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 1. If you expand the binomial expression $$(a + b)^5$$ the result would be:$$\begin{pmatrix}5\\0\\ \end{pmatrix} a^5 + \begin{pmatrix}5\\1\\ \end{pmatrix} a^4 b + \begin{pmatrix}5\\2\\ \end{pmatrix} a^3 b^2 + \begin{pmatrix}5\\3\\ \end{pmatrix} a^2 b^3 + \begin{pmatrix}5\\4\\ \end{pmatrix} ab^4 + \begin{pmatrix}5\\5\\ \end{pmatrix} b^5$$Find the coefficient of the $$a^3 b^2$$ term 2. Find the coefficient of the $$b^5$$ term 3. In the expansion of $$(c + d)^7$$ what is the coefficient of the $$c^3 d^4$$ term? 4. In the expansion of $$(e + f)^9$$ what is the coefficient of the $$e^2 f^7$$ term? 5. In the expansion of $$(2x + 3y)^4$$ what is the coefficient of the $$x^4$$ term? 6. In the expansion of $$(3x + 4y)^5$$ what is the coefficient of the $$y^5$$ term? 7. In the expansion of $$(2x + 3y)^4$$ what is the coefficient of the $$x^2y^2$$ term? 8. In the expansion of $$(3x + 4y)^5$$ what is the coefficient of the $$x^2y^3$$ term? 9. Find the constant term in the expansion of $$(2x^2 - \frac12 )^6$$ 10. Use the expansion of $$(5 + x)^3$$ to find the exact value of $$5.1^3$$.

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Level 1 - Fill in the numbers on a blank triangular grid

Level 2 - Colour in the even numbers to produce a surprising pattern

Level 3 - Colour in the multiples of 3 to produce a surprising pattern

Level 4 - Colour in the remainders when dividing by four in different colours

Level 5 - Colour in sets of six connected hexagons that have given sums

Level 6 - Use a calculator to find particularly large numbers from Pascal's Triangle

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Sieve of Eratosthenes

A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

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Investigate the properties of number with these interactive number grids which can be coloured in.

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