OCR MEI C1 (Core Mathematics 1)

1

1. Expand and simplify \(( 3 + 4 \sqrt { 5 } ) ( 3 - 2 \sqrt { 5 } )\).
2. Express \(\sqrt { 72 } + \frac { 32 } { \sqrt { 2 } }\) in the form \(a \sqrt { b }\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.

2

1. Expand and simplify \(( 7 - 2 \sqrt { 3 } ) ^ { 2 }\).
2. Express \(\frac { 20 \sqrt { 6 } } { \sqrt { 50 } }\) in the form \(a \sqrt { b }\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.

3 Rearrange the following formula to make \(r\) the subject, where \(r > 0\). $$V = \frac { 1 } { 3 } \pi r ^ { 2 } ( a + b )$$

4

1. Express \(125 \sqrt { 5 }\) in the form \(5 ^ { k }\).
2. Simplify \(10 + 7 \sqrt { 5 } + \frac { 38 } { 1 - 2 \sqrt { 5 } }\), giving your answer in the form \(a + b \sqrt { 5 }\).

5

1. Express \(\sqrt { 48 } + \sqrt { 75 }\) in the form \(a \sqrt { b }\), where \(a\) and \(b\) are integers.
2. Simplify \(\frac { 7 + 2 \sqrt { 5 } } { 7 + \sqrt { 5 } }\), expressing your answer in the form \(\frac { a + b \sqrt { 5 } } { c }\), where \(a , b\) and \(c\) are integers.

6 Make \(b\) the subject of the following formula. $$a = \frac { 2 } { 3 } b ^ { 2 } c$$

7

1. Expand and simplify \(( 7 + 3 \sqrt { 2 } ) ( 5 - 2 \sqrt { 2 } )\).
2. Simplify \(\sqrt { 54 } + \frac { 12 } { \sqrt { 6 } }\).

8 The volume \(V\) of a cone with base radius \(r\) and slant height \(l\) is given by the formula $$V = \frac { 1 } { 3 } \pi r ^ { 2 } \sqrt { l ^ { 2 } - r ^ { 2 } }$$ Rearrange this formula to make \(l\) the subject.

9

1. Express \(\sqrt { 48 } + \sqrt { 27 }\) in the form \(a \sqrt { 3 }\).
2. Simplify \(\frac { 5 \sqrt { 2 } } { 3 - \sqrt { 2 } }\). Give your answer in the form \(\frac { b + c \sqrt { 2 } } { d }\).

10

1. Simplify \(\frac { \sqrt { 48 } } { 2 \sqrt { 27 } }\).
2. Expand and simplify \(( 5 - 3 \sqrt { 2 } ) ^ { 2 }\).

11

1. Express \(\sqrt { 75 } + \sqrt { 48 }\) in the form \(a \sqrt { 3 }\).
2. Express \(\frac { 14 } { 3 - \sqrt { 2 } }\) in the form \(b + c \sqrt { d }\).

12

1. Express \(\frac { 1 } { 5 + \sqrt { 3 } }\) in the form \(\frac { a + b \sqrt { 3 } } { c }\), where \(a , b\) and \(c\) are integers.
2. Expand and simplify \(( 3 - 2 \sqrt { 7 } ) ^ { 2 }\).

13 Make \(v\) the subject of the formula \(E = \frac { 1 } { 2 } m v ^ { 2 }\).

14 Make \(t\) the subject of the formula \(s = \frac { 1 } { 2 } a t ^ { 2 }\).

15

1. Simplify \(\sqrt { 98 } \quad \sqrt { 50 }\).
2. Express \(\frac { 6 \sqrt { 5 } } { 2 + \sqrt { 5 } }\) in the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are integers.

16 The volume of a cone is given by the formula \(V = \frac { 1 } { 3 } \pi r ^ { 2 } h\). Make \(r\) the subject of this formula.

17

1. Simplify \(5 \sqrt { 8 } + 4 \sqrt { 50 }\). Express your answer in the form \(a \sqrt { b }\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.
2. Express \(\frac { \sqrt { 3 } } { 6 \sqrt { 3 } }\) in the form \(p + q \sqrt { 3 }\), where \(p\) and \(q\) are rational.