Mathematics 0580 · IGCSE · Sequences

Sequences — practice question

The grid displays the first three diagrams in a sequence. Every diagram is built from identical small squares. Each square has side lengths of 1 unit.
(a(i))[1]

Draw Diagram 4 on the grid.

(a(ii))[1]

Fill in the table.

(a(iii))[2]

Find an expression, in terms of $n$, that gives the perimeter of Diagram $n$.

(a(iv))[2]

One diagram in the sequence has a perimeter of 300 units. Work out its Diagram number.

(a(v))[3]

Calculate the volume of the box. Include the units in your answer.

(b(i))[1]

Write down how many lines of symmetry Diagram 3 has.

(b(ii))[2]

Finish the table.

(b(iii))[1]

Find a formula, in terms of $n$, that gives the total number of small triangles, $t$, in Diagram $n$.

(b(iv))[2]

Show that this formula produces the right number of white triangles when $n = 3$.

(b(v))[3]

Finish this statement for Diagram 15. When $n = 15$, $w = \ldots\ldots\ldots\ldots$, $g = \ldots\ldots\ldots\ldots$ and $t = \ldots\ldots\ldots\ldots$.

Worked solution & mark scheme

This 18-mark question has a full step-by-step worked solution and mark scheme. One marking point: Diagram 4 drawn correctly

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