Maria's copy of Foundation mathematics

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Maria Aneiros 5 years, 10 months ago

Created this as a copy of Foundation mathematics.

Name	Status	Author	Last Modified
Foundation mathematics	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Maria's copy of Foundation mathematics	draft	Maria Aneiros	23/05/2019 03:07

There are 4 other versions that do you not have access to.

Question groups

Group 51 questions

1.
draft

Questions testing understanding of numerators and denominators of numerical fractions.
2.
draft

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions.
3.
Ready to use

Questions testing understanding of the precedence of operators using BIDMAS applied to integers. These questions only test IDMAS. That is Indices, Division/Multiplication and Addition/Subtraction.
4.
Ready to use

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.
5.
Ready to use

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.
6.
Ready to use

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.
7.
Ready to use

Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.
8.
draft

Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.
9.
draft

Express $\displaystyle a \pm \frac{c}{x + d}$ as an algebraic single fraction.
10.
Ready to use

Express $\displaystyle \frac{a}{x + b} \pm \frac{c}{x + d}$ as an algebraic single fraction over a common denominator.
11.
draft

Express $\displaystyle b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
12.
draft

Express $\displaystyle ax+b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
13.
draft

Express $\displaystyle \frac{ax+b}{x + c} \pm \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator.
14.
draft

Express $\displaystyle \frac{ax+b}{cx + d} \pm \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator.
15.
draft

Harder questions testing addition, subtraction, multiplication and division of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.
16.
Ready to use

Questions testing rather basic understanding of the index laws.
17.
draft

Questions testing understanding of the index laws.
18.
Ready to use

Questions testing understanding of the index laws.
19.
draft

Questions testing understanding of the index laws.
20.
draft

Questions testing understanding of the index laws.
21.
Ready to use

Solve for $x$ : $\displaystyle ax+b = cx+d$
22.
Ready to use

Solve for $x$ : $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$ .
23.
Ready to use

Solve for $x$ : $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$
24.
Ready to use

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$
25.
draft

Find $B$ and $C$ such that $x^2+bx+c = (x+B)^2+C$ .
26.
Ready to use

Find the equation of the straight line parallel to the given line that passes through the given point $(a,b)$ .
27.
Ready to use

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$ .
28.
draft

Find the equation of the straight line which passes through the points $(a,b)$ and $(c,d)$ .
29.
draft

Express the equation of the given line in the form $y=mx+c$ .
30.
draft

Find the equation of the straight line perpendicular to the given line that passes through the given point $(a,b)$ .
31.
Ready to use

Find the centre and radius of a circle when given an equation in standard form.
32.
draft

Find $a$ , $B$ and $C$ such that $ax^2+bx+c = a(x+B)^2+C$ .
33.
Ready to use

Find the points of intersection of a straight line and a circle.
34.
Ready to use

Find the points of intersection of two circles.
35.
Needs to be tested

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.
36.
Ready to use

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).
37.
draft

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.
38.
draft

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.
39.
Ready to use

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.
40.
draft

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.
41.
draft

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.
42.
draft

A question testing the application of the Sine Rule when given two sides and an angle. In this question the triangle is obtuse and the first angle to be found is obtuse.
43.
Has some problems

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.
44.
Ready to use

Express $\displaystyle \frac{ax+b}{x + c} \pm \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator.
45.
draft

Express $\displaystyle a \pm \frac{c}{x + d}$ as an algebraic single fraction.
46.
Ready to use

Express $\displaystyle \frac{a}{x + b} \pm \frac{c}{x + d}$ as an algebraic single fraction over a common denominator.
47.
draft

Express $\displaystyle b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
48.
draft

Express $\displaystyle ax+b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
49.
Ready to use

Add/subtract fractions and reduce to lowest form.
50.
draft

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions.
51.
Has some problems

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$ .

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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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Maria Aneiros 5 years, 10 months ago

Question groups

Topics

Learning objectives

Base diagnostic algorithm

Custom diagnostic algorithm

On leaving a question

On timeout

5 minutes before timeout