SAT Advanced Math

El método, paso a paso

1. 1

   Choose the right quadratic method

   factorise if it factorises; otherwise formula or completing the square

   Check for a simple factorisation first, since it is much faster when available. The discriminant tells you whether one exists, and knowing when to stop looking is worth as much as knowing how to look.

2. 2

   Read a parabola's form for what it reveals

   vertex form y = a(x − h)² + k gives the vertex at (h, k)

   Each form of a quadratic exposes different information: factorised form gives the roots, vertex form gives the turning point, and standard form gives the y-intercept. Questions often ask which form reveals a stated feature.

3. 3

   Recognise exponential growth and decay

   y = a(b)ˣ — growth if b > 1, decay if 0 < b < 1

   Exponential models multiply by a constant factor per period, while linear models add a constant amount. Questions frequently ask students to identify which model a described situation requires, and the word 'each year by a percentage' signals exponential.

4. 4

   Handle function notation as substitution

   if f(x) = 2x + 1 then f(3) = 7 and f(a + 1) = 2(a + 1) + 1

   f(x) is not multiplication — it names an output for a given input. Composite functions such as f(g(x)) mean working from the inside out, which is the step most often reversed.

5. 5

   Use Desmos for graphing questions

   graph both sides and read the intersection

   The built-in graphing calculator turns many equation-solving questions into reading intersections off a graph. On questions asking where two functions are equal, this is often the fastest correct route.

Three forms, three different jobs

Standard form ax² + bx + c shows the y-intercept immediately. Factorised form a(x − p)(x − q) shows the roots. Vertex form a(x − h)² + k shows the turning point. All three describe the same curve, and questions test whether a student knows which one answers a given question.

The recurring question type gives an equation and asks which form displays a particular feature as constants. It requires no calculation at all — just knowing what each form exposes — which makes it a reliable mark for a prepared student.

• Standard form → y-intercept
• Factorised form → roots
• Vertex form → turning point
• Exponential: multiply per period; linear: add per period
• f(g(x)) works inside out

Telling linear from exponential

A quantity increasing by a fixed amount each period is linear. One increasing by a fixed percentage each period is exponential. The distinction is examined directly and it is a reading question rather than a mathematical one.

Population growth, compound interest, radioactive decay and depreciation are all exponential. Wages rising by a fixed sum, or a tank filling at a constant rate, are linear. The phrase 'by a percentage' or 'by a factor of' is the reliable signal.

Why this area matters most for high scores

The hardest questions on the Math section concentrate here, which means students aiming at the upper score bands cannot avoid it. A student secure in algebra and data analysis but weak in advanced math will plateau at a predictable point.

It is also the area where the adaptive second module differs most. Students who perform well on the first module meet noticeably harder advanced math questions in the second, which is where the additional score is available.

How we teach advanced math

We drill the three quadratic forms and what each reveals, as recall rather than as calculation. The questions asking which form displays which feature are free marks for a student who has memorised the mapping and awkward for one who has not.

We also teach Desmos deliberately rather than leaving students to discover it. Knowing that an equation-solving question can be answered by graphing both sides and reading the intersection saves time on precisely the questions where time is shortest.