Mock Final B, Paper 8

For sections lettered B, with applications to biology and the life sciences. The whole course, ending with Taylor polynomials, Newton’s method and differential equations: solving them, slope fields, Euler’s method, logistic growth and phase lines. Twenty short answers, then five longer problems in parts. Papers 5 to 8 each have one capstone part, the shape of the hardest question on a final.

Before you start

This is a closed-book exam. Calculators, notes and other aids may not be used.
Questions 1 to 20 are short: only the final answer is marked.
Questions 21 to 35 are five longer problems, each in three parts, set out in the steps a marker would look for; each part is marked on its answer.
Answers must be simplified and calculator-ready: write pi/3 or sqrt(2), not a decimal approximation.
Some answers are formulas, such as a derivative or the equation of a line. Type them in the variables the question uses.
Every question is worth the marks shown beside it. There is no penalty for a wrong answer.
You may move between questions freely and flag any question to come back to.
Your answers are kept in this browser as you go, so a refresh will not lose your work. Only a submitted paper counts towards your progress.
At 0:00 the paper is submitted as it stands.