Numeracy Intermediate June 2023 Unit 2 Q8
8. Paper comes in standard sizes.
| Paper size | A0 | A1 | A2 | A3 | A4 | |
|---|---|---|---|---|---|---|
| Dimensions: | Length (cm) | 118·9 | 84·1 | 59·4 | 42·0 | 29·7 |
| Width (cm) | 84·1 | 59·4 | 42·0 | 29·7 | 21·0 | |
Which paper size has an area of approximately 500 000 mm\(^{2}\)?
Circle your answer. [1]
A0 A1 A2 A3 A4
The mass of paper is measured in grams.
The quality of paper is given by its mass per square metre of paper.
The quality of a sheet of A2 paper used for printing is stated as 120 g/m\(^{2}\).
Complete the following statement. [4]
‘This sheet of A2 paper has a mass of …………………… g.’
Sheets of A4 and A5 paper are mathematically similar.
Diagram not drawn to scale
Calculate the length of the diagonal of a sheet of A5 paper.
You must show all your working. [5]
The measurements for the A1 sheet of paper in the table are correct to the nearest mm.
Calculate the greatest possible perimeter of an A1 sheet of paper. [3]
| Scheme | Marks | Comments |
|---|---|---|
| A1 | B1 |
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 59.4 × 42(.0) ÷ (100 × 100) or 0.594 × 0.42 | M2 | For a product using the correct place value in the conversion of units (= 0.249(48 m\(^{2}\)) or 0.25 (m\(^{2}\))) Do not accept use of 59 instead of 59.4 for M2 M1 for a calculation including the product of digits 59(.4) and 42(.0), which may include error(s) due to place value | ||||||||
| × 120 | m1 | FT from M2 or M1 | ||||||||
| 29.9376(g) or 29.94(g) or an answer in the range 29.8 (g) to 30 (g) | A1 | CAO. Statement answer space takes precedence If incorrect size of paper selected, award SC2 for the following answers, allow suitable rounding, or truncation at 1 or more decimal place(s):
OR Award SC1 for the appropriate digits with a place value error |
| Scheme | Marks | Comments |
|---|---|---|
| (Diagonal A4\(^{2}\) =) 21\(^{2}\) + 29.7\(^{2}\) | M1 | May be shown in further working |
| Diagonal\(^{2}\) = 1323.09 or (Diagonal =) √1323.09 | A1 | |
| (Diagonal A4 =) 36 (cm) or 36.3(7... cm) or 36.4 (cm) | A1 | FT from M1 for the correctly evaluated square root of ‘their 1323.09’ provided ‘their answer’ > 29.7 (cm) Must be from correct working |
| (Diagonal A5) 36.37... × 21(.0) ÷ 29.7 or 36.37... × 0.7(0....) or 36.37... ÷ (29.7 ÷ 21(.0)) or 36.37… ÷ 1.4(1…) | M1 | FT ‘their derived diagonal’ or ‘their stated diagonal’ provided ≠ 21 or ≠ 29.7 |
| Answer in the range 25.2 (cm) to 26(cm) | A1 | Answer must be from correct working. |
Alternative
8(c) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| (Side of A5) 21(.0) × 21(.0) ÷ 29.7 or 21 × 0.7(0...) or 21 ÷ 1.4(1...) or 29.7 ÷ 2 | M1 | May be shown in further working |
| Answer in the range 14.7 (cm) to 15(cm) | A1 | Must be from correct working |
| (Diagonal A5\(^{2}\) =) 21(.0)\(^{2}\) + 14.848...\(^{2}\) | M1 | FT ‘their derived side of A5’ or ‘their stated side of A5’ provided ≠ 21 or ≠ 29.7 |
| Diagonal\(^{2}\) = 661.4775.... or (Diagonal =) √661.4775... | A1 | |
| (Diagonal A5) Answer in the range 25.2 (cm) to 26(cm) | A1 | Answer must be from correct working. FT from M1 for the correctly evaluated square root of ‘their 661.4775...’ provided ‘their answer’ > 21 (cm) |
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Penalise incorrect unit -1 once (withhold B or A mark) | ||||||||||
| Sight of 84.15(cm) or 841.5(mm) and 59.45 (cm) or 594.5(mm) or equivalents in m | B1 | Award B1 for sight of 4 × 0.05 in an appropriate calculation Allow 0.04999(....) for 0.05, must clearly be a recurring 9 digit | ||||||||
| 2 × (84.15 + 59.45) or 2 × (84.1 + 59.4) + 4 × 0.05 or equivalent | M1 | Or equivalent in mm or m If B0, FT provided unambiguously chosen: 84.1 < ‘their 84.15’ ≤ 84.2 and 59.4 < ‘their 59.45’ ≤ 59.5 | ||||||||
| 2872 (mm) or 287.2 (cm) or 2.872 (m) | A1 | CAO. Allow 287.1999 (cm) or equivalent (Note: Not using bounds leads to an incorrect answer of 287cm B0 M0 A0) If incorrect size of paper selected, award SC1 for the following answers, or equivalents:
|