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Yes. The full 3-page Nonlinear Systems sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Nonlinear Systems revision sheet cover?

What a nonlinear system is asking, The setup, every single time, the curve, in the shape the question hands you, the line, set the two expressions for y equal, then collect on one side, the discriminant of THAT collected quadratic decides how many solutions, Worked: substitution start to finish, Graph it before you solve it, How many solutions does the system have, The same count, drawn twice, Worked: a letter in the coefficients, The three shapes this topic comes in.

Is this for Digital SAT SAT Math?

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

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Nonlinear Systems — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Nonlinear Systems, 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 Systems revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Nonlinear Systems in one look

a line, a curve, and the two, one or none places they meet

What a nonlinear system is asking

a system is two equations that have to hold at the same time. Nonlinear only means one of them is not a straight line, and on this test that curve is nearly always a parabola
a solution is an ordered pair (x,y) satisfying both equations, and on a graph it is a point where the two graphs cross
a line and a parabola can cross twice, touch once, or miss entirely, so the number of solutions is always two, one or zero
the question almost never wants the full pair. Read the last line again: it asks for the positive x, or for y, or for the sum of the solutions

The setup, every single time

the curve, in the shape the question hands you y=ax^2+bx+c
the line y=mx+k
set the two expressions for y equal, then collect on one side Ax^2+Bx+C=0
the discriminant of THAT collected quadratic decides how many solutions D=B^2-4AC

Worked: substitution start to finish

Q. y=x^2-4 and y=x-2. If (x,y) is a solution of the system and x>0, what is the value of y?

both equations already give y, so the two expressions are equal: x^2-4=x-2
collect everything on one side: x^2-x-2=0
factorise: (x-2)(x+1)=0, so x=2 or x=-1
the question fixes x>0, so x=2. Substitute into the easier equation: y=x-2=2-2=0
check the other one: x^2-4=4-4=0, the same y, so the pair (2,0) really does satisfy both

Answer: y=0, from the solution point (2,0)

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Nonlinear Systems sheet covers

What a nonlinear system is asking
The setup, every single time
the curve, in the shape the question hands you
the line
set the two expressions for y equal, then collect on one side
the discriminant of THAT collected quadratic decides how many solutions
Worked: substitution start to finish
Graph it before you solve it
How many solutions does the system have
The same count, drawn twice
Worked: a letter in the coefficients
The three shapes this topic comes in
Find the solution
Count the solutions
Find the constant
Read the graph
Pacing, the calculator and the typed answers
Symbols and terms
Traps that cost points
Tricks that save time

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