OCR MEI C1 (Core Mathematics 1)

Evaluate the following.

1. \(200^0\) [1]
2. \(\left(\frac{25}{9}\right)^{-\frac{1}{2}}\) [3]

1. Evaluate \(\left(\frac{1}{27}\right)^{\frac{2}{3}}\). [2]
2. Simplify \(\frac{(4a^2c)^3}{32a^4c^7}\). [3]

You are given that \(n\), \(n + 1\) and \(n + 2\) are three consecutive integers.

1. Expand and simplify \(n^2 + (n + 1)^2 + (n + 2)^2\). [2]
2. For what values of \(n\) will the sum of the squares of these three consecutive integers be an even number? Give a reason for your answer. [2]

1. Evaluate \((0.2)^{-2}\). [2]
2. Simplify \((16a^{12})^{\frac{3}{4}}\). [3]

Find the value of each of the following.

1. \(\left(\frac{5}{3}\right)^{-2}\) [2]
2. \(81^{\frac{1}{4}}\) [2]

1. Evaluate \(\left(\frac{1}{5}\right)^{-2}\). [2]
2. Evaluate \(\left(\frac{8}{27}\right)^{\frac{2}{3}}\). [2]

1. Simplify \(\frac{10(\sqrt{6})^3}{\sqrt{24}}\). [3]
2. Simplify \(\frac{1}{4 - \sqrt{5}} + \frac{1}{4 + \sqrt{5}}\). [2]

1. Evaluate \(9^{-\frac{1}{2}}\). [2]
2. Simplify \(\frac{(4x^4)^3 y^2}{2x^4 y^5}\). [3]

Expand and simplify \((n + 2)^3 - n^3\). [3]

1. Evaluate \(\left(\frac{9}{16}\right)^{-\frac{1}{2}}\). [2]
2. Simplify \(\frac{(2ac^2)^3 \times 9a^2c}{36a^4c^{12}}\). [3]

1. Write down the value of each of the following.
   1. \(4^{-2}\) [1]
   2. \(9^0\) [1]
2. Find the value of \(\left(\frac{64}{125}\right)^{\frac{4}{3}}\). [2]