Foundation January 2022 Paper 2 Q12
12 The diagram shows a box B and a carton C
Diagram NOT accurately drawn
The box B is in the shape of a cuboid.
Each carton C is in the shape of an 8 cm cube.
Martha is going to put as many of the cartons as possible into the box.
She has enough cartons to do this.
Martha will then fill the remaining space inside the box with packing material.
Work out the volume of the space inside the box that Martha will fill with packing material.
(5)
| Scheme | Marks |
|---|---|
| two of: 60 ÷ 8 (= 7.5) or 7 20 ÷ 8 (= 2.5) or 2 24 ÷ 8 (= 3) | M1 |
| “7” × “2” × “3” (= 42) or “7” × 8 (= 56) and “2” × 8 (= 16) and “3” × 8 (= 24) | M1 |
| 60 × 24 × 20 (= 28 800) or 8 × 8 × 8 (= 512) or (7 × 8) × (2 × 8) × (3 × 8) (= 21 504) oe eg 56 × 16 × 24 (= 21 504) | M1 |
| “28 800” – “42” × “512” or “28 800” – “21 504” | M1 |
| 7296 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: at least two divisions to find number of cartons for \(l\) or \(w\) or \(h\).
Could be written on sides of box
M1: correct method to find the number of cartons that fit or finding the dimensions of the occupied space
M1: method to work out volume of either B or C
M1: complete method to find volume of packing material.
A1: allow 7300 from correct working
If no marks scored
SC B3 for
60 × 24 × 20 – “56” × 8 × 8 × 8
(= 128)
Alternative: finding space left
| Scheme | Marks |
|---|---|
| two of 7 × 8 (= 56), 3 × 8 (= 24), 2 × 8 (= 16) or two of 60 – 56 (= 4), 20 – 16 (= 4), 24 – 24 (= 0) | M1 |
| “4” × 24 × 20 (= 1920) or “4” × 24 × 60 (= 5760) or “4” × “4” × 24 (= 384) or “4” × 24 × “16” (= 1536) or “4” × 24 × “56” (= 5376) | M1 |
| M1 | |
| eg “1920” + “5760” – “384” or “1536” + “384” + “5376” or “5760” + “1536” or “1920” + “5376” oe | M1 |
| 7296 | A1 |
M1: two lengths of filled space found
or
two lengths of empty space found.
M1: at least one correct product seen
M1: at least two correct products seen
M1: complete method to find volume of packing material.