Section 3 of 3

Regression: let the tilde solve it

The 8 chapters

1. Chapter 3.1

   Single Variable Equations

   Turn any equation into a regression by swapping x for x1 and equals for a tilde.

   What you practise

   • Recognising the pattern: any expression set equal to another expression
   • The two changes: x becomes x1, equals becomes tilde
   • Reading x1 and then substituting it into the expression the question asks for
   • "Is equivalent to" counts as an equals sign
   • When you can't use regression: nothing is set equal to anything except the function definition
   • Regression returns one solution only

2. Chapter 3.2

   Constants

   Solve for a constant by letting the variable vary across a list of values.

   What you practise

   • Recognising the pattern: the question asks for a constant, not the variable
   • Why the first result is wrong – change x1 and the "constants" change with it
   • Constants have to stay constant while the variables vary
   • Setting x1 = [1...10] to simulate the variable varying
   • Any list works as long as it doesn't contradict the question
   • How many numbers you need: more than the number of constants you're solving for
   • random(10) as a shortcut
   • The check: if you're solving for a constant, a variable should never appear in the regression parameters
   • When you don't need the list – the question already tells you what the variable equals
   • Worked example: adding {k > 0} so every stated condition is met

3. Chapter 3.3

   Infinite Solutions

   Use regression when the question tells you there are infinitely many solutions.

   What you practise

   • Recognising the pattern: the question states there are infinitely many solutions and asks for a constant
   • Why regression works here – infinite solutions means the two sides are literally the same graph
   • Setting left side ~ right side with x1 = a list of numbers
   • Only when infinite solutions is given, never when it's one of the answer choices
   • Never try it for no solutions, one solution or two solutions

4. Chapter 3.4

   Systems of Equations

   Solve systems with bracket regression, matching every left side to every right side.

   What you practise

   • Why two separate regressions don't work – Desmos doesn't link the two x's
   • Bracket regression: every left side in one list ~ every right side in the other
   • The order of the two lists has to match
   • Deleting the lists before you ask for x1 or y1, or Desmos gets confused
   • What it's really doing (86 = 86, 12 = 12) – the same idea as x1 = a list
   • The percent word-problem shape
   • Building it as L = [...], R = [...] then L ~ R, so you can see whether the sides really match
   • You can't set a variable equal to a list once you're using brackets
   • Varying one variable by hand instead, to check the constant holds
   • When the question says "n is a constant", everything else is a variable
   • Don't over-constrain – pinning both variables makes the system impossible to solve
   • When the constant won't stay constant
   • Doing it by graphing instead: graph both equations and read the intersection

5. Chapter 3.5

   Given Points

   Turn the given points into a table and fit the right equation through them.

   What you practise

   • Recognising the pattern: any time the question gives you points
   • Only graph the points you know, never the one you're solving for
   • You can graph a point containing a constant, as long as that isn't the constant you want
   • The three steps
   • Method 1: the add regression drop-down
   • Method 2: typing the custom regression yourself
   • The only two equations you have to memorise
   • Regression won't draw the graph unless it's in y = form; duplicate the line and strip the regression to see it
   • How many points you need
   • The one exception: standard form of a line
   • When the regression refuses to pass through the points
   • Zooming out when the question asks for the greatest possible value
   • What a table actually is: x1 = [list] and y1 = [list]

6. Chapter 3.6

   Isolation

   Rearrange a formula by giving every constant a different value and testing each answer choice.

   What you practise

   • Recognising the pattern: "expresses R in terms of P, Q and F"
   • Type the equation and change equals to tilde
   • Give every constant a different value
   • Type each answer choice and see which one equals the isolated constant

7. Chapter 3.7

   Choosing Your Method

   Decide quickly whether a question is a graphing question or a regression question.

   What you practise

   • Whether the question can be done in Desmos at all
   • Can you use regression, vs is the graph faster
   • The branches that don't use regression
   • The regression branches

8. Chapter 3.8

   Desmos Theory

   Meet every condition the question states, then type in what is asked and read the answer.

   What you practise

   • The framework: meet every condition the question states, then type in what's asked and read the answer
   • Turning a question into a checklist of conditions
   • Worked example: an absolute value function with a > b > 87 and two function values
   • Solution 1, regression: define the function, write the two conditions, add the constraint
   • Solution 2, sliders: pick any two numbers that satisfy the constraint, define the constants, type the expression
   • Constants go on the left of the equals sign and the value on the right
   • Confirming the numbers you picked don't matter by moving them