IB Math AI SL - May 2025 - Paper 2 - TZ 3 скачать в хорошем качестве

IB Math AI SL - May 2025 - Paper 2 - TZ 3

0:00 - Intro Question 1 - Financial Mathematics: Sequences & Compound Interest (18 marks) 00:11 - 1.a.i) Common difference of arithmetic sequence (SL1.2) 01:53 - 1.a.ii) Finding nth term of arithmetic sequence (SL1.2) 04:17 - 1.b) Showing sum formula for arithmetic sequence (SL1.2) 10:00 - 1.c) Calculating total amount after n years (SL1.2) 12:42 - 1.d.i) Writing compound interest growth factor (SL1.4) 20:44 - 1.d.ii) Comparing arithmetic vs compound interest accounts (SL1.2, SL1.4) 23:04 - 1.e) Finding when compound interest exceeds arithmetic (SL1.2, SL1.4) 34:53 - 1.f) Calculating total compound interest earned (SL1.4) Question 2 - Normal & Binomial Distributions (17 marks) 38:25 - 2.a) Normal distribution probability (SL4.7) 42:58 - 2.b.i) Inverse normal calculation and sketch (SL4.7) 48:36 - 2.c.i) Normal probability within range (SL4.7) 51:40 - 2.c.ii) Expected value calculation (SL4.5) 53:45 - 2.d) Binomial probability for exact value (SL4.7) 56:26 - 2.e) Binomial probability for "at least" (SL4.7) 59:15 - 2.f) Combined probability with independent events (SL4.6, SL4.7) Question 3 - Optimization: Cuboid & Cylinder (20 marks) 1:06:25 - 3.a) Writing relationship between dimensions (SL1.1) 1:07:14 - 3.b) Finding dimensions from volume constraint (SL3.1) 1:11:19 - 3.c) Calculating surface area of cuboid (SL3.1) 1:14:57 - 3.d) Height of cylinder in terms of radius (SL3.1) 1:18:13 - 3.e) Showing surface area expression (SL3.1, SL5.1) 1:24:58 - 3.f) Finding derivative dA/dr (SL5.6) 1:28:39 - 3.g.i) Finding radius to minimize surface area (SL5.8) 1:34:05 - 3.g.ii) Finding minimum surface area (SL5.8) 1:35:24 - 3.h) Comparing total material costs with percentages (SL1.6, SL5.8) Question 4 - Trigonometric Modeling: Tides (13 marks) 1:40:18 - 4.a) Finding period parameter (SL2.5) 1:43:31 - 4.b) Evaluating cosine function at given time (SL2.5) 1:46:04 - 4.c.i) Finding amplitude from graph (SL2.5) 1:48:29 - 4.c.ii) Finding equation of principal axis (SL2.5) 1:51:16 - 4.d) Solving trigonometric inequality for time (SL2.5) 1:35:24 - 4.e) Finding maximum time interval between events (SL2.5) Question 5 - Numerical Integration & Applications (12 marks) 2:04:56 - 5.a) Using trapezoidal rule to find area (SL5.7) 2:13:30 - 5.b) Calculating volume from flow rate (SL3.1, SL5.7) 2:20:38 - 5.c) Finding distance between points (SL3.1) 2:22:55 - 5.d) Finding maximum of quadratic function (SL2.6, SL5.6) 2:25:28 - 5.e) Determining if object clears obstacle (SL2.6)