Are these Nonlinear Equations in One Variable notes free?

Yes. The full 4-page Nonlinear Equations in One Variable sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Nonlinear Equations in One Variable revision sheet cover?

Three families, one habit, The lines that solve most of these, if a product is zero, one factor is zero, the quadratic formula, always available, the discriminant decides how many real solutions, the axis of symmetry, and the vertex x, sum and product of the two solutions, Every quadratic is symmetric, Worked: a quadratic that factors, Pick the method before you start, Where extraneous solutions come from, Worked: a radical equation with a false candidate.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Nonlinear Equations in One Variable — Digital SAT SAT Math revision notes

A 4-page visual revision sheet for Nonlinear Equations in One Variable, 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.

Nonlinear Equations in One Variable revision notes, page 1 of 4 — A preview of page 1 — all 4 pages open full size in the app.

Nonlinear Equations in One Variable in one look

quadratics, radicals and rational equations, and the roots that are not really there

Three families, one habit

quadratic: everything ends up as ax^2+bx+c=0. Factor it if the numbers are friendly, use the formula if they are not
radical: the unknown sits under a root sign. Isolate the root, square both sides, and then CHECK every candidate in the original equation
rational: the unknown sits in a denominator. Multiply through to clear the fractions, and then reject anything that made a denominator zero
the habit both of the last two need is the same: squaring and multiplying up can invent solutions that the original equation never had. Substituting back is not optional here
at 95 seconds a question on average across the 44-question, 70-minute Math section, a quadratic you cannot factor within about fifteen seconds should go straight to the graph or to the formula

The lines that solve most of these

if a product is zero, one factor is zero (x-p)(x-q)=0⇒ x=p or x=q
the quadratic formula, always available x=frac-b±√b^2-4ac2a
the discriminant decides how many real solutions D=b^2-4ac
the axis of symmetry, and the vertex x x=-b/2a
sum and product of the two solutions p+q=-b/a, pq=c/a

Page 1 of 4. The full sheet, all 4 pages, opens free in the app.

What this Nonlinear Equations in One Variable sheet covers

Three families, one habit
The lines that solve most of these
if a product is zero, one factor is zero
the quadratic formula, always available
the discriminant decides how many real solutions
the axis of symmetry, and the vertex x
sum and product of the two solutions
Every quadratic is symmetric
Worked: a quadratic that factors
Pick the method before you start
Where extraneous solutions come from
Worked: a radical equation with a false candidate
Two more pictures worth carrying
Calculator and timing, concretely
Traps that cost points
Tricks that save time

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