Foundation June 2017 Unit 1 Q19
19. In the diagram below,
- ABCD is a rectangle, and
- PQ is parallel to AD.
Diagram not drawn to scale
The area of ABCD is 52 cm2.
The area of APQD is 20 cm2.
Calculate the values of \(f\) and \(g\).
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Use of area of PBCQ =) 52 – 20 (= 32 cm2) | B1 | Answers /working may be seen on diagram. |
| (Area of PBCQ =) 8 × f = 32 | M1 | F.T. ‘their derived 32’ but not 52 [B1M1 implied by 8f = 32] |
| f = 4 | A1 | C.A.O. (implies B1M1A1) |
| (Area of APQD =) 4 × g = 20 | M1 | F.T. ‘their f’. |
| g = 5 | A1 |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| f × (g + 8) = 52 [fg + 8f = 52] | M1 | |
| fg = 20 [M2 implied by 20 + 8f = 52 or 8f = 32] | M1 | |
| f = 4 | A1 | C.A.O. |
| 4 × g = 20 | M1 | FT ‘their f’. |
| g = 5 | A1 |