Problems to study for Math 115 Exam 2

Here is a breakdown of Math 115 Exam 2 by topic. Each problem reference is a link, so you can click on it to see the problem. Your browser should take you to the right page of the exam, but keep in mind that the problem you're looking for might be toward the bottom of the page. Next to each problem you'll see a # character. If you click on that, it should take you to the solution.

Old exam problems should not be the only thing you study. They are designed to test knowledge, not teach it. And there's a danger that you might start thinking you know exactly what will be on the test. While there are some predictable topics, there will undoubtedly be questions on this year's exam which are different from any that have appeared before. So keep in mind that you're training yourself to approach hard problems, not memorizing how to do particular types.

Here's my suggestion for how to use this page:

  1. Try a sampling of problems to identify an area that you need help with.
  2. Go to your book to read about the topic.
  3. Come back here and find more problems on the same topic, to see if you got it.

Don't omit step 2.

I'm not entirely happy with the topics shown below. Please make suggestions on how to better categorize problems.

Let me know any errors you find, and any other feedback you have on how well it works and how to make it more useful. Links to all the exams are at the bottom of the page.

Topic 2001–2012 2013–present
Optimization [track(12)#] [door(10)#] [rectangle(2)#] [trough(10)#] [wire(10)#] [dosage(7)#] [bucket(10)#] [golden eggs(7)#] [bat(10)#] [logistic(3b)#] [box(10)#] [string(7)#] [cylinder(6)#] [gift boxes(1a)#] [telephone line(6)#] [paraboloid cup(4)#] [Octopus(7)#] [octopus2(4)#] [window(8)#] [microphone(5)#] [smokestack(2)#] [Idaho(7)#] [peak oil(2)#] [7#] [turtle river(4)#] [exam score(8)#] [EPA(7)#] [graduation party(3)#] [cattle fence(8)#] [hoophouse(1)#] [gutter(2)#] [prism(3)#] [window(6)#] [love cookie(7)#] [rect under curve(5)#] [fence(3)#] [smokestacks(8)#] [bookcase(2)#] [wire(2)#] [swimming pool(1)#] [festive table(8)#] [gold platinum(6b)#] [garden(4)#] [prison break 1(4)#] [flowers(8)#] [fence(1)#] [paper cup(2)#] [tent(3)#] [conical tank(3)#] [rain shelter(3)#] [station(5)#] [cardboard box(7)#] [wire box(8)#] [pyramid hat(11)#] [washer(8)#] [bucket(9)#] [pyramids(5)#] [sign(6)#] [salt shed(7)#] [garden(8)#] [box model(5)#] [box(10)#] [garden(4)#] [tank(6)#] [donut case(5)#] [donut frosting(6)#] [waffle cones(4)#] [oats(6)#] [data loss(6)#] [coffee(7)#] [box(5)#] [cans(7)#] [beam(8)#] [suitcase(2)#] [Tycho Brahe(6efg)#] [Stan Lee 2(4)#] [garden(2)#] [kite(3)#] [can(3)#] [box(7)#]
Derivatives: Formula [3#] [5#] [7#] [11#] [1a#] [4#] [1#] [5#] [1b#] [2b#] [3#] [6#] [8#] [9a#] [9abc#] [3bc#] [3#] [5#] [U Value(2)#] [car(8c)#] [5a#] [10#] [ship(4)#] [party(9)#]
Tangents through origin [1#] [drive to Chicago(7)#] [9#]
Product/quotient/chain rules [2#] [3#] [4#] [7#] [3#] [3#] [orange juice(10d)#] [3#] [5#] [ideal gas(8)#] [1#] [balloon animal(4)#] [F=ma(5)#] [3#] [1abd#] [kinetic energy(7)#] [gift boxes(1b)#] [8#] [2#] [marathon(4b)#] [2#] [3#] [2#] [4#] [parasitoids(6)#] [6#] [8#] [3#] [3ab#] [gravity(6ab)#] [2#] [1#] [2#] [antihistamine(4d)#] [gold vs oil(5b)#] [7#] [6#] [8b#] [2#] [8#] [Metal ring(8acd)#] [4#] [1#] [5#] [2#] [1ce#] [1#] [1#] [2#] [6c#] [1#] [4#] [1a#] [4a#] [1d#] [1#] [3#] [3c#] [2a#] [6a#] [4#] [1a#] [2a#] [2ab#] [6cde#] [2#] [1#] [1cd#] [1#] [1abc#] [1#] [1#] [3c#] [1b#] [1#] [1#] [5a#]
Inverse function [2#] [Beans to Frogs(8cd)#] [3d#] [soda(2a)#] [plane ticket(9b)#] [8c#] [Metal ring(8a)#] [3#] [water temp(9)#] [3c#] [4b#] [rain bucket(8ab)#] [orchard(8b)#] [4#] [9b#] [1#] [unicycle(1ab)#] [2a#] [6a#] [4#] [2a#] [2c#] [12e#] [toy airplane(3d)#] [1b#] [1c#] [steamer(9)#]
Implicit differentiation [6#] [bungee(7)#] [5#] [Descartes folium(7)#] [4b#] [7#] [ellipse(6)#] [Descartes folium(4)#] [5#] [5#] [hyperbola(3)#] [4#] [ellipse(5)#] [7ab#] [portfolio(6)#] [Kampyle of Eudoxus(7)#] [hyperbola(5)#] [5#] [rose curve(8)#] [3#] [1#] [7#] [2#] [6#] [8#] [11#] [6#] [5#] [7#] [3#] [3#] [10#] [9#] [8#] [2#] [4#] [9#] [4#] [9#] [10#] [8#] [7#] [9#] [3d#] [7#] [8#] [2#] [bowtie(9)#] [10#] [8#] [9#] [6#] [7#] [8#] [steamer(9b)#] [9ab#] [5#] [10#] [7#] [8#]
Families of functions [9#] [7#] [5#] [9b#] [bell curve(4)#] [6#] [5#] [pesticide(4)#] [3#] [3#] [San Diego Zoo(6)#] [4#] [peak oil(2)#] [4#] [2#] [9#] [1#] [FarmVille(1)#] [atomic force(7)#] [4#] [8#] [8#] [7#] [4#] [3#] [5#] [9#] [6#] [ice(9)#] [2#] [7#] [7#] [7#] [7#] [9b#] [7#] [10#] [5#] [2#] [balloon(4)#] [7#] [8#] [oil(8)#] [2#]
Marginal cost and revenue [buses(10)#] [BarBQ Ice Cream(12)#] [average cost(8)#] [widgets(11)#] [4c#] [Mammoth Corp(5)#] [ball bearings(8)#] [orange juice(10)#] [lemonade(3)#] [tutoring(8)#] [truck(8)#] [football tickets(7)#] [salary(9)#] [OSU tickets(10)#] [gift boxes(1bcd)#] [marathon security(6)#] [tiles(8)#] [7d#] [T shirt company(5)#] [WiFi Up High(8)#] [prints(7)#] [building(4)#] [GBC(6)#] [wind turbines(7)#] [social network(5)#] [7cd#] [Canco(6)#] [Minestromnia(3)#] [9a#] [cat clothes(2)#] [ice(9)#] [kale(3)#] [storytelling(9)#] [hot chocolate(10)#] [fruit punch(5)#] [apples(10)#] [bee farm(10)#] [protein powder(2)#] [Brangelina(3)#] [cabbage juice(6)#] [embroidery(7)#] [shampoo(5)#] [bagels(6)#] [books(9)#] [2d#] [feed corn(7)#] [vacuum(7)#] [4d#] [Stan Lee 4(8)#] [9c#] [knitting(9)#] [timber/honey(9)#]
Related Rates [speeder(9)#] [cone(12)#] [boat(8)#] [snowball(4)#] [isosceles(7)#] [ships(8)#] [icicles(9)#] [shadow(9)#] [merry go round(9)#] [Dr Octopus(6)#] [Grinch(8)#] [hot air balloon(6)#] [Mackinac Bridge(7)#] [WolverineAid(5)#] [tugboat(5)#] [octopus1(3)#] [Madam Whippy(5)#] [bellows(6)#] [circulation(5)#] [coffee filter(5)#] [spherical balloon(6)#] [potter(5)#] [UM mug(4c)#] [icicle(5)#] [train+camera(8)#] [melon(5)#] [crankshaft hourglass(3)#] [white whale(9)#] [ship(1)#] [ice cube(9)#] [squirrel(6)#] [marshmallow(2c)#] [gold platinum(6a)#] [trains(5)#] [chocolate cone(4)#] [baseball(5)#] [shadow(3)#] [aluminum cone(2)#] [bar in oven(5)#] [vase(6a)#] [sea level(7a)#] [spider(4)#] [concrete(4)#] [showpigs(7)#] [stalagmites(4)#] [coffee(3)#] [snowball(6)#] [clock(10)#] [cars 2(6)#] [Michigan Jane(9)#] [11#] [balloon(9)#] [stereo(6)#]
Riemann Sums [gas leak(6)#] [naked mile(4)#] [6#] [7#] [4#] [3b#] [eggnog(5)#] [4#] [3b#] [5bcf#] [9b#] [2#] [4a#] [2#] [car(4ab)#] [traffic(6a)#] [4a#] [GBC(6c)#] [coal plant(7d)#] [baby growth(6)#] [bessie(4)#] [Twitter(8)#] [truck(3cde)#] [Canco(6)#] [5d#] [9d#] [excitement density(1)#] [marshmallow(2b)#] [Usain Bolt(7bc)#] [braking(2c)#] [8bc#] [3cd#] [1d#] [11d#] [pipeline(2bcd)#] [1d#] [more donuts(4)#] [wind up mouse(3ab)#] [puddle(4bcd)#] [Brangelina(3bcd)#] [unicycle(2ab)#] [6bc#] [8de#] [7def#] [1ef#] [1efg#] [1fg#] [1efg#] [1abc#] [1def#]
Birth Rate/Death Rate [glacier(11)#] [Black Friday(9)#] [mosquitos(9)#] [ATP(9)#] [Galleon(1)#] [The Victors(8)#] [Mt. Arvon(3)#] [donuts(3)#] [tank(8)#] [trees(2)#] [cabbage(9)#] [wolves(5)#] [pond(6)#] [poker(5)#] [Twisties(3)#] [3#] [oak leaves(3)#] [krill(8)#]
Fund. Thm. Of Calc. [9#] [1b#] [3#] [Hankytown3(6d)#] [2#] [6#] [theme park(6b)#] [mosquitos(9)#] [1e#] [Frosty(7cd)#] [Beans to Frogs(8e)#] [2#] [7ab#] [2a#] [8bcd#] [Oscar's apartment(6)#] [5d#] [7#] [snowstorm(7ad)#] [5c#] [3bc#] [7bcd#] [soda(2cd)#] [icicle(5c)#] [traffic(6d)#] [4bc#] [6eg#] [3b#] [Mt. Arvon(3)#] [Twitter(8c)#] [2ef#] [4#] [bucket(6)#] [5#] [8#] [balloon(10)#] [7#] [Metal ring(8b)#] [water tank(3)#] [basketball laps(8)#] [water temp(9)#] [1#] [marshmallow(2)#] [5#] [1#] [braking(2b)#] [4#] [typing(7)#] [driving(1)#] [7#] [acorns(8)#] [1b#] [race(3)#] [4e#] [rain bucket(8c)#] [9#] [Demon Drop(4)#] [6ab#] [donuts(3)#] [more donuts(4)#] [5#] [11#] [wind up mouse(3cd)#] [6#] [1e#] [trout(3a)#] [puddle(4a)#] [5#] [tank(8)#] [1#] [trees(2ab)#] [6e#] [cabbage(8a)#] [10#] [3#] [litter(9)#] [6e#] [7a#] [books(9)#] [4b#] [4b#] [9fghi#] [1a#] [2b#] [Twisties(3)#] [Tycho Brahe(6abcd)#] [meme(9cd)#] [1cd#] [2#] [3#] [1f#] [2b#] [7#] [1a#] [3b#] [4#] [5#] [krill(8)#]
Average Value [1a#] [11#] [3d#] [1c#] [North Pole(5)#] [ice cream store(4b)#] [2c#] [3b#] [Turtle vs Bunny(6a)#] [traffic(6b)#] [6f#] [3c#] [bucket(6e)#] [8#] [Basketball(6c)#] [1b#] [typing(7d)#] [3e#] [1c#] [rain bucket(8d)#] [6d#] [5e#] [2a#] [1c#] [trees(2a)#] [unicycle(2c)#] [3e#] [litter(9c)#] [11ef#] [3d#] [7b#] [1ab#] [water temp(8d)#] [9de#] [1b#] [Twisties(3e)#] [1b#] [4b#]
Even/Odd Integral [2#] [3#] [2e#] [4bd#] [3a#] [7#] [2d#] [1#] [1#] [5cd#] [9c#] [1#] [3f#] [3#] [2b#]
Piecewise linear integral [3#] [5#] [Simpsons(9)#] [3#] [8bcd#] [Oscar's apartment(6)#] [7#] [5b#] [2#] [2#] [Turtle vs Bunny(6)#] [7#] [snow removal(8)#] [Mt. Arvon(3)#] [5#] [balloon(10)#] [Basketball(6)#] [7#]
Basic rules of integrals [2#] [1b#] [1bc#] [6#] [2#] [3#] [1bd#] [2#] [4#] [2a#] [2#] [2#] [4ad#] [3#] [8#] [9#] [4a#] [7#] [3a#] [2#] [1#] [6#] [11d#] [6e#] [5#] [orchard(8g)#] [1d#] [3d#] [8abc#] [1c#] [1c#] [9abcj#] [1a#]
Integral: Formula [1ad#] [3#] [music trading(2)#] [4bc#] [theme park(6)#] [2#] [3#] [2#] [3#] [4e#] [3b#] [4bc#] [9c#] [basketball laps(8)#] [11c#] [10b#] [9a#]
Integral: Graph [mountain(8)#] [6#] [treetrunk(8)#] [7#] [1c#] [3#] [Black Friday(9)#] [reaction(5)#] [6#] [3#] [4#] [5a#] [taxi(7bcd)#] [mosquitos(9)#] [1f#] [2#] [sand hole(9)#] [5#] [Simpsons(9)#] [3#] [8bcd#] [flood(7)#] [3b#] [model rocket(6b)#] [snowstorm(7)#] [3#] [5a#] [Galleon(1)#] [2#] [7#] [1#] [Turtle vs Bunny(6bc)#] [7a#] [bicyclist(9)#] [4bcd#] [snow removal(8)#] [2c#] [6efg#] [7#] [1a#] [3#] [5#] [Mt. Arvon(3)#] [2#] [4#] [bucket(6)#] [5#] [balloon(10)#] [Basketball(6)#] [7#] [water tank(3)#] [5#] [1#] [4#] [typing(7)#] [driving(1)#] [7#] [1#] [race(3)#] [Demon Drop(4)#] [6#] [11#] [2#] [1b#] [wolves(5)#] [2#]
Integral: Numbers [gas leak(6)#] [9b#] [naked mile(4)#] [8#] [7#] [4bc#] [5b#] [Tigers(4b)#] [car(4)#] [7#] [traffic(6a)#] [2d#] [baby growth(6)#] [Twitter(8)#] [1#] [5#] [1#]
Integral: Words [music trading(2)#] [theme park(6)#] [taxi(7)#] [mosquitos(9)#] [3#] [eggnog(5)#] [Frosty(7ab)#] [Beans to Frogs(8e)#] [2#] [ice cream store(4a)#] [Galleon(1)#] [3c#] [soda(2ce)#] [icicle(5c)#] [traffic(6a)#] [plane ticket(9cd)#] [coal plant(7)#] [solar panel(4)#] [car(8)#] [braking(4)#] [butter(4)#] [RDeVark(8a)#] [puddle(4a)#] [turbine(8)#] [2b#] [meme(9a)#]

All Exam 2's, with their medians:

Winter, 2001 Exam Solutions NONE Winter, 2014 Exam Solutions 60
Fall, 2001 Exam Solutions 74 Fall, 2014 Exam Solutions 78
Winter, 2002 Exam Solutions 63 Winter, 2015 Exam Solutions 67
Fall, 2002 Exam Solutions 65 Fall, 2015 Exam Solutions 73
Winter, 2003 Exam Solutions 60 Winter, 2016 Exam Solutions 74
Fall, 2003 Exam Solutions 68 Fall, 2016 Exam Solutions 73
Winter, 2004 Exam Solutions 61 Winter, 2017 Exam Solutions 70
Fall, 2004 Exam Solutions 62 Fall, 2017 Exam Solutions 74
Winter, 2005 Exam Solutions 52 Winter, 2018 Exam Solutions 70
Fall, 2005 Exam Solutions 53 Fall, 2018 Exam Solutions 84
Winter, 2006 Exam Solutions 58 Winter, 2019 Exam Solutions 72
Fall, 2006 Exam Solutions 63 Fall, 2019 Exam Solutions 71
Winter, 2007 Exam Solutions 62 Winter, 2020 Exam Solutions 77
Fall, 2007 Exam Solutions 73 Fall, 2020 Exam Solutions 75
Winter, 2008 Exam Solutions 59 Winter, 2021 Exam Solutions 63
Fall, 2008 Exam Solutions 52 Fall, 2021 Exam Solutions 79
Winter, 2009 Exam Solutions 42.5 Winter, 2022 Exam Solutions 62
Fall, 2009 Exam Solutions 50 Fall, 2022 Exam Solutions 66
Winter, 2010 Exam Solutions 68 Winter, 2023 Exam Solutions 59
Fall, 2010 Exam Solutions 64 Fall, 2023 Exam Solutions 72.5
Winter, 2011 Exam Solutions 57.5 Winter, 2024 Exam Solutions 60
Fall, 2011 Exam Solutions 64 Fall, 2024 Exam Solutions 61.2
Winter, 2012 Exam Solutions 53 Winter, 2025 Exam Solutions 56
Fall, 2012 Exam Solutions 62  
Winter, 2013 Exam Solutions 62  
Fall, 2013 Exam Solutions 66  

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