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SHSAT: Mathematics

SHSAT · Work through your exam, one topic at a time.

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Mathematics

What the section covers

Math spans arithmetic (fractions, decimals, percents, ratios, proportions), algebra (linear equations and inequalities, systems, exponent rules, factoring, quadratics), geometry (angles, triangles including similarity and the Pythagorean theorem, circles, area and volume, coordinate geometry), and data (mean, median, range, counting, simple probability). About a third of the questions are grid-ins with no answer choices, so estimation and clean arithmetic matter as much as method.

Traps to expect

Percent language causes the most errors: a 25% discount followed by 8% tax is not 33%, because each percent applies to a different base. Average speed is total distance divided by total time, never the average of two speeds. Scale factors behave differently for length, area, and volume. "Must be" questions require a statement true for every permitted value, so test a negative, zero, and a fraction. Also watch units, order of operations, and sign errors when distributing a negative.

Worked example

An $80 jacket is marked down 25%, then 8% tax is added. The discount gives 0.75 × 80 = $60. Tax applies to the sale price: 1.08 × 60 = $64.80. Applying the 8% to the original $80 instead yields $86.40 - the classic wrong answer.

Rule of thumb

With five ordered answer choices, start from the middle choice and test it; one comparison usually eliminates two or three options. On grid-ins, estimate the answer first so a misplaced decimal is immediately obvious.