{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"SM286D · Introduction to Applied Mathematics with Python · Spring 2020 · Uhan
\n",
"\n",
"Exam 1 — Review Problems — Solutions
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 1"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"What's up?\n"
]
}
],
"source": [
"message = \"What's up?\"\n",
"print(message)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The answer is 15.\n"
]
}
],
"source": [
"x = 5\n",
"y = 10\n",
"z = x + y\n",
"print(f'The answer is {z}.')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45\n"
]
}
],
"source": [
"L = list(range(1,10))\n",
"s = 0\n",
"for i in range(0, 9):\n",
" s = s + L[i]\n",
"print(s)\n",
"# or just sum(L)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"110\n"
]
}
],
"source": [
"s = 0\n",
"for i in range(1,21): \n",
" if i % 2 == 0: #Missing :\n",
" s = s + i\n",
"print(s)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1\n"
]
}
],
"source": [
"n = 0\n",
"while n <= 21:\n",
" n += 1\n",
" if n % 4 == 1:\n",
" break # need the spacing!\n",
"print(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 2"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10405071317\n"
]
}
],
"source": [
"s = 0\n",
"for i in range(1,11):\n",
" s = s + i**i\n",
"print(s)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10405071317\n"
]
}
],
"source": [
"s = sum([i**i for i in range(1,11)])\n",
"print(s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 3"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"36\n"
]
}
],
"source": [
"x = 1\n",
"while (x >= 0) and (x <= 19):\n",
" for i in range(2, 4):\n",
" x = i*x\n",
"print(x)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6\n",
"36\n"
]
}
],
"source": [
"x = 1\n",
"while (x >= 0) and (x <= 19):\n",
" for i in range(2, 4):\n",
" x = i*x\n",
" print(x)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2\n",
"6\n",
"12\n",
"36\n"
]
}
],
"source": [
"#Part c:\n",
"x = 1\n",
"while (x >= 0) and (x <= 19):\n",
" for i in range(2,4):\n",
" x = i*x\n",
" print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 4"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"ename": "KeyboardInterrupt",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mW\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'a'\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mW\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m't'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mW\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;31m# It runs forever unless you stop the kernel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
]
}
],
"source": [
"W = ['m', 'a', 't', 'h']\n",
"i = 0\n",
"while W[i] != 'a' or W[i] != 't':\n",
" i += 1\n",
" W.append(W[i])\n",
"print(W)\n",
"# It runs forever unless you stop the kernel"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['m', 'a', 't', 'h']\n"
]
}
],
"source": [
"W = ['m', 'a', 't', 'h']\n",
"i = 0\n",
"while W[i] == 'a' or W[i] == 't':\n",
" i += 1\n",
" W.append(W[i])\n",
"print(W)\n",
"# This will print ['m', 'a', 't', 'h'] since it will never enter the while loop"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['m', 'a', 't', 'h', 'a', 't']\n"
]
}
],
"source": [
"W = ['m', 'a', 't', 'h']\n",
"i = 0\n",
"while W[i] == 'm' or W[i] == 'a':\n",
" i += 1\n",
" W.append(W[i])\n",
"print(W) \n",
"# Here the first two intances of the while loop are true so we carry out the \n",
"# instructions. \n",
"# Note that the variable i changes before we add letters to the string. Hence \n",
"# we add 'a' and 't'."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 5"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"def sumavefunc(L):\n",
" s = sum(L)\n",
" a = sum(L) / len(L)\n",
" return [s,a]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make a file called `sumavefunc.py` that has this function in it.\n",
"Then in a another file have the scripts:\n",
"\n",
"```\n",
"from sumavefunc import sumavefunc\n",
"```\n",
"\n",
"Then you can call this function from this separate file as long as these \n",
"files are in the same directory."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 6"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def truckprice(model, wd, color, accessories):\n",
" if model == 101:\n",
" price = 10000\n",
" elif model == 201:\n",
" price = 12000\n",
" if wd == 4:\n",
" price = price + 2000\n",
" if color == 'metallic':\n",
" price = price + 500\n",
" elif color == 'race stripe':\n",
" price = price + 700\n",
" for x in accessories:\n",
" price = price + 200\n",
" return price"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"12400"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"truckprice(101, 4, 'red', ['heated seats', 'premium sound'])"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"12900"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"truckprice(201, 2, 'race stripe', ['sun roof'])"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"ename": "UnboundLocalError",
"evalue": "local variable 'price' referenced before assignment",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mUnboundLocalError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtruckprice\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m301\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'blue'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'self drive'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'self wash'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m\u001b[0m in \u001b[0;36mtruckprice\u001b[0;34m(model, wd, color, accessories)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mprice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m12000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mwd\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mprice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprice\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'metallic'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mprice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprice\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m500\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mUnboundLocalError\u001b[0m: local variable 'price' referenced before assignment"
]
}
],
"source": [
"truckprice(301, 4, 'blue', ['self drive', 'self wash'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 7"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def fibsq(f1, f0=1): # The == should be = and Missing the : and the default argument should follow the non-default argument.\n",
" F = [f0, f1]\n",
" sumsq = lambda x, y : x**2 + y**2 # == should be : and ^ should be **\n",
" lastnumber=0\n",
" while lastnumber < 100: # delete for\n",
" lastnumber = sumsq(F[-1], F[-2])\n",
" F.append(lastnumber)\n",
" return F"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1, 3, 10, 109]"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fibsq(3)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[4, -2, 20, 404]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fibsq(-2, 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 8"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"D = {'Alice': 45, 'Bob': 22, 'Carl': 11, 'Diana': 57}\n",
"\n",
"L = []\n",
"for x in D.keys():\n",
" L.append(x)\n",
"\n",
"S = 0\n",
"for y in D.values():\n",
" S += y"
]
}
],
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"display_name": "Python 3",
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"codemirror_mode": {
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"file_extension": ".py",
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