Circles — Digital SAT SAT Math revision notes
A 3-page visual revision sheet for Circles, 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
Circles in one look
a fraction of the whole turn, and one equation built from Pythagoras
Degrees, radians and what the sheet gives you
- the reference sheet tells you a full circle is 360 degrees and 2π radians, and it gives the area and the circumference. That is all of it
- arc length, sector area and the equation of a circle are not on the sheet, so those three are the ones to carry in your head
- a radian is just a different unit for the same turn, so converting is one multiplication and never a formula worth fearing
- answers stay in terms of π far more often than they go decimal. Read the options, or the wording, before you reach for 3.14
The lines to memorise
- circumference and area, both given on the sheet
C=2π r, A=π r^2 - degrees into radians
×π/180 - radians into degrees
×180/π - arc length, angle in degrees
s=θ/360×2π r - sector area, angle in degrees
A=θ/360×π r^2 - arc length when the angle is already in radians
s=rθ
Worked: a conversion each way
Q. convert 150° into radians, then convert 7π/9 radians into degrees
- degrees into radians: 150×π/180=150π/180
- cancel 30 from top and bottom: 5π/6
- the other way: 7π/9×180/π, and the π cancels
- 7×180/9=7×20=140
Answer: 150°=5π/6 radians, and 7π/9 radians =140°
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Circles sheet covers
- Degrees, radians and what the sheet gives you
- The lines to memorise
- circumference and area, both given on the sheet
- degrees into radians
- radians into degrees
- arc length, angle in degrees
- sector area, angle in degrees
- arc length when the angle is already in radians
- Worked: a conversion each way
- An arc and a sector are just fractions of the whole
- Worked: the area of a sector
- Symbols and terms
- Worked: centre and radius from an expanded equation
- The equation of a circle is Pythagoras in disguise
- 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 Circles 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
- Area and Volume
- 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
- Percentages
- Probability and Conditional Probability
- Ratios, Rates and Proportions
- Systems of Equations
- Triangles and Trigonometry
- Two-variable Data
- Units, Rates and Conversions