SAT · SAT Math domains
Problem Solving and Data Analysis
Decimal computation inside rate, unit and measurement problems.
A note on this mapping: Decimal arithmetic is assumed rather than assessed; it is tagged here because every rate and unit question is written in decimals.
Percentages, percent change, discount, tax and interest.
Ratios, rates, proportional relationships and unit conversion.
Proportional relationships: the constant of proportionality from a table, a graph or an equation.
Reading and interpreting graphs, tables and scatterplots.
Growth and decay models expressed as a constant percent rate.
A note on this mapping: The SAT splits exponential work: the symbolic side sits in Passport to Advanced Math, the "population grows 4% a year" side in Problem Solving and Data Analysis.
Probability of a single event from counts, tables and two-way tables.
Conditional and compound probabilities read from two-way tables.
Relative frequency, proportional reasoning and prediction from observed data.
Probabilities of compound events, almost always presented as a two-way table.
A note on this mapping: The SAT rarely asks for a multi-stage probability in the abstract; it asks for one read out of a table of counts, which is the same computation in another dress.
Reading and interpreting tables, bar graphs, histograms, line graphs and two-way tables.
Mean, median and mode, and the effect of adding or removing a value.
Range and the comparison of spread between two data sets.
Scatterplots, lines of best fit, and interpreting slope and intercept in context.
Random sampling, inference about a population, and margin of error.
Standard deviation as a comparison of spread between data sets.
A note on this mapping: The SAT asks students to compare standard deviations qualitatively rather than to compute one, so this skill goes further than the test does.
Two-way tables: joint, marginal and conditional relative frequencies and association.
Reading histograms, dot plots and box plots; shape, centre and spread of a distribution.
Lines of best fit, residuals and the strength of a linear association.
Percent growth and decay, compound interest and exponential models in context.
Proportions of a normal distribution from the mean and standard deviation.
The 21 skills that cover it
- DecimalsRead, compare and compute with decimals, and convert between decimals and fractions.Read the lesson →
- PercentsTreat a percent as a fraction out of 100 and solve percent-of, percent-change and discount problems.Read the lesson →
- Ratios & ProportionsCompare quantities with ratios, find unit rates, and solve proportions that scale a relationship up or down.Read the lesson →
- Proportional RelationshipsRecognise when two quantities grow in lockstep, find the constant of proportionality from a table, a graph or an equation, and compare unit rates across representations.Read the lesson →
- Graphs, Tables & EquationsMove fluently between the four faces of a function: equation, table, graph and words.Read the lesson →
- Exponential FunctionsModel repeated growth and decay with y = a * b^x, and contrast constant differences with constant ratios.Read the lesson →
- Outcomes & ProbabilityMeasure how likely something is on a scale from 0 to 1 by comparing favourable outcomes with all the outcomes there are.Read the lesson →
- Complements, Or & AndCombine probabilities: the complement rule for "not", the addition rule for "or", and the multiplication rule for independent events.Read the lesson →
- Experimental ProbabilityEstimate a probability by running the experiment and counting, then use that estimate to predict what a longer run will do.Read the lesson →
- Compound EventsWork out probabilities for experiments with more than one stage, and keep track of whether the first stage changes the second.Read the lesson →
- Reading Data DisplaysPull exact answers out of tables, bar charts, pictographs, two-way tables and line graphs without being misled by the picture.Read the lesson →
- Mean, Median & ModeSummarise a data set with a single number, and choose the summary that tells the truth about the data you actually have.Read the lesson →
- Range & SpreadMeasure how spread out a data set is with the range, the quartiles and the interquartile range, and use the spread to spot outliers.Read the lesson →
- Scatter Plots & TrendsPlot two measurements against each other, describe the association you see, and fit a straight line you can predict from.Read the lesson →
- Samples & InferenceUse a sample to say something about a population you cannot count, and be honest about how much the answer could be out by.Read the lesson →
- Standard Deviation & z-scoresMeasure spread with the average squared distance from the mean, and use z-scores to compare values from different data sets.Read the lesson →
- Two-Way TablesCross two yes-or-no questions in one table, turn the counts into relative frequencies by row or column, and say whether the answers to one question lean on the other.Read the lesson →
- Histograms, Box Plots & ShapeRead a dot plot, a histogram and a box plot, build the five-number summary a box plot is drawn from, describe the shape of a distribution as symmetric or skewed, and compare two distributions by centre and spread.Read the lesson →
- Correlation & RegressionUse a fitted line to predict and to measure how far each point misses it, read the strength and direction of a relationship from the correlation coefficient r, and keep correlation apart from causation.Read the lesson →
- Compound Interest & Exponential ModelsTurn a percent rate into a growth factor, compound it monthly, daily or continuously with e, and build the exponential model behind interest, population and half-life problems.Read the lesson →
- The Normal DistributionUse the bell curve to turn a value into a proportion and back: the empirical rule, z-scores with a table, percentiles, the value behind a percentage, and comparing scores from different distributions.Read the lesson →
What a student should be able to do
- Compare and order decimals using place value.
- Add, subtract, multiply and divide decimals.
- Convert between decimals and fractions in both directions.
- Round decimals and use them in money and measurement problems.
- Convert among percents, decimals and fractions.
- Find a percent of a number, mentally where possible.
- Find the whole given a part and a percent.
- Compute percent increase, decrease, discount and tax.
- Write and simplify a ratio, and find an equivalent ratio.
- Compute a unit rate and use it to compare deals.
- Solve a proportion for an unknown value.
- Use proportional reasoning for scaling, recipes and maps.
- Decide whether a table, a graph or an equation shows a proportional relationship.
- Find the constant of proportionality k and write the equation y = kx.
- Read the unit rate off a graph as the y-value at x = 1 and interpret the point (1, k).
- Compare two proportional relationships given in different forms.
- Build a table of values from an equation.
- Read a slope and intercept off a graph or a table.
- Match a graph to its equation.
- Describe a function in words from any representation.
- Evaluate an exponential function at a given input.
- Identify growth and decay from the base.
- Write an exponential model from a starting amount and a rate.
- Compare linear and exponential growth over time.
- List the sample space of a one- or two-stage experiment and count its outcomes.
- Write the probability of an event as a fraction in lowest terms.
- Express the same probability as a fraction, a decimal and a percent.
- Describe an event as impossible, unlikely, even, likely or certain, and compare two events.
- Use P(not A) = 1 - P(A) to find the probability of a complement.
- Add probabilities for events that cannot both happen, and subtract the overlap when they can.
- Multiply probabilities for independent events joined by "and".
- Answer an "at least one" question by working with the complement instead.
- Compute a relative frequency from a table of trial results.
- Predict how often an outcome will occur in a longer run of trials.
- Compare an experimental probability with a theoretical one and say why they differ.
- Explain why more trials give a more trustworthy estimate.
- Find the probability of a two-stage event with replacement.
- Adjust both the numerator and the denominator when there is no replacement.
- Read a probability off an organised list or a two-way table of a sample space.
- Handle an "at least one" compound event through its complement.
- Read a value, a total and a difference from a frequency table or bar chart.
- Use the key of a pictograph to turn symbols back into counts.
- Read a cell, a row total and a column total from a two-way table.
- Describe how a quantity changes over time from a line graph.
- Compute the mean of a small data set.
- Find the median of a data set with an odd or an even number of values.
- Identify the mode, including when there is more than one or none at all.
- Say which average describes a data set best when an outlier is present.
- Compute the range of a data set.
- Find the lower and upper quartiles of an ordered data set.
- Compute the interquartile range and say what it measures that the range does not.
- Test a value for outlier status with the 1.5 x IQR rule.
- Describe an association as positive, negative or absent from a scatter plot.
- Find the slope of a line of best fit through two points on it.
- Use a trend line to predict a value, and say when the prediction is trustworthy.
- Interpret the slope and the intercept of a trend line in context.
- Estimate a population total from the proportion found in a random sample.
- Judge whether a sampling method is likely to be representative.
- Estimate a population size with the capture-recapture method.
- State a margin of error and the interval of plausible values around an estimate.
- Compute the variance of a small data set from its mean.
- Compute the standard deviation and state it in the units of the data.
- Convert a value to a z-score and read a z-score back into a value.
- Apply the 68-95-99.7 rule to a roughly bell-shaped data set.
- Complete a two-way table from a description using row and column totals.
- Compute joint, marginal and conditional relative frequencies as fractions or percents.
- Compare a conditional relative frequency across rows to decide whether there is an association.
- Build a two-way table from survey results and read it critically.
- Read counts and totals from a dot plot or a histogram.
- Find the five-number summary of a data set and read a box plot back into it.
- Describe the shape of a distribution and say which summary of centre suits it.
- Compare two distributions by their centres and their spreads.
- Use a given regression equation to predict a value and interpret its slope and intercept in context.
- Compute a residual as actual minus predicted, and say what its sign means.
- Interpret a correlation coefficient r for strength and direction, and match r to a scatter plot.
- Explain why a strong correlation does not by itself show that one variable causes the other.
- Write an exponential model from a starting amount and a percent growth or decay rate.
- Compute compound interest with n compounding periods per year, and continuous growth with e.
- Model half-life and population change, and find a growth factor from two readings.
- Compare models and rates, including the effective annual rate.
- Use the empirical rule to find the proportion of a normal distribution within or beyond 1, 2 or 3 standard deviations.
- Convert a value to a z-score and use a table to find the proportion below, above or between values.
- Find the value that sits at a given percentile.
- Compare two values from different normal distributions using z-scores.