SHSAT Math practice: topics and sample problems

What SHSAT Math covers

The Math section draws on middle-school content, but questions often combine several ideas in one problem.

• Number sense: fractions, decimals, percents, ratios, and rates.
• Algebra: expressions, linear equations, inequalities, and systems.
• Geometry: angles, area, perimeter, volume, and the Pythagorean theorem.
• Probability, statistics, and data interpretation.
• Multi-step word problems.

Sample problem: percent change

A jacket costs $80. It is discounted 25%, and then the sale price is discounted another 10%. What is the final price?

Solution: 25% off leaves 75% of $80, which is $60. Another 10% off leaves 90% of $60, which is $54. The final price is $54, not $52. Successive discounts do not simply add together.

Sample problem: ratios

The ratio of boys to girls in a club is 3:5. If there are 40 students, how many are girls?

Solution: The ratio has 3 + 5 = 8 parts, so each part is 40 ÷ 8 = 5 students. Girls make up 5 parts, or 25 students.

Sample problem: grid-in

If 3x − 7 = 2x + 5, what is the value of x?

Solution: Subtract 2x from both sides to get x − 7 = 5, then add 7 to get x = 12. On grid-in questions there are no answer choices to check against, so substitute the answer back: 3(12) − 7 = 29 and 2(12) + 5 = 29.

Habits that raise math scores

• Write every step; mental math causes most careless errors without a calculator.
• Re-read the question before choosing an answer to confirm what is being asked.
• Estimate first so unreasonable answers stand out.
• Skip and return to long problems instead of getting stuck.
• Keep an error log and review it weekly.