Percentages — Digital SAT SAT Math revision notes
A 3-page visual revision sheet for Percentages, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Percentages in one look
every percent question is a multiplication once you decide what the whole is
Percent is just a fraction with 100 underneath
- per cent means per hundred, so 37 percent is 37/100 and nothing more. Turn it into a decimal the moment you see it: 0.37
- the word OF means multiply. 37 percent of 250 is 0.37×250
- the word IS marks the part, and the words OF THE marks the whole. Naming those two before touching the arithmetic settles most of these questions
- a percent on its own is meaningless until you know what it is a percent of. Half the wrong options in this topic are the right percent of the wrong base
The four you actually need
- a percent of a number
P=p/100× N - what percent one number is of another
p=part/whole×100 - percent change, always over the OLD value
p=new-old/old×100 - the multiplier form, an increase of p percent
new=old×(1+p/100)
Worked: percent increase
Q. a town's recycling rose from 250 tonnes a month to 320 tonnes a month. What was the percent increase?
- the change: 320-250=70 tonnes
- divide by the OLD value, not the new one: 70/250=0.28
- multiply by 100: 0.28×100=28
Answer: a 28 percent increase
Multipliers worth knowing by sight
- Up 25 percent: multiply by 1.25
- Down 25 percent: multiply by 0.75
- Up 8 percent twice: multiply by 1.08 and again by 1.08
- Down to 40 percent: multiply by 0.40, a fall of 60 percent
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Percentages sheet covers
- Percent is just a fraction with 100 underneath
- The four you actually need
- a percent of a number
- what percent one number is of another
- percent change, always over the OLD value
- the multiplier form, an increase of p percent
- Worked: percent increase
- Multipliers worth knowing by sight
- Up 25 percent
- Down 25 percent
- Up 8 percent twice
- Down to 40 percent
- Worked: up 20 then down 20 is not back where you started
- Worked: working backwards
- Interest, simple against compound
- simple interest, the same amount added each year
- compound interest, a fixed percent each year
- value falling by r percent a year
- Reading a percent off a chart
- Chaining and reversing
- What is the question actually asking for
- Pacing, the calculator, and typed answers
- Traps that cost points
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Percentages the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.
More SAT Math revision notes
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- Circles
- Equivalent Expressions and Polynomials
- Evaluating Statistical Claims
- Inference and Margin of Error
- Linear Equations
- Linear Functions
- Linear Inequalities
- Lines, Angles, Triangles
- Nonlinear Equations in One Variable
- Nonlinear Functions
- Nonlinear Systems
- One-variable Data
- Probability and Conditional Probability
- Ratios, Rates and Proportions
- Systems of Equations
- Triangles and Trigonometry
- Two-variable Data
- Units, Rates and Conversions