Vectors

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 1 month ago

Created this.

Name	Status	Author	Last Modified
Vectors	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
MATH6005 Vectors	draft	Julie Crowley	26/07/2016 12:53
Eryk's copy of MATH6005 Vectors	draft	Eryk Wilczy?ski	03/06/2016 13:44
Stephen's copy of MATH6005 Vectors	draft	Stephen Bowlzer	21/06/2016 17:45
Gareth's copy of MATH6005 Vectors	draft	Gareth Woods	26/08/2016 09:11
Maria's copy of Vectors	draft	Maria Aneiros	23/05/2019 03:02

There are 5 other versions that do you not have access to.

Question groups

Group 11 questions

1.
Ready to use

Given vectors $\boldsymbol{v,\;w}$ , find the angle between them.
2.
Has some problems

A plane goes through three given non-collinear points in 3-space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$ . There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.
3.
Has some problems

Find the Cartesian form $ax+by+cz=d$ of the equation of the plane $\boldsymbol{r=r_0+\lambda a+\mu b}$ . The solution is not unique. The constant on right hand side could be given to ensure that the left hand side is unique.
4.
Has some problems

When are vectors $\boldsymbol{v,\;w}$ orthogonal? Part b) is not answered in Advice, the given solution is for a different question.
5.
Ready to use

Determine if various combinations of vectors are defined or not.
6.
Has some problems

Find angle between plane $\Pi_1$ , given by three points, and the plane $\Pi_2$ given in Cartesian form. The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.
7.
Ready to use

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$ , find their inner product.
8.
Has some problems

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector. The correct solution is given, however the accuracy of 0.001 is not enough as in some cases answers near to the correct solution are also marked as correct.
9.
Ready to use

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.
10.
Ready to use

Given vectors $\boldsymbol{A,\;B}$ , find $\boldsymbol{A\times B}$
11.
Ready to use

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Topics

No topics have been defined.

Diagnostic algorithm

Extend built-in algorithm?

Base diagnostic algorithm

state (Produces the initial value of the state object): // should be renamed "initial_state"
    [
        "topics": map(
            [
                "topic": topic,
                "status": "unknown" // "unknown", "passed", or "failed"
            ],
            topic,
            values(topics)
        ),
        "retries": 3,
        "finished": false,
    ]

topics_by_objective (A dictionary mapping a learning objective name to a list of indices of topics):
    dict(map(
        let(
            ltopics, values(topics),
            indices, filter(lo["name"] in ltopics[j]["learning_objectives"], j, 0..len(ltopics)-1),
            [lo["name"],indices]
        ),
        lo,
        learning_objectives
    ))

unknown_topics (Which topics are still unknown?): 
    map(x["topic"],x,filter(x["status"]="unknown",x,state["topics"]))

first_topic (The first topic to pick a question on):
    unknown_topics[floor(len(unknown_topics)/2)]["name"]

first_question (The first question to show the student):
    random(topics[first_topic]["questions"])

get_dependents (An expression which gets the topics to update after answering a question):
    expression("""
        [target] + flatten(map(eval(get_dependents,["target":t,"correct":correct]),t,topics[target][if(correct,"depends_on","leads_to")]))
    """)

correct (Did the student get the current question right?):
    current_question["credit"]=1

after_answering (Update the state after the student answers a question):
    let(
        ntopics, eval(get_dependents,["target":current_topic,"correct":correct])
    ,   nstate, state + ['topics': map(
                    if(tstate["topic"]["name"] in ntopics, tstate + ["status":if(correct,"passed","failed")], tstate),
                    tstate,
                    state["topics"]
                )]
    , nstate
    )

action_retry (Use up one retry and visit the same topic again):
    [
        "label": translate("diagnostic.use retry"),
        "state": state + ["retries": state["retries"]-1],
        "next_question": random(topics[current_topic]["questions"])
    ]

action_stop (Stop the exam):
    [
        "label": translate("diagnostic.end test"),
        "state": state,
        "next_question": nothing
    ]

action_move_on (Move to the next topic, or end the exam if there are no more):
    let(
        state, after_answering,
        immediate_next_topics, topics[current_topic][if(correct, "leads_to", "depends_on")],
        unknown_topics, map(x["topic"],x,filter(x["status"]="unknown",x,state["topics"])),
        unknown_immediate_topics, filter(x["name"] in immediate_next_topics,x,unknown_topics),
        next_topics, if(len(unknown_immediate_topics), unknown_immediate_topics, unknown_topics),
        finished, len(next_topics)=0 or state["finished"],
        topic,
            if(not finished,
                next_topics[floor(len(next_topics)/2)]["name"]
            ,
                nothing
            ),
        [
            "label": translate("diagnostic.move to next topic"),
            "state": after_answering,
            "next_question": if(not finished, random(topics[topic]["questions"]), nothing)
        ]
    )

can_move_on:
    action_move_on["next_question"]<>nothing

next_actions (Actions to offer to the student when they ask to move on):
    let(
        feedback, retries_feedback+"\n\n"+translate("diagnostic.next step question")
    ,   [
            "feedback": feedback,
            "actions": if(not correct and state["retries"]>0, [action_retry], []) + if(can_move_on,[action_move_on],[action_stop])
        ]
    )

after_exam_ended (Update the state after the exam ends):
    let(
        state, after_answering,
        ntopics, map(t+["status": if(t["status"]="unknown","failed",t["status"])],t,state["topics"]),
        state+["finished": true]
    )

finished (Is the test finished? True if there are no unknown topics):
    len(unknown_topics)=0 or state["finished"]

total_progress:
    let(
        num_topics, len(state["topics"]),
        known, filter(tstate["status"]<>"unknown",tstate,state["topics"]),
        passed, filter(tstate["status"]="passed",tstate,known),
        num_known, len(known),
        num_passed, len(passed),
        [
            "name": translate("control.total"),
            "progress": if(num_topics>0,num_known/num_topics,0), 
            "credit": if(num_known>0,num_passed/num_topics,0)
        ]
    )

learning_objective_progress:
    map(
        let(
            tstates, map(state["topics"][j],j,topics_by_objective[lo["name"]]),
            known, filter(tstate["status"]<>"unknown",tstate,tstates),
            passed, filter(tstate["status"]="passed",tstate,known),
            num_topics, len(tstates),
            num_known, len(known),
            num_passed, len(passed),
            ["name": lo["name"], "progress": if(num_topics>0,num_known/num_topics,0), "credit": if(finished,num_passed/num_topics,if(num_known>0,num_passed/num_known,0))]
        ),
        lo,
        learning_objectives
    )

progress (Progress on each of the learning objectives, plus total progress):
    learning_objective_progress+
    total_progress

retries_feedback:
    translate("diagnostic.now assessing topic", ["current_topic": current_topic]) + " " +
    let(
        retries, state["retries"], 
        pluralise(retries, translate("diagnostic.one retry left"), translate("diagnostic.retries left", ["retries": retries ]))
    )
    + " " +
    let(
        p,total_progress["progress"],
        percentage, dpformat(100p, 0),
        translate("diagnostic.percentage completed", ["percentage": percentage])
    )

weak_objective_threshold (The amount of credit below which a learning objective is considered weak):
    0.6

finished_feedback:
    let(
        weak_objectives, filter(p["credit"]<weak_objective_threshold, p, learning_objective_progress),
    //
        translate("diagnostic.test is over") + " "
        +
        if(len(weak_objectives)=0,
            translate("diagnostic.passed all lo")
        ,
            translate("diagnostic.more work on lo", ["los": 
                join(map(lo["name"], lo, weak_objectives),", ")])
        )
    )

feedback:
    if(finished,
        finished_feedback,
        retries_feedback
    )

Custom diagnostic algorithm

Interface theme

Upload a new theme

Interface language

Allow students to print question content?

Show student's name?

Enter review mode immediately on ending the exam?

	Always	In submitted mode	Only in review mode	Never
Show answer correctness
Show the student's score
Show the maximum score
Show part feedback messages
Show expected answers
Show question advice

Pass threshold

Feedback messages

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 1 month ago

Question groups

Topics

Learning objectives

Base diagnostic algorithm

Custom diagnostic algorithm

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