// Numbas version: exam_results_page_options {"name": "Q3.Homework7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "advice": "

When $n$ is positive, we multiply $10$ by itself $n$ times,

\\[\\text{e.g. } 10^3 = 10 \\times 10 \\times 10 = 1000 \\text{ .}\\]

When $n$ is negative, we can think of $10^{-n}$ as $\\frac{1}{10^{n}}$,

\\[\\text{e.g. } 10^{-3} = \\frac{1}{10^3} = \\frac{1}{1000} = 0.001\\text{ .}\\]

When $n = 0$:

\\[10^{0} = 1 \\text{ .}\\]

Generally, we can think of $10^n$ as a number in standard form $1 \\times 10^n$. Then $n$ always tells us the number of decimal places to move the decimal point in $1.0$, for example

\\[10^{-3} = 1.0 \\times 10^{-3} \\text{ and since } n = - 3 \\text{, we go } 3 \\text{ places back as follows: } 1.0 ⇒ 0.1 ⇒ 0.01 ⇒ 0.001 \\text{ .}\\]

A complete table of powers of ten for $n$ from $-6$ to $6$ is:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$n$	$10^n$
$-6$	$0.000001$
$-5$	$0.00001$
$-4$	$0.0001$
$-3$	$0.001$
$-2$	$0.01$
$-1$	$0.1$
$0$	$1$
$1$	$10$
$2$	$100$
$3$	$1000$
$4$	$10000$
$5$	$100000$
$6$	$1000000$

", "name": "Q3.Homework7", "tags": [], "variables": {"k": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "k", "definition": "random(-5..5#1)"}, "a": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "a", "definition": "random(1..3#1)"}, "b": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "b", "definition": "random(1..3#1)"}, "g": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "g", "definition": "[3,1,2]"}, "gp": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "gp", "definition": "[k,l,m]"}, "p": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "p", "definition": "random(1..5#1)"}, "h": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "h", "definition": "[3,2,1]"}, "n": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "n", "definition": "random(-3..3#2)"}, "m": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "m", "definition": "random(-5..5#1)"}, "o": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "o", "definition": "random(-3..3#2)"}, "l": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "l", "definition": "random(-5..5#1)"}, "hp": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "hp", "definition": "[n/2,o/2,p]"}}, "metadata": {"description": "

Fill in a table of powers of 10.

", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "

Use the table below to find $f'(\\var{a})$ and $w'(\\var{b})$ if $f(x)=g(h(x))$ and $w(x)=h(g(x))$.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$x$	$g(x)$	$g'(x)$	$h(x)$	$h'(x)$
1	3	$\\var{gp[0]}$	3	$\\var{hp[0]}$
2	1	$\\var{gp[1]}$	2	$\\var{hp[1]}$
3	2	$\\var{gp[2]}$	1	$\\var{hp[2]}$

$f'(\\var{a})=$[[0]]

$w'(\\var{b})=$[[1]]

", "type": "gapfill", "gaps": [{"showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "minValue": "(hp[a-1])*gp[(h[a-1])-1]", "correctAnswerFraction": false, "maxValue": "(hp[a-1])*gp[(h[a-1])-1]", "variableReplacements": [], "marks": 1, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": true, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "minValue": "(gp[b-1])*hp[(g[b-1])-1]", "correctAnswerFraction": false, "maxValue": "(gp[b-1])*hp[(g[b-1])-1]", "variableReplacements": [], "marks": 1, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": true, "showFeedbackIcon": true}], "marks": 0, "showFeedbackIcon": true}], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "extensions": [], "statement": "

Answer the following:

", "ungrouped_variables": ["a", "g", "gp", "h", "hp", "b", "k", "l", "m", "n", "o", "p"], "type": "question", "contributors": [{"name": "Patrick Joyce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1674/"}]}]}], "contributors": [{"name": "Patrick Joyce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1674/"}]}