Problems to study for Math 115 Exam 3

Here is a breakdown of Math 115 Exam 3 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
True-False/Multiple Choice [1#] [9#] [1#] [3#] [1#] [1#] [5#] [1#] [1#] [1#] [1#] [1#] [8#] [9#] [2#] [1#] [9#] [7#] [11#] [10#] [9#]
Marginal cost and revenue [buses(10)#] [BarBQ Ice Cream(12)#] [averqage cost(8)#] [widgets(11)#] [4c#] [Mammoth Corp(5)#] [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)#] [books(9)#] [2d#] [feed corn(7)#] [vacuum(7)#] [4d#] [Stan Lee 4(8)#] [knitting(9)#] [timber/honey(9)#]
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#]
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(9c)#] [meme(9d)#] [1cd#] [2#] [3#] [1f#] [2b#] [7#] [1a#] [3b#] [4#] [5#] [krill(8)#]
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#]
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: 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)#]
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: Formula [1a#] [1d#] [3#] [music trading(2)#] [4bc#] [theme park(6)#] [2#] [3#] [2#] [3#] [4e#] [3b#] [4bc#] [9c#] [basketball laps(8)#] [11c#] [10b#] [9a#]
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#]
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)#]
Even/Odd Integral [2#] [3#] [2e#] [4bd#] [3a#] [7#] [2d#] [1#] [1#] [5cd#] [9c#] [1#] [3f#] [3#] [2b#]
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#]
Optimization [track(12)#] [door(10)#] [rectangle(2)#] [widgets(11)#] [trebuchet(5)#] [trough(10)#] [ball bearings(8)#] [orange juice(10)#] [biomass(9)#] [wire(10)#] [dosage(7)#] [Saruman(8)#] [bucket(10)#] [lemonade(3)#] [golden eggs(7)#] [tutoring(8)#] [bat(10)#] [logistic(3b)#] [truck(8)#] [box(10)#] [football tickets(7)#] [string(7)#] [OSU tickets(10)#] [cylinder(6)#] [gift boxes(1a)#] [telephone line(6)#] [paraboloid cup(4)#] [Octopus(7)#] [octopus2(4)#] [tiles(8)#] [window(8)#] [microphone(5)#] [smokestack(2)#] [Idaho(7)#] [peak oil(2)#] [7#] [The Victors(8)#] [turtle river(4)#] [T shirt company(5)#] [exam score(8)#] [WiFi Up High(8)#] [EPA(7)#] [prints(7)#] [graduation party(3)#] [cattle fence(8)#] [building(4)#] [hoophouse(1)#] [gutter(2)#] [prism(3)#] [window(6)#] [love cookie(7)#] [rect under curve(5)#] [fence(3)#] [smokestacks(8)#] [bookcase(2)#] [wire(2)#] [Minestromnia(3)#] [swimming pool(1)#] [festive table(8)#] [ship(4)#] [party(9)#] [gold platinum(6b)#] [garden(4)#] [caffeine(9)#] [prison break 1(4)#] [prison break 2(9)#] [dog park(6)#] [flowers(8)#] [fence(1)#] [homework run(7)#] [fruit punch(5)#] [paper cup(2)#] [code output(5)#] [tent(3)#] [apiary(8)#] [conical tank(3)#] [Blizzard melting(5)#] [10#] [rain shelter(3)#] [chlorine(7)#] [Brangelina(3ef)#] [station(5)#] [cardboard box(7)#] [wire box(8)#] [pyramid hat(11)#] [washer(8)#] [bucket(9)#] [pyramids(5)#] [krypton(6)#] [sign(6)#] [fan club(5)#] [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)#] [9#] [10d#] [data loss(6)#] [coffee(7)#] [box(5)#] [cans(7)#] [beam(8)#] [suitcase(2)#] [5#] [Tycho Brahe(6efg)#] [Stan Lee 2(4)#] [Stan Lee 3(5)#] [9c#] [garden(2)#] [kite(3)#] [can(3)#] [box(7)#]
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)#]
Derivatives: Words [6#] [7#] [taxi(7a)#] [airline tickets(6)#] [hummingbird(8)#] [Beans to Frogs(8bd)#] [Oscar's apartment(6)#] [3d#] [soda(2b)#] [plane ticket(9a)#] [turbine(8)#]
Derivatives: Numbers [9c#] [4a#] [4a#] [1c#] [6#] [Tigers(4a)#] [car(4c)#] [3#] [traffic(6c)#] [2b#] [Metal ring(8cd)#] [braking(2)#] [4#]
Derivatives: Graph [Hankytown3(6ab)#] [5bc#] [1a#] [hummingbird(8)#] [3a#] [8a#] [3a#] [model rocket(6a)#] [1abcd#] [6abcd#] [1b#] [Mt. Arvon(3)#] [1e#]
Linear approximation [gold(13)#] [1#] [7c#] [1a#] [5ae#] [3a#] [1e#] [2a#] [truck(3ab)#] [11b#] [9ab#] [10a#] [9a#] [orchard(8def)#] [trout(3bc)#] [9#] [cabbage(8bc)#] [1c#] [2d#] [1d#] [2c#] [1d#] [1e#] [4c#] [6c#]
Critical pts, Inflection pts, extrema [7#] [1c#] [7#] [6#] [U Value(2c)#] [atomic force(7)#] [8c#] [7#] [balloon(10)#] [1b#] [5bc#] [9b#] [5#] [potential energy(3)#] [8#] [6#] [ice(9)#] [7#] [2#] [11a#] [1#] [7#] [9c#] [6#] [7#] [6f#] [plant survival(8)#] [unicycle(1e)#] [cabbage(9abc)#] [6de#] [10#] [11#] [2f#] [5#] [6abcd#] [9#] [3#] [7#] [10abcd#] [6ab#] [2#] [10#]
Interpret the meaning of ƒ,ƒ′,ƒ−1,(ƒ−1)′ [2#] [3c#] [Frosty(7a)#] [plane ticket(9)#] [coal plant(7)#] [solar panel(4)#] [Twitter(8b)#] [Minestromnia(3d)#] [water temp(9)#] [butter(4)#] [robots(10)#] [acorns(8)#] [RDeVark(8)#] [Zoltan(8)#] [orchard(8c)#] [vase(6c)#] [sea level(7b)#] [cabbage(9d)#] [turbine(8)#] [2a#] [3#] [water temp(8abc)#] [meme(9b)#] [cars(5)#]
Inverse function [2#] [Beans to Frogs(8cd)#] [3d#] [soda(2a)#] [plane ticket(9b)#] [Metal ring(8a)#] [water temp(9)#] [4b#] [rain bucket(8ab)#] [orchard(8b)#] [9b#] [unicycle(1ab)#] [6a#] [2c#]
Draw a graph with certain properties [8#] [3#] [4#] [7#] [10#] [2#]
Misc [essay(10)#] [1d#] [essay(11)#] [10#]
Trig Functions [tank(3)#] [Coil of Doom(6)#] [exam score(8)#] [bessie(4)#] [11a#]
Average rate of change [9d#] [Hankytown3(6c)#] [11#] [4d#] [unicycle(2c)#] [1a#] [1d#] [5#]
Definition of the Derivative [4#] [5#] [FarmVille(1a)#] [8a#] [3#] [1a#] [8a#] [illumisqati(5)#] [4c#] [6#] [10d#] [12a#] [4#] [9d#] [1a#] [unicycle(1c)#] [3b#] [3a#] [1a#] [2e#] [1c#] [1a#]
Continuity and Limits [6#] [7#] [3#] [6#] [9#] [ice(9)#] [8#] [1#] [4#] [9#] [10#] [10c#] [3#] [7b#] [1#] [1#] [1#] [4#] [9#] [1ab#] [8#] [6#] [6abcd#] [3b#] [4#] [3a#] [5#] [4#] [6#] [7#] [10#] [4#] [5#] [2#] [5#] [1a#] [6#] [2a#] [1#] [4c#] [6b#] [1#] [3#] [4a#] [1#] [10g#] [2#] [4#] [7#]

All Exam 3's, with their medians:

Winter, 2001 Exam Solutions NONE Winter, 2014 Exam Solutions 53
Fall, 2001 Exam Solutions 72 Fall, 2014 Exam Solutions 71
Winter, 2002 Exam Solutions NONE Winter, 2015 Exam Solutions 67
Fall, 2002 Exam Solutions 59 Fall, 2015 Exam Solutions 66
Winter, 2003 Exam Solutions 55 Winter, 2016 Exam Solutions 65
Fall, 2003 Exam Solutions 70 Fall, 2016 Exam Solutions 67
Winter, 2004 Exam Solutions 63 Winter, 2017 Exam Solutions 69
Fall, 2004 Exam Solutions 71 Fall, 2017 Exam Solutions 80
Winter, 2005 Exam Solutions 55 Winter, 2018 Exam Solutions 70
Fall, 2005 Exam Solutions 70 Fall, 2018 Exam Solutions 65
Winter, 2006 Exam Solutions 55 Winter, 2019 Exam Solutions 65
Fall, 2006 Exam Solutions 60 Fall, 2019 Exam Solutions 73
Winter, 2007 Exam Solutions 60 Winter, 2020 Exam Solutions 75
Fall, 2007 Exam Solutions 70 Fall, 2022 Exam Solutions 71
Winter, 2008 Exam Solutions Fall, 2023 Exam Solutions 59
Fall, 2008 Exam Solutions 70 Winter, 2024 Exam Solutions 63
Winter, 2009 Exam Solutions 67 Fall, 2024 Exam Solutions 67
Fall, 2009 Exam Solutions 60 Winter, 2025 Exam Solutions 56
Winter, 2010 Exam Solutions 69  
Fall, 2010 Exam Solutions 65  
Winter, 2011 Exam Solutions 60  
Fall, 2011 Exam Solutions 49  
Winter, 2012 Exam Solutions 56  
Fall, 2012 Exam Solutions 67  
Winter, 2013 Exam Solutions 70  
Fall, 2013 Exam Solutions 62  

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