4MA0 Higher January 2017 Paper 4R Q21
21 A rectangular piece of card has length \((3x - 13)\) cm and width \((x - 2)\) cm.
A square, with sides of length 25 cm, is removed from each corner of the card.
Diagram NOT accurately drawn
The card is then folded along the dashed lines to make an open box with height 25 cm as shown below.
Diagram NOT accurately drawn
(a) Show that the length of the open box is \((3x - 63)\) cm. (1)
The volume of the open box is 81 900 cm\(^3\)
(b) Find the value of \(x\).
Show clear algebraic working. (5)
Show clear algebraic working. (5)
| Scheme | Marks |
|---|---|
| \(3x - 13 - 50\) | B1 |
| (1) |
Notes
B1: or \(3x - 13 - 25 - 25\)
| Scheme | Marks |
|---|---|
| \(x - 52\) | B1 |
| \(25(3x - 63)(x - 52)\) (= 81900) | M1 |
| eg \(3x^2 - 156x - 63x + 3276\) (= 3276) or \(75x^2 - 3900x - 1575x + 81900\) (= 81900) | M1 |
| eg \(3x^2 - 219x = 0\) or \(3x(x - 73) = 0\) or \(75x^2 - 5475x = 0\) | M1 |
| (\(x = 0\)) or \(x = 73\) Answer: 73 | A1 |
| (5) | |
| (6 marks) |
Notes
B1: or \(x - 2 - 25 \times 2\)
M1: For a correct expression for volume of box
M1: For brackets correctly expanded
M1: For correctly reducing to 2 term quadratic equation
A1: For \(x = 73\)
NB: A1 dependent on at least 2 method marks