SAT Math: Problem-Solving, Data Analysis, Geometry and Trigonometry

Write the units down

Nearly every rate and proportion question is decided by units. Minutes against hours, centimetres against kilometres, dollars per litre against litres per dollar - write what you have and what you want, and the arithmetic follows.

Percent change is always over the original

The change divided by the amount you started with, not the amount you ended with. Two successive changes multiply rather than add: a 20% cut followed by another 20% cut leaves 64% of the price, not 60%.

Statistics questions are about how the data was collected

For a conclusion to apply to a whole population, the sample has to have been drawn at random from that population - and for the conclusion to be about cause rather than association, subjects have to have been assigned to groups at random. The two are separate conditions, and most wrong choices fail exactly one of them.

What is on the reference sheet, and what is not

The area and volume formulas, the Pythagorean theorem and both special right triangles are given to you on screen. The trigonometric ratios, the slope and distance formulas, and the equation of a circle in the xy-plane are not - those you need to know.

Numbers about the real world, and how far they can be trusted.

Ratios, rates, proportions, and units

Scaling one quantity against another, and converting between units without losing a factor.

Percentages

Percent of, percent change, and two changes applied one after the other.

One-variable data (center and spread)

Mean, median and spread, read from a table, a list or a bar graph.

Two-variable data (scatterplots)

Scatterplots and lines of best fit - reading a prediction off the model and comparing it with the data.

Probability

The share of outcomes that count, often from a two-way table.

Inference from sample statistics

Applying a sample's result to the population it was drawn from, with a margin of error.

Evaluating statistical claims

Whether the study design supports the conclusion someone has drawn from it.

Shapes, angles and the xy-plane.

Area and volume

Areas of plane figures and volumes of solids, including scaling and composites.

Lines, angles, and triangles

Parallel lines, angle relationships, similar triangles and the angle sum.

Right triangles and trigonometry

The Pythagorean theorem, the special right triangles, and sine, cosine and tangent.

Circles

Radius, area and circumference, arcs and sectors, and the equation of a circle in the xy-plane.

What helps

• Read the axis labels before the shape of the graph

  A scatterplot question is usually decided by a unit or a scale, not by the trend, which is visible at a glance anyway.

• Draw the figure when you are not given one

  Geometry questions written in words are often easy once they are on paper. A rough sketch with the given numbers on it is thirty seconds well spent.

• Learn the three trig ratios properly

  They are not on the reference sheet, they appear in every math section, and they take an evening to learn for good.

Loading the questions...

Practice the rest of it

Every page here ends with two or three questions. The app has hundreds more, sorted by skill, with a full-length test that adapts the way the real one does.