4MA0 Higher January 2015 Paper 4 Q8
8 The diagram shows a triangle.
Diagram NOT accurately drawn
The lengths of the sides of the triangle are \(3x\) cm, \((3x - 5)\) cm and \((4x + 2)\) cm.
The perimeter of the triangle is 62 cm.
Work out the value of \(x\).
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
| \(3x - 5 + 3x + 4x + 2\) \((= 10x - 3)\) | M1 |
| \(3x - 5 + 3x + 4x + 2 = 62\) or \(\text{“}10x - 3\text{”} = 62\) | M1 |
| eg. \(10x - 3 = 62\) | M1 |
| 6.5 or \(6\frac{1}{2}\) | A1 |
| (4 marks) |
Notes
M1: correct expression for perimeter
(may be seen in an equation)
M1: dep
M1: (dep) correct method to collect \(x\) terms in a correct equation
A1: dep on all method marks
SC:
B2 for \(x = 6.5\) and 3×6.5 – 5 + 3×6.5 + 4×6.5 + 2 = 62
(B1 for a value for \(x\) substituted into correct expression for perimeter
eg. 3×6 – 5 + 3×6 + 4×6 + 2 )