Numeracy Intermediate June 2017 Unit 1 Q8
8. Bethan builds a rectangular sheep pen.
(a) The perimeter fence of the sheep pen is 18 m long.
It costs her £1.10 for every 0·5 metres of fencing used to make the sheep pen.
It costs her £1.10 for every 0·5 metres of fencing used to make the sheep pen.
(i) Calculate the cost of the fencing used to make this sheep pen. [2]
Cost is £ ……………
(ii) The length of Bethan’s sheep pen is two times its width.
Find the length and width of this sheep pen.
You must show your working. [2]
Find the length and width of this sheep pen.
You must show your working. [2]
Length is …………… metres
Width is …………… metres
(b) Bethan decides to build a new sheep pen.
The perimeter fence of the new sheep pen is 16 m long.
The length of the new sheep pen is 3 metres longer than the width.
The perimeter fence of the new sheep pen is 16 m long.
The length of the new sheep pen is 3 metres longer than the width.
Form an equation and solve it to find the dimensions of this new sheep pen. [3]
Length is …………… metres
Width is …………… metres
| Scheme | Marks | Comments |
|---|---|---|
| (i) 2 × 18 × 1.1(0) or 1.1 × 18 ÷ 0.5 or equivalent | M1 | |
| (=£) 39.6(0) | A1 | Award M1 A1 for a correct response from an error in notation such as 18 × 0.5 = 36 with 36 × 1.1 = (£)39.6(0) Note: 18 ÷ 0.5 = 9, 9 × 1.1 = (£)9.9(0) is M1 A0 as full method shown in stages, but only if the full method is seen, not for an answer of (£)9.9(0) |
| (ii) (Length) 6 (m) AND (width) 3 (m) | B2 | Accept in either order in the answer space B1 for any 1 of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| x + 3 + x + 3 + x + x = 16 or x + 3 + x = 8 or equivalent | M1 | Accept any variable for 'x' |
| 4x + 6 = 16 or 4x = 16 – 6 or 4x = 10 or 2x + 3 = 8 or equivalent | m1 | Depends on the previous M1 This m1 implies the previous M1 |
| (Length) 5.5 (m) and (width, x) 2.5 (m) | A1 | CAO Needs to be in the correct order in the answer space, or clearly labelled Alternative method to work with y – 3 and y leading to y = 5.5 If no marks, allow SC1 for answers of 5.5(m) and 2.5(m) if no equation given or if ‘their equation’ not used to elicit these answers, OR SC1 for answers of 9.5(m) and 6.5(m) from sight of x + x + 3 = 16 |