OCR MEI C1 (Core Mathematics 1)

1

1. Solve the equation \(2 x ^ { 2 } + 3 x = 0\).
2. Find the set of values of \(k\) for which the equation \(2 x ^ { 2 } + 3 x - k = 0\) has no real roots.

2 Make \(x\) the subject of the equation \(y = \frac { x + 3 } { x - 2 }\).

3 Solve the equation \(y ^ { 2 } - 7 y + 12 = 0\).
Hence solve the equation \(x ^ { 4 } - 7 x ^ { 2 } + 12 = 0\).

4

1. Write \(\sqrt { 48 } + \sqrt { 3 }\) in the form \(a \sqrt { b }\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.
2. Simplify \(\frac { 1 } { 5 + \sqrt { 2 } } + \frac { 1 } { 5 - \sqrt { 2 } }\).

5 Solve the equation \(\frac { 4 x + 5 } { 2 x } = - 3\).

6 Make \(a\) the subject of the equation $$2 a + 5 c = a f + 7 c$$

7 Find the set of values of \(k\) for which the equation \(2 x ^ { 2 } + k x + 2 = 0\) has no real roots.

8 One root of the equation \(x ^ { 3 } + a x ^ { 2 } + 7 = 0\) is \(x = - 2\). Find the value of \(a\).
\(9 n\) is a positive integer. Show that \(n ^ { 2 } + n\) is always even.

10 Make \(C\) the subject of the formula \(P = \frac { C } { C + 4 }\).

11

1. Find the range of values of \(k\) for which the equation \(x ^ { 2 } + 5 x + k = 0\) has one or more real roots.
2. Solve the equation \(4 x ^ { 2 } + 20 x + 25 = 0\).