analysis for the SAT Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Confusing percent change with percent of total — 'increased by 20%' vs '20% of the total'
• !Misinterpreting a two-way frequency table — calculating a row proportion when a column proportion is needed
• !Selecting 'mean' when the question requires 'median' (or vice versa) based on the distribution shape
• !Misreading the unit on a graph's axis — answering in the wrong order of magnitude

Study tips

• 1For percentage problems, build a formula bank: % change = (new − old)/old × 100; % of total = part/whole × 100; part = % × whole.
• 2For two-way frequency tables, identify whether the question asks for a row conditional probability or a column conditional probability before calculating.
• 3Practice interpreting scatter plots: identify positive vs negative correlation, approximate the line of best fit, and interpolate or extrapolate values.
• 4Memorise the five statistical measures: mean (sum/n), median (middle value), mode (most frequent), range (max − min), standard deviation (spread). Know which is resistant to outliers (median is; mean is not).

Sample SAT Math — Problem Solving & Data Analysis questions

These sample items mirror the format and difficulty of real SAT questions. Practice with thousands more on the free Koydo question bank.

1. 1

   A store originally sells a jacket for $80. After a 25% discount, the sale price is:

   • A$55
   • B$60Correct
   • C$65
   • D$70
   Why this answer?

   Discount amount = 25% × $80 = $20. Sale price = $80 − $20 = $60.

2. 2

   A scatter plot shows a strong positive linear correlation between study hours and test scores. This means:

   • AStudying more causes higher test scores
   • BStudents who study more tend to have higher test scoresCorrect
   • CThere is no relationship between study hours and scores
   • DAll students who study 5+ hours score 100%
   Why this answer?

   Correlation indicates a tendency or association, not causation. Option A makes a causal claim that cannot be inferred from correlation data alone. The correct interpretation is that the two variables tend to increase together.