OCR MEI C1 (Core Mathematics 1)

1 Evaluate the following.

1. \(200 ^ { \circ }\)
2. \(\left( \frac { 25 } { 9 } \right) ^ { - \frac { 1 } { 2 } }\)

2

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

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. 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.

4

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

5 Find the value of each of the following.

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

6

1. Evaluate \(\left( \frac { 1 } { 5 } \right) ^ { - 2 }\).
2. Evaluate \(\left( \frac { 8 } { 27 } \right) ^ { \frac { 2 } { 3 } }\).
   \(7 \quad\) (i) Simplify \(\frac { 10 ( \sqrt { 6 } ) ^ { 3 } } { \sqrt { 24 } }\).
3. Simplify \(\frac { 1 } { 4 - \sqrt { 5 } } + \frac { 1 } { 4 + \sqrt { 5 } }\).

8

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

9 Expand and simplify \(( n + 2 ) ^ { 3 } - n ^ { 3 }\).

10

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

11

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