Numeracy Higher November 2016 Unit 2 Q3
3. The wire window guard shown below is to be made.
Diagram not drawn to scale
The length of the sides of each small wire square shown is 3·3 cm.
Diagram not drawn to scale
Llinos considers the length of the diagonal of each small square.
Diagram not drawn to scale
She says,
The height of the window guard is equal to 9·5 diagonals of the square.
The width of the window guard is equal to 11 diagonals of the square.
The width of the window guard is equal to 11 diagonals of the square.
(a) Calculate the length of the diagonal of a small square.
Give your answer correct to 1 decimal place. [3]
Give your answer correct to 1 decimal place. [3]
(b) Calculate the area of the window guard.
You must show all your working. [3]
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (diagonal2 =) 3.32 + 3.32 diagonal2 = 21.78 or diagonal = √21.78 diagonal is 4.7 (cm) | M1 A1 A1 | Scale drawings are not accepted in Q3 FT from M1 for the correctly evaluated square root of ‘their 21.78’ provided ‘their answer’ > 3.3 (cm) Must be to 1 d.p. Accept an unsupported 4.7(cm) |
| Scheme | Marks | Comments |
|---|---|---|
| 11 × 4.6(669…) × 9.5 × 4.6(669…) or 11 × 4.7 × 9.5 × 4.7 or 104.5 × (4.7)2 | M2 | FT for ‘their derived diagonal’, but not 3.3 cm M1 for sight of either 11 × 4.6(669…) or 9.5 × 4.6(669…) (Height 44.3355… cm; width 51.3359…cm) |
| (Area =) 2276(.01cm2) | A1 | Accept answers in the range 2211 (cm2) to 2308.41 (cm2) from appropriate working (Note: e.g. use of a diagonal such as 5.27(cm) allow appropriate calculation with 5.2 (cm) or 5.3 (cm) for M2, A1; however use of 5 throughout is a possible M2, A0) |