Problem-Solving & Data Analysis
Ratios, percentages, scatterplots, and probability. The category where most students lose points to careless mistakes -- learn to be precise.
Ratios & Rates
Rate = slope. In any graphical or linear data question, rate is your cue for change in y over change in x.
Scratch paper is mandatory: never do unit conversions in your head.
Scale factor rule: for similar shapes, sides are k, area is k^2, volume is k^3.
Random = unbiased: for a ratio to be generalized to a population, the sample must be random.
Percentages
"Is/Was" = equals. The most reliable way to turn word problems into math.
100% is your starting point. Always add to or subtract from 100 when the problem mentions increase or decrease.
You must keep the percentage on the number it is intended for. Do not switch it to the resulting number.
Random = generalizable. A percentage from a sample can only be generalized if the sample was random.
Scatterplots & Data
Desmos shortcuts: use Zoom Fit to automatically scale axes to the data.
Mean = finger balance point. Median = resistant to outliers. Standard deviation = how much data varies from the mean.
"Is/Was" = equal sign for all word problem translations.
Higher sample size = lower margin of error.
Probability
Total must come first. You cannot pick a target until you know the boundaries of your population.
Target must be a subset of the total. If the numerator is not part of the denominator group, your logic is flawed.
"Is/Was" = equals for any probability word problem involving variables.
Randomization is mandatory for any probability-based study to establish cause and effect.