OCR MEI C1 (Core Mathematics 1)

1 Solve the inequality \(\frac { 4 x - 5 } { 7 } > 2 x + 1\).

2 Solve the inequality \(3 x ^ { 2 } + 10 x + 3 > 0\).

3 Solve the inequality \(5 x ^ { 2 } - 28 x - 12 \leqslant 0\).

4 Solve the following inequality. $$\frac { 2 x + 1 } { 5 } < \frac { 3 x + 4 } { 6 }$$

5 Solve the inequality \(6 ( x + 3 ) > 2 x + 5\).

6 Solve the inequality \(5 - 2 x < 0\).

7 Solve the following inequalities.

1. \(2 ( 1 - x ) > 6 x + 5\)
2. \(( 2 x - 1 ) ( x + 4 ) < 0\)

8 Solve the inequality \(\frac { 5 x - 3 } { 2 } < x + 5\).

9 Solve the inequality \(x ( x - 6 ) > 0\).

10 Solve the inequality \(7 - x < 5 x - 2\).

11 Solve the inequality \(3 x - 1 > 5 - x\).

12 Solve the inequality \(1 - 2 x < 4 + 3 x\).

13 Solve the inequality \(x ^ { 2 } + 2 x < 3\).

14 Solve the inequality \(\frac { 3 ( 2 x + 1 ) } { 4 } > - 6\).

15

1. Write \(x ^ { 2 } - 5 x + 8\) in the form \(( x - a ) ^ { 2 } + b\) and hence show that \(x ^ { 2 } - 5 x + 8 > 0\) for all values of \(x\).
2. Sketch the graph of \(y = x ^ { 2 } - 5 x + 8\), showing the coordinates of the turning point.
3. Find the set of values of \(x\) for which \(x ^ { 2 } - 5 x + 8 > 14\).
4. If \(\mathrm { f } ( x ) = x ^ { 2 } - 5 x + 8\), does the graph of \(y = \mathrm { f } ( x ) - 10\) cross the \(x\)-axis? Show how you decide.