← Back to AMC course

Full AMC 12 Mock · No. 1

AMC 12 · 25 problems · 75 min
AMC 12 contest simulation: 25 problems in 75 minutes. AMC 12 leans harder on algebra, complex numbers, logs, and trig than AMC 10 — the hard tail (#21-#25) needs Newton's sums, vectors, advanced NT, generating functions. Scoring: +6 correct, 0 wrong, +1.5 blank (random guessing across 5 options averages 1.2 — less than blank). AIME cutoff via AMC 12: ~100 pts (17 correct + 8 blank). Year-8 honest take: AMC 12 is normally taken at grades 11-12. A Year-8 strong first attempt: 30-50 pts. The 1% problems (#21-#25) require the AMC 12 1% lessons — Newton's sums, orders of elements, advanced trig, etc.
Year-8 notation glossary — open this BEFORE you start
(nk)\binom{n}{k}
Choose kk from nn. (52)=10\binom{5}{2} = 10.
n!n!
n×(n−1)×⋯×1n \times (n-1) \times \dots \times 1. 5!=1205! = 120.
Roots of P(x)P(x)
Values of xx where P(x)=0P(x) = 0. Roots of x2−5x+6x^2 - 5x + 6 are 2,32, 3.
e1,e2,…e_1, e_2, \dots (Vieta)
Elementary symmetric sums of roots: e1=∑rie_1 = \sum r_i, e2=∑i<jrirje_2 = \sum_{i<j} r_i r_j, etc. Read directly from polynomial coefficients.
pkp_k (power sum)
r1k+r2k+⋯r_1^k + r_2^k + \cdots — sum of kk-th powers of the roots. See Newton's Sums lesson.
ordn(a)\text{ord}_n(a)
Smallest positive kk with ak≡1(modn)a^k \equiv 1 \pmod n. See Orders of Elements lesson.
∣z∣|z|
Modulus of complex z=a+biz = a + bi: ∣z∣=a2+b2|z| = \sqrt{a^2 + b^2}.
u⋅v\mathbf{u} \cdot \mathbf{v} (dot product)
u⋅v=u1v1+u2v2\mathbf{u} \cdot \mathbf{v} = u_1 v_1 + u_2 v_2; perpendicular iff zero.
log⁡bx\log_b x
Power of bb giving xx. log⁡28=3\log_2 8 = 3.
How scoring works
  • +6 points for each correct answer.
  • 0 points for each wrong answer.
  • +1.5 points for each question left blank — so guessing randomly is usually worse than leaving it blank.
  • Max possible: 150 points.