Hey guys, I've got some math problems for all of you ! Problems are sorted according to their difficulty; easier ones are on top. Rules: -No cheating! -You may use a four function calculator or a standard scientific calculator. Nothing else please (no graphing calculators, CAS, Java, etc.) Yes, you may use pencil, paper, ruler, reference books, etc. -Try to do them without looking at the [possible] solutions below. -Feel free to ask for hints, though I may or may not give them. It depends. -You may collaborate with other people or forum users. -I strongly encourage you to show your work and post it here, but you don't have to if you can't. -Don't make random guesses when solving the problems. -Don't worry if there are problems you can't do; just do the ones you can. Spoiler: #1 I have 17 apples. I eat 4 of them. How many do I have left? Spoiler: #2 Bob has 23 lego bricks. He receives 49 more of them. How many lego bricks does he have? Spoiler: #3 A theater has 9 rows of seats. Each row has 7 seats. How many seats are there? Spoiler: #4 Alice has $55. She plans to split them among 7 friends. How much money will she have left? CLARIFICATION: Alice will keep the remainder. She is not among her 7 friends that she is splitting money to. Spoiler: #5 If 1 mile equals 1.609 kilometers, how many miles are in 14 kilometers? Spoiler: #6 A test has 100 questions. It is worth 256 points. Each multiple choice question on the test is worth 2 points, while each fill-in-the-blank question is worth 6 points. How many of each question type are there? Spoiler: #7 A rectangular patio is made up of tiles are are 1 meter long each. A tile becomes removed from the edge of the patio. What will happen to the patio's perimeter? Spoiler: #8 How many ways can a deck of cards be arranged? Hint: there are 52 cards in a deck. Spoiler: #9 Bob has 10 candy in a pile. How many ways can he choose 3 candies from that pile? The order of which he chooses does not matter. Spoiler: #10 How many 5-letter words can be made from the English alphabet? Nonsense words like "ehgyo" do count. Spoiler: #11 The price of gasoline is defined by the function , where f(x) is the price and x is the amount in litres. What price does f(x) approach the more gas you buy? Spoiler: #12 A train leaves the station at x = 0 hours. Its speed is defined by the function , where f(x) is the speed in km/h and x is the time in hours. At x = 4, what is the train's acceleration in km/h/h (kilometers per hour per hour)? Spoiler: #13 A 17m long ladder is leaning 5m on a wall. It is sliding off the wall at a rate of 0.5 m/s. At this time, how fast is the bottom of the ladder moving (the side of the ladder that is touching the ground)? Spoiler: #14 Water filling a sink is defined by the function , where f(x) is the volume of water filled in litres and x is the time since the tap was turned on in minutes. How much water (in mililitres) was filled between x=5 and x = 7? Spoiler: #15 The amount of money going into a savins account is defined by the function , where f(x) is the amount of money being filled into the account at any given moment, which is defined by x. How much money was filled in to the account between x = 32 and x = 128? Spoiler: Bonus #1 Add up all the numbers from 1 to 452 in under 45 seconds. Spoiler: Bonus #2 Evaluate the following limits. Spoiler: Bonus #3 Evaluate the following radicals. Spoiler: Bonus #4 Is this equation true or false? Spoiler: Bonus #5 Solve this rebus . Good luck have fun !

1. You would have 13 apples left. 2. 72 lego bricks. 3. There are 63 seats total in the theater. 4. Alice would have $7.85 5. There would be 9 miles. 6. 7. There are 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 way to arrange a deck of cards. 8. 9. 10. 14400 5 letter words can be made from the alphabet. 11. *gets lost at this point*

1. 17 - 4 = 13 apples 2. 23 + 49 = 72 bricks 3. 9 * 7 = 63 seats 4. 55 / 7 = about $7.85 5. 1/1.609 * 14 = 8.7mi 6. 2x + 6y = 256 x + y = 100 2x + 2y = 200 4y = 56 y = 14 fill-in-the-blank x = 86 multiple choice 7. Does not change... 8. 52! = too much that you gotta do it yourself (about 8x10^67) 9. 10C3 = 120 10. 26P5 = 7893600 11. x < 80 if that condition is fulfilled then it the more gas you buy the cheaper it is 12. at 0h, speed is 1km/h at 4h, speed is 16km/h acceleration = (4-0)/(16-1) = 0.267 km/h^2 (3 s.f.) 13. Can't really understand the exact question of the position of the ladder but I'll draw it as: .| .\ .| .\ 5m .| .\ 17m .| .\ .|_____\ v264 ( this 'triangle' was better in my text box) I'm not sure if I gotta use differentiation to do this but, at 1s; 4.5m on a wall; v(17^2-4.5^2) = x x - v264 = 0.146m/s (3 s.f.) this one's probably wrong 14. f(7) - f(5) = 436L = 436000ml 15. f(128) - f(32) = -0.155 dollars apparently (3s.f.) I probably have to use differentiation for no. 13-15 but I'm too lazy so I just do the 'logical' way. Not even gonna do the bonus ones...

I tried this all without a calculator or paper/pencil: Spoiler: My awnsers 1) 17 - 4 = 3 2) 23 + 49 = 72 3) 9 x 7 = 63 4) I gave up after this one

I tried, here are my solutions, probably made some mistakes though. Spoiler: 4 Each friend gets 7.85, there are 55-(7 * 7.85) = 0.05 left. Spoiler: 5 14/1.609 = 8.701 Spoiler: 6 x := # multiple choice quistions y := # fill-in-the-blank questions x + y = 100 => x = 100 - y 2x + 6y = 256 2(100 - y) + 6y = 256 4y = 56 => y = 14 => x = 100 - 14 = 86 Spoiler: 7 I guess it depends on which tile is removed? Spoiler: 8 52! = 8.066 * 10^67 Spoiler: 9 (10 choose 3) = 10! / (3! - (10 - 3)!) = 120 Spoiler: 10 26^5 = 11881387 Spoiler: 11 50x / (x - 80) -(x -> inf)-> 50 / 1 = 50 (l.Hospital) Spoiler: 12 f(x) = 2^x f'(x) = ln(2) 2^x f'(4) = ln(2) 2^4 = 11.090 Spoiler: 13 0.5 * (sqrt(17^2 - 5^2) / 5) = 1.625 Spoiler: 14 f(x) = 2x^3 + 4 F(x) = 0.5x^4 + 4x F(7) - F(5) = 0.5 * 7^4 + 4 * 7 - 0.5 * 5^4 - 4 * 5 = 896 Spoiler: 15 f(x) = (6x^2 + 3x - 2) / (x^3 - 2x^2) = (6x^2 + 3x - 2) / ((x - 2) * x^2) = 7 / (x - 2) + (-x - 1) / x^2 int(x = 32 to 128) f(x) dx = int(x = 32 to 128) 7 / (x - 2) dx + int(x = 32 to 128) (-x - 1) / x^2 dx = 7 ln(126) - 7 ln(30) - 1/2 ln(16641) + 1/2 ln(1089) = 8.682 notes: https://imgur.com/a/n4meo Edit: Spoiler: Bonus 1 (452 * 453) / 2 = 102378 Spoiler: Bonus 2 -inf, +inf Spoiler: Bonus 3 i, 15i, 12i Spoiler: Bonus 5 I ate some pie

#6 We literally had this at school today! {6x + 2y = 256. {x + y = 100 y = -x + 100 6x + 2 ( -x + 100 ) = 256 6x - 2x + 200 = 256 4x = 56 x = 14 14 + y = 100 y = 86 So: 86 multiple choice questions and 14 fill-in-the-blank questions! @CyanYellow