Skills Audit for Maths and Stats - Science and Engineering Foundation Year (MAS003)

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Will Morgan

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Will Morgan

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Ready to use

8 months, 3 weeks ago

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Will Morgan 8 months, 3 weeks ago

Gave some feedback: Ready to use

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Will Morgan 9 months, 3 weeks ago

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Will Morgan 10 months, 1 week ago

Gave some feedback: Needs to be tested

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Will Morgan 10 months, 1 week ago

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Question groups

Group 64 questions

1.
Ready to use

"Convert" from millilitres to cubic centimeters.
2.
Ready to use

convert from inches to cm.
3.
Ready to use

Identify the truth value of an inequality (T/F) between two numbers
4.
Ready to use

Calculating the LCM and HCF of numbers by using prime factorisation.
5.
Ready to use

Calculating the LCM and HCF of numbers by using prime factorisation.
6.
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.
7.
Ready to use

Round numbers to a given number of decimal places.
8.
Ready to use

Round numbers to a given number of significant figures.
9.
Ready to use

Round numbers to a given number of significant figures.
10.
Ready to use

Calculations with negative numbers.
11.
Ready to use

Compound percentage change.
12.
Ready to use

Find the original price before a discount by dividing the new price by the percentage discount.
13.
Ready to use

Calculate one number as percentage of another.
14.
Ready to use

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.
15.
Ready to use

Several problems involving the multiplication of fractions, with increasingly difficult examples, including a mixed fraction and a squared fraction. The final part is a word problem.
16.
Ready to use

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions.
17.
Ready to use

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.
18.
Ready to use

Put fractions in size order.
19.
Ready to use

Convert a percentage to a fraction.
20.
Ready to use

Convert a decimal to a fraction.
21.
Ready to use

Convert a fraction into a decimal.
22.
Ready to use

Dividing amounts in ratios
23.
Ready to use

Calculations involving Standard form.
24.
Ready to use

perform a calculation involving negative indices.
25.
Ready to use

Simple exercise in collecting terms in different powers of $x$
26.
Ready to use

Simple exercise in collecting terms in different powers of $x$
27.
Ready to use

Filling in the blanks from the answer to a simplified expression involving indices.
28.
Ready to use

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.
29.
Ready to use

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4
30.
Ready to use

Expanding two linear brackets multiplied together.
31.
Ready to use

Expand two brackets involving powers of $x$ .
32.
Ready to use

Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$ .
33.
Ready to use

Solve linear equations with unkowns on both sides. Including brackets and fractions.
34.
Ready to use

Solve linear equations with unkowns on both sides. Including brackets and fractions.
35.
Ready to use

Substitute values into an algebraic expression and calculate the result.
36.
Ready to use

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.
37.
Ready to use

Rearrange a specific formula. No randomisation.
38.
Ready to use

Solve linear equations with unkowns on both sides. Including brackets and fractions.
39.
Ready to use

Factorise three quadratic equations of the form $x^2+bx+c$ . The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
40.
Ready to use

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$ -term having a coefficient of 1.
41.
Ready to use

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$ .
42.
Ready to use

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
43.
Ready to use

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$ , using the difference of two squares formula.
44.
Ready to use

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d) x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.
45.
Ready to use

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.
46.
Ready to use

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).
47.
Ready to use

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

48.

Ready to use

Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.

Variable	Value	Description
statement2
sh2_gen

49.

Ready to use

Finding the area of a circle when given the diameter of the circle.

Variable	Value	Description
d

50.
Ready to use

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.
51.
Ready to use

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.
52.
Ready to use

Find the diagonal or one side of a rectangle using Pythagoras' theorem.
53.
Ready to use

Draws a triangle based on 3 side lengths. Randomises asking angle or side.
54.
Ready to use

Draws a triangle based on 3 side lengths. Randomises asking angle or side.
55.
Ready to use

Draws a triangle based on 3 side lengths. Randomises asking angle or side.
56.
Ready to use

Calculating gradient and finding intercept from a geogebra graph.
57.
Ready to use

Multiple choice - select the quadratic graph.
58.
Ready to use

Interpreting the elements of a box plot
59.
Ready to use

This question provides a list of data to the student. They are asked to find the "range".
60.
Ready to use

Calculating the Mean from a basic list of integers.
61.
Ready to use

This question provides a list of data to the student. They are asked to find the "median".
62.
Ready to use

Identifying measures of spread or location (average)
63.
Ready to use

Tests understanding of scatter plots and related concepts.
64.
Ready to use

Calculate probability of selecting coloured counters from a bag.

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 - Science and Engineering Foundation Year (MAS003)

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Will Morgan 8 months, 3 weeks ago

Will Morgan 9 months, 3 weeks ago

Will Morgan 10 months, 1 week ago

Will Morgan 10 months, 1 week ago

Question groups

Topics

Learning objectives

Base diagnostic algorithm

Custom diagnostic algorithm

On leaving a question

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