June 2016 Paper 1 Q6
6 \(mx + 4 - 2(x + p) \equiv 6(x + 1) \qquad\) where \(m\) and \(p\) are integers.
Work out the values of \(m\) and \(p\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(mx + 4 - 2x - 2p\) or \(6x + 6\) | M1 | allow one error on the left hand side |
| \(mx - 2x = 6x\) or \(4 - 2p = 6\) | M1 | oe eg. \(m - 2 = 6\) ft their expansion if 1st M1 earned |
| \(m = 8\) | A1 | |
| \(p = -1\) | A1 | |
| Alternative method 2 | ||
| \(mx + 4 - 2x - 2p = 6x + 6\) | M1 | At most one error in total in the expansion and the simplifying |
| \(mx - 2p = 8x + 2\) | M1 | This must be in the form \(ax + b = cx + d\) |
| \(m = 8\) | A1 | |
| \(p = -1\) | A1 | |
| Alternative method 3 | ||
| An equation obtained by substituting a value for \(x\) in the identity | M1 | eg \(\quad x = 0 \quad 4 - 2p = 6\) \(\qquad x = 1 \quad m + 4 - 2 - 2p = 12\) \(\qquad x = 2 \quad 2m + 4 - 4 - 2p = 18\) |
| A second equation obtained by substituting a value for \(x\) in the identity | M1 | |
| \(m = 8\) | A1 | |
| \(p = -1\) | A1 | |
Additional guidance
\(mx + 4 - 2x + 2p\) is one error in the left hand side
\(mx + 4 - 2x - p\) is one error in the left hand side
\(mx + 4 - 2x + p\) is two errors in the left hand side
In alt 2 ... allow at most one error in the expansion and the simplifying (the first two M marks) ... one error can then score M1 M1, two errors will score M1 M0
Also, in alt 3, allow at most one error in forming their two simultaneous equations