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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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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

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## Description of Levels

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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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#### Number Grids

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

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##### Related

A simulation of a Quincunx (Galton Board) which can be used to create the bell shaped curve of the normal distribution.

#### Pascal's Patterns

See the number patterns on Pascal's Triangle with this colourful, interactive application.