OCR MEI C1 (Core Mathematics 1)

1

1. Express \(\frac { 81 } { \sqrt { 3 } }\) in the form \(3 ^ { k }\).
2. Express \(\frac { 5 + \sqrt { 3 } } { 5 - \sqrt { 3 } }\) in the form \(\frac { a + b \sqrt { 3 } } { c }\), where \(a , b\) and \(c\) are integers.
   \(2 \quad\) (i) Simplify \(\left( 5 a ^ { 2 } b \right) ^ { 3 } \times 2 b ^ { 4 }\).
3. Evaluate \(\left( \frac { 1 } { 16 } \right) ^ { - 1 }\).
4. Evaluate \(( 16 ) ^ { \frac { 3 } { 2 } }\).

3 Make \(y\) the subject of the formula \(a = \frac { \sqrt { y } - 5 } { c }\).

4

1. Find the value of \(144 ^ { - \frac { 1 } { 2 } }\).
2. Simplify \(\frac { 1 } { 5 + \sqrt { 7 } } + \frac { 4 } { 5 - \sqrt { 7 } }\). Give your answer in the form \(\frac { a + b \sqrt { 7 } } { c }\).

5 Find the value of each of the following.

1. \(5 ^ { 2 } \times 5 ^ { - 2 }\)
2. \(100 ^ { \frac { 3 } { 2 } }\)

6 State the value of each of the following.

1. \(2 ^ { - 3 }\)
2. \(9 ^ { 0 }\)

8

1. Find the value of \(\left( \frac { 1 } { 25 } \right) ^ { - \frac { 1 } { 2 } }\).
2. Simplify \(\frac { \left( 2 x ^ { 2 } y ^ { 3 } z \right) ^ { 5 } } { 4 y ^ { 2 } z }\).

9

1. Write down the value of \(\left( \frac { 1 } { 4 } \right) ^ { 0 }\).
2. Find the value of \(16 ^ { - \frac { 3 } { 2 } }\).

10

1. Find \(a\), given that \(a ^ { 3 } = 64 x ^ { 12 } y ^ { 3 }\).
2. Find the value of \(\left( \frac { 1 } { 2 } \right) ^ { - 5 }\).

11 Find the value of each of the following, giving each answer as an integer or fraction as appropriate.

1. \(\quad \frac { 3 } { 2 }\)
2. \(\left( \frac { 7 } { 3 } \right) ^ { - 2 }\)

12

1. Simplify \(6 \sqrt { 2 } \times 5 \sqrt { 3 } \quad \sqrt { 24 }\).
2. Express \(( 23 \sqrt { 5 } ) ^ { 2 }\) in the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are integers.

13 Simplify the following.

1. \(\frac { 16 ^ { \frac { 1 } { 2 } } } { 81 ^ { \frac { 3 } { 4 } } }\)
2. \(\frac { 12 \left( a ^ { 3 } b ^ { 2 } c \right) ^ { 4 } } { 4 a ^ { 2 } c ^ { 6 } }\)