// Numbas version: exam_results_page_options {"name": "Bokstavregning og parenteser 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "b5", "c1", "c2", "c3", "c4", "d1", "d2", "d3", "d4", "b6"], "name": "Bokstavregning og parenteser 2", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
Remove the brackets and gather the x terms together and also the number terms together.
\nWhen in fraction form, get the lowest common multiple (LCM), and multiply the top line by how many times the divisor goes into the LCM.
\nRule for multiping out brackets:
\n(a$x$ - b)(c$x$ + d) = (a * c)$x^2$ + ((a * d) + ((-b) *c)))$x$ + ((-b) * d)
\nRule for squaring brackets:
\n(-a$x$ + b)$^2$ = (-a * -a)$x^2$ + (2 * (-a) *b)$x$ + (b * b)
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\n$\\var{a1}(\\var{a2}x+\\var{a3})-\\var{a4} =$
\n[[0]]
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\n$3(5a-2)=3\\cdot 5a -3\\cdot 2=15a-6$
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "Du har ikke løst opp parentesen og trukket sammen.
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", "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "Løs opp parentesene og trekk sammen
\n$\\var{b1}(\\var{b2}x-\\var{b3})-\\var{b4}(\\var{b5}x-\\var{b6})=$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Husk: Når vi multipliserer et tall med et parentesuttrykk må vi multiplisere tallet med hvert av leddene i parentesen. Eksempel:
\n$-3(5a-2)=-3\\cdot 5a -3\\cdot (-2)=-15a+6$
\n\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "Du har ikke løst opp parentesene og trukket sammen.
", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{b1*b2-b4*b5}x+{-b1*b3+b4*b6}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "Multipliser parentesene og trekk sammen
\n$(\\var{c1}a+\\var{c2}b)(\\var{c3}a-\\var{c4}b) =$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Husk: Når vi multipliserer to parentesuttrykk må vi multiplisere hvert ledd i den første parentesen med hvert av leddene i den andre parentesen. Eksempel:
\n$(x+2y)(3x-y)$ $=$ $x\\cdot 3x-x\\cdot y+2y\\cdot 3x-2y\\cdot y$
\n$=$ $3x^2-xy+6xy-2y^2$
\n$=$ $3x^2+5xy-2y^2$
\n\n(siden $yx=xy$)
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", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{c1*c3}a^2+{-c1*c4+c2*c3}a*b-{c2*c4}b^2", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "Husk at $a\\cdot a = a^2$
", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "Multipliser parentesene og trekk sammen
\n$(\\var{d1}x+\\var{d2})(\\var{d3}x-\\var{d4})-(\\var{a1}x+\\var{a2})(\\var{a3}x-\\var{a4}) =$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Husk: Når vi multipliserer to parentesuttrykk må vi multiplisere hvert ledd i den første parentesen med hvert av leddene i den andre parentesen. Eksempel:
\n$(x+2y)(3x-y)$ $=$ $x\\cdot 3x-x\\cdot y+2y\\cdot 3x-2y\\cdot y$
\n$=$ $3x^2-xy+6xy-2y^2$
\n$=$ $3x^2+5xy-2y^2$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "Du har ikke multiplisert parentesene
", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{d1*d3-a1*a3}x^2+{-d1*d4+d2*d3+a1*a4-a2*a3}x+{-d2*d4+a2*a4}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "Du kan skrive inn algebraiske uttrykk tekstboksene. For eksempel kan du skrive a^3 og få $a^3$ og enten 2*x-3*y eller bare 2x-3y og få $2x-3y$. Det anbefales at dere bruker '*' mellom variabler, for at NUMBAS skal tolke det dere skriver riktig. Skriv for eksempel a*b heller enn ab, og x^2*y heller enn x^2y for å få $x^2y$.
\nVed siden av input-boksen ser dere hvordan NUMBAS tolker det dere skriver.
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