Math — Advanced Math for the SAT Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Attempting to use the quadratic formula when factoring is faster — wasting 60+ seconds per question
• !Confusing exponential growth (multiply by r each period) with linear growth (add r each period)
• !Misreading function notation: f(a + b) ≠ f(a) + f(b) for nonlinear functions
• !Forgetting to check both solutions of a quadratic equation when the question asks for a specific one (positive, negative, or contextually valid)

Study tips

• 1Memorise the three quadratic-solving methods and when to use each: factoring (integer roots), completing the square (vertex form needed), quadratic formula (messy or complex roots).
• 2Practice reading exponential equations: y = a · b^x. Identify a as the initial value and b as the growth/decay factor. If b > 1, growth; if 0 < b < 1, decay.
• 3For function composition and transformation questions, graph both the original and transformed function in Desmos to confirm your algebraic answer.
• 4Learn vertex form y = a(x−h)² + k — the SAT often asks for the vertex of a parabola, and completing the square or rewriting in vertex form is the fastest path.
• 5Practise substitution in rational equations — extraneous solutions are a common trap.

Sample SAT Math — Advanced Math questions

These sample items mirror the format and difficulty of real SAT questions. Practice with thousands more on the free Koydo question bank.

1. 1

   The function f(x) = x² − 5x + 6 has zeros at:

   • Ax = −2 and x = −3
   • Bx = 2 and x = 3Correct
   • Cx = 1 and x = 6
   • Dx = −1 and x = −6
   Why this answer?

   Factor: x² − 5x + 6 = (x − 2)(x − 3) = 0. Zeros at x = 2 and x = 3.

2. 2

   A bacteria culture starts with 200 cells and doubles every 3 hours. The number of cells after t hours is modelled by:

   • AN(t) = 200 + 2t
   • BN(t) = 200 · 2^(t/3)Correct
   • CN(t) = 200 · 2^t
   • DN(t) = 400t
   Why this answer?

   The culture doubles every 3 hours, so the base is 2 and the exponent is t/3 (number of doubling periods). Starting with 200 cells: N(t) = 200 · 2^(t/3).

3. 3

   Which of the following is equivalent to (x² − 9) / (x − 3)?

   • Ax − 3
   • Bx + 3Correct
   • Cx² + 3x + 9
   • D(x − 3)²
   Why this answer?

   Factor the numerator: x² − 9 = (x − 3)(x + 3). Cancel (x − 3) for x ≠ 3: result is x + 3.