Skills Audit for Maths and Stats - Aerospace Engineering, Electrical and Electronic Engineering, Electronics and Computer Engineering (MAS156)

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Will Morgan

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Will Morgan

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Ready to use

7 months, 3 weeks ago

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Will Morgan 7 months, 3 weeks ago

Gave some feedback: Ready to use

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Will Morgan 9 months, 2 weeks ago

Published this.

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Will Morgan 10 months ago

Gave some feedback: Needs to be tested

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Will Morgan 10 months ago

Created this.

Name	Status	Author	Last Modified
Skills Audit for Maths and Stats - Aerospace Engineering, Electrical and Electronic Engineering, Electronics and Computer Engineering (MAS156)	Ready to use	Will Morgan	18/07/2024 13:36
Skills Audit for Maths and Stats - General Engineering (MAS161)	Ready to use	Will Morgan	18/07/2024 15:10
Skills Audit for Maths and Stats - Materials Science and Engineering (MAS153 )	Ready to use	Will Morgan	23/07/2024 14:42
Skills Audit for Maths and Stats - (ACS131)	Ready to use	Will Morgan	24/09/2024 15:47
Skills Audit for Maths and Stats - Chemical and Biological Engineering (MAS140)	Ready to use	Will Morgan	18/07/2024 15:08
Skills Audit for Maths and Stats - Civil and Structural Engineering (CIV109)	Ready to use	Will Morgan	17/07/2024 10:54
Skills Audit for Maths and Stats - Mechanical Engineering (MAS152)	Ready to use	Will Morgan	10/07/2024 13:17

Question groups

Group 40 questions

1.
Ready to use

Metric Unit conversion - division by 1000.
2.
Ready to use

State the Upper and lower bound of a distance that has been rounded to either the nearest 10 or 100 miles.
3.
Ready to use

Compound percentage change.
4.
Ready to use

Dividing amounts in ratios
5.
Ready to use

Calculations involving Standard form.
6.
Ready to use

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$ , for integers $a$ , $b$ , $m$ and $n$ .
7.
Ready to use

perform a calculation involving negative indices.
8.
Ready to use

Simple exercise in collecting terms in different powers of $x$
9.
Ready to use

Expand two brackets involving powers of $x$ .
10.
Ready to use

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.
11.
Ready to use

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.
12.
Ready to use

Rearrange a specific formula. No randomisation.
13.
Ready to use

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$ -term having a coefficient of 1.
14.
Ready to use

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$ .
15.
Ready to use

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.
16.
Ready to use

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).
17.
Ready to use

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$ .
18.
Ready to use

Basic calculation from a sum given in Sigma notation.
19.
Ready to use

Find the volume of a semicylinder from a diagram.
20.
Ready to use

Match the graphs to the functions. No randomisation. Multiple choice.
21.
Ready to use

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$ .
22.
Ready to use

Match the relevant graph (sin, cos, tan) with its equation.
23.
Ready to use

Evaluating a linear function for a given value of $x$ .
24.
Ready to use

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$ .
25.
Ready to use

Solving an equation of the form $a^x=b$ using logarithms to find $x$ .
26.
Ready to use

Differentiate a polynomial expression involving coefficients and, negative and fractional indices.
27.
Ready to use

Calculating the definite integral $\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$ .
28.
Ready to use

Finding the stationary points of a cubic equation and determining their nature.
29.
Ready to use

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.
30.
Ready to use

Calculating the derivative of an exponential function of the form $ae^{bx}$ , using a table of derivatives.
31.
Ready to use

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.
32.
Ready to use

Calculating the derivative a function of the form $ax^n \sin(bx)$ using the product rule.
33.
Ready to use

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.
34.
Ready to use

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.
35.
Ready to use

This question provides a list of data to the student. They are asked to find the "range".
36.
Ready to use

This question asks the student to choose the appropriate measure of average and spread for a data with outliers.
37.
Ready to use

Identifying measures of spread or location (average)
38.
Ready to use

Tests understanding of scatter plots and related concepts.
39.
Ready to use

Calculate probability of selecting coloured counters from a bag.
40.
Ready to use

Predicting the probability of an unbiased coin landing on heads based on the results of previous throws.

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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Skills Audit for Maths and Stats - Aerospace Engineering, Electrical and Electronic Engineering, Electronics and Computer Engineering (MAS156)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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History

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Checkpoint description

Will Morgan 7 months, 3 weeks ago

Will Morgan 9 months, 2 weeks ago

Will Morgan 10 months ago

Will Morgan 10 months ago

Question groups

Topics

Learning objectives

Base diagnostic algorithm

Custom diagnostic algorithm

On leaving a question

On timeout

5 minutes before timeout