Math Skills: Clean Setup Beats Long Computation
What is being tested
Arithmetic, fractions, decimals, percents, ratios and proportions, basic algebra, and plane geometry, plus word problems. There is no calculator, so the scoring rewards estimation and a clean setup over long computation.
Concepts to have automatic
- Order of operations and equation solving: isolate the variable by undoing operations in reverse order.
- Fractions and percents: percent change is (new minus old) divided by old, times 100. Of means multiply; per means divide.
- Ratios and unit rates: set up a proportion and cross-multiply, keeping units attached so they cancel.
- Geometry: area and perimeter of rectangles, triangles, and circles; the Pythagorean theorem; triangle angles summing to 180 degrees.
- Averages: total equals average times count, which solves most missing-value average problems.
- Word problems: translate to an equation in symbols before computing anything.
Traps
- Unit mismatches such as minutes versus hours or inches versus feet.
- Percent increase versus percent of: a 20 percent increase on 50 gives 60, not 10.
- Answering the wrong quantity, such as computing the final price when the discount was asked for.
- Distractor choices that match a common partial step.
Worked example
A helicopter flies 135 miles in 2.25 hours. What is the average speed? Speed equals distance divided by time, so 135 divided by 2.25. Multiply both numbers by 4 to clear the decimal: 540 divided by 9 equals 60 miles per hour. Estimate check: 2.25 hours is a little more than 2 hours, and 135 divided by 2 is 67.5, so the answer should be somewhat below 67.5; 60 is reasonable.
Second example: solve 5x minus 8 equals 37. Add 8 to both sides to get 5x equals 45, so x equals 9. Substitute back to verify.
Rule of thumb
Estimate first, compute exactly second, then eliminate any choice outside your estimate.