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This test contains a few easy questions on subjects covered in the GCSE syllabus. I made it to try out the \"School\" theme, adapted for younger students.

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The volume of the pool, in m3

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Number of lengths Alex swims

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The cross-section of the pool - the area of the trapezium face.

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Total distance Alex swims

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Alex visited a swimming pool. The length of the pool is {length} metres.

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Work out the volume of a prism with a trapezium cross-section.

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Alex swims a total of {total_distance_string}.

\n

How many lengths did Alex swim?

\n

[[0]] lengths

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Here is a sketch of the swimming pool.

\n

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Work out the cross section of the pool.

\n

[[0]] m2

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Work out the capacity of the pool in litres.

\n

(1 m3 = 1000 litres)

\n

[[0]] litres

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Find a formula for \\(y\\) in terms of \\(x\\).

\n

\\(y = \\) [[0]]

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Find the value of \\(y\\) when \\(x=\\var{x2}\\).

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Find the value of \\(x\\) when \\(y = \\var{y3}\\).

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You are told that \\(y\\) is proportional to \\(x^2\\) and that when \\(y=\\var{y1}\\), \\(x=\\var{x1}\\).

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Since \\(y\\) is proportional to \\(x^2\\), we can write the following equation:

\n

\\[ y = kx^2 \\]

\n

Where \\(k\\) is a number we need to work out.

\n

We're told that when \\(y=\\var{y1}\\), \\(x=\\var{x1}\\). That is,

\n

\\[ \\simplify[]{ {y1} = k*({x1}^2)} = k \\times \\var{x1^2} \\]

\n

So

\n

\\[ k = \\simplify[]{ {y1} / {x1^2} } = \\var{k} \\]

\n

We can now write down the formula for \\(y\\) in terms of \\(x\\):

\n

\\[ y = \\var{k}x^2 \\]

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Work out \\(k\\) when \\( y = kx^2\\).

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Complete the following statement to show the range of possible values for \\(L\\).

\n

[[0]] \\(\\leq L \\lt \\) [[1]]

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Jim rounds a number, \\(x\\), to one decimal place.

\n

The result is {dpformat(x,1)}.

\n

Write down the error interval for \\(x\\).

\n

[[0]] \\( \\leq x \\lt \\) [[1]]

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The length, \\(L\\) cm, of a line is measured as {length} cm correct to the nearest centimetre.

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One of the men and one of the women are going to be chosen to make a pair to sing the first song.

\n

Work out the number of different pairs that can be chosen.

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Two of the men are going to be chosen to make a pair to sing the second song.

\n

Ben thinks the number of different pairs that can be chosen is {comb(num_men,2)}.

\n

Mark thinks the number of different pairs that can be chosen is {perm(num_men,2)}.

\n

Who is correct, Ben or Mark?

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Ben

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Mark

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There are {num_men} men and {num_women} women in a choir.

\n

The choir is going to sing at a concert.

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Number of ways of picking 2 men; order doesn't matter.

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Marie has {num_cards} cards.

\n

Each card has a different symbol on it.

\n

Marie gives one card to Shelley and one card to Pauline.

\n

In how many different ways can Marie do this?

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There are {num_boys} boys and {num_girls} girls in David's class.

\n

David is going to pick three different students from his class and write their names in a list in order.

\n

The order will be

\n\n

or

\n\n

How many different lists can David write?

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Number of ways of giving one card to each of two people.

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Number of ways of writing a list boy-girl-boy or girl-boy-girl.

"}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question"}, {"name": "Product rule for counting", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "

Use the product rule (number of ways of doing A and B = (no. for A)*(no. for B)) to count the number of ways of doing two independent tasks.

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There are {num_a} boys and {num_b} girls in a class.

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Work out the total number of ways that 1 boy and 1 girl can be chosen from the class.

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This test contains a few easy questions on subjects covered in the GCSE syllabus.

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