The math crap they're counting on.
The SAT doesn't test whether you can do the math. It tests whether you'll fall for the same twelve traps as everyone else. Here they are, fixed in two lines each.
x² + y² − 6x + 4y − 12 = 0 is a circle. What is its radius?
- A) 5
- B) 12
- C) 13
- D) 25
The 12 traps
Each one shows up on almost every test, and each one has a wrong answer waiting for you in the choices. Cross it out before you start.
The radius is the square root
(x−3)² + (y+2)² = 25, so r = 25The right side is r². Radius is 5. And the center is (3, −2): signs flip.
"Exactly one solution" means the discriminant is zero
One solution, so x = 1Set b² − 4ac = 0 and solve for the unknown constant.
The minimum value is the y, not the x
Vertex at x = 3, so the minimum is 3Plug x = −b/(2a) back in. The minimum is f(3), not 3.
Percents multiply, they don't add
Up 25% then down 20% = up 5%1.25 × 0.80 = 1.00. No change at all.
Inside the parentheses is backwards
f(x − 2) moves the graph left 2f(x − 2) is RIGHT 2. Only the "+3" outside goes the way it looks (up 3).
Squaring creates fake answers
√(2x + 7) = x + 2, so x = 1 and x = −3Check both in the original. −3 gives 1 = −1. Only x = 1.
"No solution" doesn't mean you solved it wrong
(x+3)/(x−2) = 5/(x−2), so x = 2x = 2 makes the denominator zero. No solution is the answer.
A zero at 3 is the factor (x − 3)
p(3) = 0, so (x + 3) is a factorFactor theorem: p(a) = 0 means (x − a). Sign flips.
Area scales by k², volume by k³
Sides 1.5× bigger, so area is 1.5× biggerArea is 2.25× bigger. Double a sphere's radius and volume goes up 8×.
Infinitely many solutions = the same line
Set the two equations equal and solveMake one equation a multiple of the other. Coefficients AND constants must match. If only the coefficients match, it's no solution.
The outlier moves the mean, not the median
3, 5, 5, 8, 9, 30 — "cannot be determined"Mean 10, median 6.5. Big high value → mean > median. You never need to compute standard deviation, just compare spread.
The slope is "per," the intercept is "start"
C = 45 + 0.20m, so 45 is the cost per mile0.20 is the cost per mile (it multiplies m). 45 is the fee when m = 0.
Formulas the reference sheet doesn't give you
The SAT hands you area and volume. These are the ones it makes you remember.
| Situation | What to use |
|---|---|
| How many solutions? | b² − 4ac: positive → 2, zero → 1, negative → none |
| Max or min of a parabola | x = −b/(2a), then plug in for the value |
| Sum / product of solutions | −b/a and c/a (no factoring needed) |
| Growth or decay | a(1 + r)^t grows, a(1 − r)^t shrinks; "every n years" → t/n |
| Same base, solve exponents | 32 = 2⁵, 27 = 3³, then set exponents equal |
| Circle equation | (x − h)² + (y − k)² = r², center (h, k) |
| Arc length / sector area | (θ/360)·2πr and (θ/360)·πr² |
| sin(x°) = cos(y°) | x + y = 90 |
| Percent change | (new − old) / old |
| |A| < c | −c < A < c (sandwich); |A| > c is two separate pieces |
| Density | mass = density × volume; convert units first |
Work through it with a person
One hour, online, with a tutor who has watched hundreds of students fall for these and knows exactly which one you're about to. Bring a practice test you've already taken; the wrong answers are the lesson plan.
- SAT math, including the hard second module
- GED math, from the calculator up
- ACT math if that's the test you're stuck on
Booking opens in a new tab. Weekend and Friday times only for now; more open up as the semester settles.
One trap a day, under 40 seconds
The videos are the cheat sheet, read out loud by someone who's on your side. New one every day.