Pascal's Triangle

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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

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2. Find the coefficient of the \( b^5 \) term

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3. In the expansion of \( (c + d)^7 \) what is the coefficient of the \( c^3 d^4 \) term?

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4. In the expansion of \( (e + f)^9 \) what is the coefficient of the \( e^2 f^7 \) term?

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5. In the expansion of \( (2x + 3y)^4 \) what is the coefficient of the \( x^4 \) term?

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6. In the expansion of \( (3x + 4y)^5 \) what is the coefficient of the \( y^5 \) term?

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7. In the expansion of \( (2x + 3y)^4 \) what is the coefficient of the \( x^2y^2 \) term?

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8. In the expansion of \( (3x + 4y)^5 \) what is the coefficient of the \( x^2y^3 \) term?

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9. Find the constant term in the expansion of \( (2x^2 - \frac12 )^6 \)

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10. Use the expansion of \( (5 + x)^3 \) to find the exact value of \( 5.1^3 \).

Correct Wrong

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Bidmaze

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Find your way through the maze encountering mathematical operations in the correct order to achieve the given total. This is an addictive challenge that begins easy but develops into quite a difficult puzzle.

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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

Level 7 - Learn about the binomial theorem by answering questions about expanding brackets

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The function to work out a number in Pascal's Triangle appears as nCr where:

nCr Formula nCr button on calculator

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