SAT Math Pattern Recognition Set

Two different scenarios in a word problem (two unknowns, a total count and a total cost)

Write each scenario as its own equation in Standard Form (Ax + By = C). You're building a system. Solve by substitution.

A starting value plus a constant rate of change

Use slope-intercept form (y = mx + b). Starting value is b, the rate is m.

A value doubles, halves, triples, or changes by a factor at set intervals

Use the exponential growth/decay formula y = a(b)^x. Starting value is a, multiplier is b. The exponent is the number of intervals, not the raw time.

A complete equation with every number filled in, attached to a context

Don't solve. Either interpret what a number means (slope = rate, constant = starting value) or plug in to find a point.

A question mentions both mean and median

It's testing the outlier effect. The mean gets dragged toward the outlier, the median barely moves.

Three numbers given as percentages of each other (a is 50% of b, b is 30% of c)

Treat each statement as its own equation and chain them. Substitute down the line to solve.

The problem has a two-way table of counts

It's a probability question. Read the condition to pick the right denominator (row total, column total, or grand total).

The phrase "selecting at random" or "a random sample"

It's a statistics/sampling problem. Find the sample proportion and scale it up to the full population.

Parallel lines cut by a transversal

Use corresponding angles (equal) or alternate interior angles (equal). Same-side interior angles add to 180. Every angle is one of two values.

A right triangle

Two sides and want the third → Pythagorean theorem. An angle is involved → SOHCAHTOA.

You see an angle written as 90 - x

Use the complementary angle theorem: sin(x) = cos(90 - x) and cos(x) = sin(90 - x).

You see a sqrt(3)

Likely a 30-60-90 triangle. Sides are in ratio x : x(sqrt3) : 2x.

You see a sqrt(2)

Likely a 45-45-90 triangle. Sides are in ratio x : x : x(sqrt2). The hypotenuse carries the sqrt(2).

An equilateral triangle (you need height or area)

Drop an altitude to split it into two 30-60-90 triangles, then solve for the height.

A square (the diagonal matters)

The diagonal splits it into two 45-45-90 triangles. The diagonal is side x sqrt(2).

Two triangles with no mention of area

Use similar triangles. Find the scale factor from a matching pair of sides, then apply it to the side you want.

Two similar non-triangle shapes

Use the scale factor: lengths scale by k, areas by k squared, volumes by k cubed. Don't mix them up.

One shape inscribed in another

Find the length they share (square's diagonal = circle's diameter, etc.). That shared length bridges the two shapes.

A pyramid

Probably surface area, which needs slant height. Watch the difference between vertical height and slant height.

A circle with a "pizza slice" sector

Use the fraction of the circle: central angle over 360. Multiply by circumference for arc length, by area for sector area.

A line tangent to a circle

The radius to the point of tangency is perpendicular to the tangent. This creates a right triangle to solve.

Multiple data points listed

Put them in a Desmos table and run a regression (y1 ~ mx1 + b) to find the line or curve of best fit.

The problem asks for a number of solutions (0, 1, 2, infinite)

Graph it in Desmos with the unknown constant as a slider. Slide until the graph shows the condition.

A single-variable equation

Graph it in Desmos (no table) and read the x-intercepts, or graph both sides and read the intersection.

More unknowns than equations, but a useful constraint (x > 1, "for all real x")

The constraint is the missing piece. "For all x" means match coefficients on both sides.

"Which of the following is equivalent to..."

Graph the original and each candidate in Desmos. The equivalent one makes the identical graph. Or plug in a test number.

"Is (expression) a factor of (polynomial)"

Graph both in Desmos and check for a shared x-intercept. A factor's root must also be a root of the polynomial.

Answer choices contain variables (p, z, w)

Don't solve symbolically. Plug in a simple number, run it through the problem, and test each choice with that same number.

The problem contains an altitude

Use the 3 altitude formulas or similar triangles to solve.

The problem includes a function with different input/output combinations.

Use regression w/o a table (with functions) to solve.