| Section | Questions | Time | Calculator | Weight |
|---|---|---|---|---|
| I, Part A | 28 MC | 80 min (~2.9 min/q) | 🚫 none | 62.5% total for Section I |
| I, Part B | 12 MC | 40 min (~3.3 min/q) | 📱 graphing required | (with Part A) |
| II, Part A | FRQ 1 & 2 | 30 min | 📱 graphing required | 37.5% total for Section II |
| II, Part B | FRQ 3 & 4 | 30 min | 🚫 none | (with Part A) |
Content spread (Section I): Unit 1 ≈ 30–40%, Unit 2 ≈ 27–40%, Unit 3 ≈ 30–35%. Unit 4 (parametrics, vectors, matrices) is not assessed — if a practice resource drills those for the AP exam, it's mis-aimed.
No formula sheet. Everything in Lessons 1–24 rebuilds from a small kernel (unit circle values, the transformation template, exponent/log dictionary, sum formulas) — rebuild beats recall.
maximum is a local max: check endpoints on closed intervals (the Lesson 3 trap).FRQ 1 — Non-periodic modeling (calc). Rhythm: compute AROC → interpret with units → justify/produce a model (differences, ratios, or regression) → predict → state a limitation. Magic sentences: "average rate of change of ___ per ___"; "outside the observed data"; "the model predicts impossible values beyond x = …".
FRQ 2 — Periodic modeling (calc). Pipeline: midline = (max+min)/2 → amplitude = (max−min)/2 → period from the story → b = 2π/T → pick sin/cos + sign from the start position. Check t = 0 and half-period. Part (c) is a rate sentence: fastest at midline crossings, momentarily zero at extremes.
FRQ 3 — Symbolic manipulations (no calc). Exponent/log dictionary, inverse-solving, identity work. Rituals: placeholder zeros in division, extraneous-solution check on every log equation, exact form unless told otherwise, x = 0 spot-checks after rewrites.
FRQ 4 — Communicating about functions (no calc). Every claim gets a because-clause tied to rates of change, definitions, or structure: "increasing at a decreasing rate because the AROCs over successive equal intervals are positive and decreasing." Use limit notation for end behavior and asymptotes. Vocabulary is the rubric: concave, multiplicity, period, midline, one-to-one, residual.
Two passes recommended before mock exam 2:
1. (A). (27 − 1)/(3 − 1) = 13. [L1]
lim x→−∞ (−2x⁴ + 7x) =2. (B). Leading term −2x⁴: even degree, negative → both ends −∞. [L5]
3. (C). (x−1)(x+1)/(x−1): hole at x = 1, height = simplified (x+1) at 1 = 2. [L6]
4. (D). n − 1 ≥ 4 → degree ≥ 5. [L3]
5. (A). Divide: x² + x + 1 = (x − 1)(x + 2) + 3 → y = x + 2. [L7]
6. (C). All even exponents: x⁴ − 3x². [L4]
7. (B). +2 inside → left 2; −3 outside → down 3. [L8]
8. (A). 2^(x+1) = 2⁵ → x = 4. [L11]
9. (B). x = 4^(3/2) = (√4)³ = 8. [L15]
10. (B). Three half-lives: 80 → 40 → 20 → 10 g. [L12]
11. (C). 2 ln x + ln y. (B) doubles y's log too. [L15]
12. (D). y = eˣ + 2 → x = ln(y − 2): ln(x − 2). [L14/L15]
13. (A). actual − predicted = 50 − 54 = −4 (model overestimates). [L12]
14. (C). Straight on semi-log ⇔ exponential. [L16]
15. (D). QII, reference π/6, sine positive: 1/2. [L17]
16. (B). 2π/2 = π. [L19]
17. (A). tan(π/3) = √3 → π/3 (in arctan's range). [L20]
18. (C). Cosine positive in QI and QIV: π/4, 7π/4. (A) is sine's symmetry. [L21]
19. (A). cos 2θ = 1 − 2sin²θ = 1 − 2/9 = 7/9. [L22]
20. (D). n = 4 even → 2n = 8 petals. [L23]
Scoring guide: 18–20 → you're ready for Mock Exam 2 at full timing. 14–17 → revisit the lessons named beside your misses, then mock. Below 14 → redo the (e) sections of your three weakest lessons before mocking.
Let f(x) = (2x² − 2x − 12)/(x² − 9).
(a) (i) Write f in factored form and state its domain. (ii) Classify the graph's behavior at x = 3 and x = −3, with multiplicity justification. Give the coordinates of any hole.
(b) (i) Using limit notation, describe the end behavior of f and identify the horizontal asymptote. (ii) Justify with the ratio of leading terms.
(c) (i) Find the zeros and the y-intercept of f. (ii) A student claims f is positive everywhere to the right of its vertical asymptote. Using a sign analysis on the interval between the asymptote and the zero — evaluate f at one convenient point if helpful — assess the claim.
(a) [2 pts] (i) [1 pt] f(x) = 2(x² − x − 6)/((x − 3)(x + 3)) = 2(x − 3)(x + 2)/((x − 3)(x + 3)); domain x ≠ ±3. (ii) [1 pt] At x = 3: multiplicities 1 = 1 → hole; simplified form 2(x + 2)/(x + 3) at x = 3: 2(5)/6 = 5/3 → hole at (3, 5/3). At x = −3: denominator only → vertical asymptote x = −3.
(b) [2 pts]
(i) [1 pt] lim x→−∞ f(x) = 2 and lim x→∞ f(x) = 2; horizontal asymptote y = 2.
(ii) [1 pt] Numerator and denominator have equal degree, so for large |x| the function behaves like 2x²/x² = 2.
(c) [2 pts] (i) [1 pt] Zero: x = −2 (from the surviving factor x + 2; x = 3 is a hole, not a zero) → (−2, 0). y-intercept: f(0) = (−12)/(−9) = 4/3 → (0, 4/3). (ii) [1 pt] The claim confuses "right of the asymptote" with "always positive." Between the asymptote x = −3 and the zero x = −2, test x = −2.5: simplified f = 2(−0.5)/(0.5) = −2 < 0. So f is negative on (−3, −2) and only becomes positive for x > −2. The claim is false — the graph emerges from −∞ at the asymptote, crosses zero at x = −2, and then stays positive (approaching y = 2, passing through the hole's gap at x = 3).
1. (A). (27 − 1)/(3 − 1) = 13. [L1] 2. (B). Leading term −2x⁴: even degree, negative → both ends −∞. [L5] 3. (C). (x−1)(x+1)/(x−1): hole at x = 1, height = simplified (x+1) at 1 = 2. [L6] 4. (D). n − 1 ≥ 4 → degree ≥ 5. [L3] 5. (A). Divide: x² + x + 1 = (x − 1)(x + 2) + 3 → y = x + 2. [L7] 6. (C). All even exponents: x⁴ − 3x². [L4] 7. (B). +2 inside → left 2; −3 outside → down 3. [L8] 8. (A). 2^(x+1) = 2⁵ → x = 4. [L11] 9. (B). x = 4^(3/2) = (√4)³ = 8. [L15] 10. (B). Three half-lives: 80 → 40 → 20 → 10 g. [L12] 11. (C). 2 ln x + ln y. (B) doubles y's log too. [L15] 12. (D). y = eˣ + 2 → x = ln(y − 2): ln(x − 2). [L14/L15] 13. (A). actual − predicted = 50 − 54 = −4 (model overestimates). [L12] 14. (C). Straight on semi-log ⇔ exponential. [L16] 15. (D). QII, reference π/6, sine positive: 1/2. [L17] 16. (B). 2π/2 = π. [L19] 17. (A). tan(π/3) = √3 → π/3 (in arctan's range). [L20] 18. (C). Cosine positive in QI and QIV: π/4, 7π/4. (A) is sine's symmetry. [L21] 19. (A). cos 2θ = 1 − 2sin²θ = 1 − 2/9 = 7/9. [L22] 20. (D). n = 4 even → 2n = 8 petals. [L23]
Scoring guide: 18–20 → you're ready for Mock Exam 2 at full timing. 14–17 → revisit the lessons named beside your misses, then mock. Below 14 → redo the (e) sections of your three weakest lessons before mocking.
🎯 Final tip: The exam rewards systems, not heroics: the quarter-period ruler, the multiplicity sort, the log dictionary, the residual sentence, the range triple. You've built all of them across 25 lessons. Mock Exam 2 under real timing is the dress rehearsal — take it in one sitting, with the calculator rules enforced, and grade yourself with the rubrics. Then trust the systems.