4400 Higher June 2009 Paper 3 Q13
13 Here is a cuboid with length \(L\), width \(W\) and height \(H\).
The total surface area, \(A\), of the cuboid is given by the formula\[A = 2(LW + HW + HL)\]
Work out the value of \(L\). (3)
| Scheme | Marks |
|---|---|
| \(12L + 16 = 70\) or \(8L + 4L = 54\) or \(12L = 54\) or \(6L + 8 = 35\) or \(4L + 2L = 27\) or \(6L = 27\) | M2 |
| 4.5 oe | A1 |
| (3) |
Notes
M2: for correctly collecting \(L\)s or constants or both
M1 for correct substitution in given formula or in a correct rearrangement of the given formula in which \(L\) is not the subject
eg \(70 = 2(4L + 2 \times 4 + 2L)\) or \(70 = 2(4L + 8 + 2L)\) or \(35 = 4L + 2 \times 4 + 2L\) or \(35 = 4L + 8 + 2L\) or \(70 - 2 \times 2 \times 4 = 8L + 4L\) or \(35 - 2 \times 4 = 4L + 2L\)
A1: depends on M2
Alternative method
\(L = \dfrac{A - 2HW}{2(W + H)}\) oe M1 for making \(L\) the subject of the given formula
eg \(\dfrac{70 - 2 \times 2 \times 4}{2(4 + 2)}\) M1 for correct substitution into a correct expression for \(L\)
4.5 oe A1 depends on both method marks
| Scheme | Marks |
|---|---|
\(A = 2LW + 2WH + 2HL\) or \(\dfrac{A}{2} = LW + WH + HL\) | M1 |
\(A - 2HL = 2LW + 2WH\) or \(\dfrac{A}{2} - HL = LW + WH\) | M1 |
\(A - 2HL = 2W(L + H)\) or \(A - 2HL = W(2L + 2H)\) or \(\dfrac{A}{2} - HL = W(L + H)\) | M1 |
| \(\dfrac{A - 2HL}{2(L + H)}\) or \(\dfrac{A - 2HL}{2L + 2H}\) or \(\dfrac{\frac{A}{2} - HL}{L + H}\) oe | A1 |
| (4) | |
| (7 marks) |
Notes
M1: for a correct equation following expansion or division by 2
May be implied by second M1
M1: for correct equation with \(W\) terms isolated
M1: for correct equation with \(W\) as a factor