Which paper size has an area of approximately 500 000 mm\(^2\)? Circle your answer. [1]
A0 A1 A2 A3 A4
(b)
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.’
(c)
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]
(d)
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]
Mark scheme (a)
Scheme
Marks
Comments
A1
B1
Mark scheme (b)
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):
A0*
A1
A3
A4
119.993..(g)*
59.946…(g)
14.9688(g)
7.4844(g)
*Paper size A0 appropriate working or 119.9(…) must be seen OR Award SC1 for the appropriate digits with a place value error
Mark scheme (c)
Scheme
Marks
Comments
(Diagonal A4\(^{2}\) =) 21\(^{2}\) + 29.7\(^{2}\)
M1
May be shown in further working
Diagonal\(^{2}\) = 1323.09 or (Diagonal =) \(\sqrt{1323.09}\)
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
4(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
FT ‘their derived side of A5’ or ‘their stated side of A5’ provided ≠ 21 or ≠ 29.7
Diagonal\(^{2}\) = 661.4775.... or (Diagonal =) \(\sqrt{661.4775...}\)
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)
Note:
Side A5
Diagonal\(^{2}\)
Answer, in cm
14
637
25.23…
14.7
657.09
25.63…
14.8
660.04
25.69.. or 25.7
14.84
661.2256
25.71...
14.85
661.5225
25.72…
14.9
663.01
25.748… or 25.75
15
666
25.8…
Mark scheme (d)
Scheme
Marks
Comments
Sight of 84.15(cm) or 841.5(mm) and 59.45 (cm) or 594.5(mm) or equivalents in m
B1
Penalise incorrect unit -1 once (withhold B or A mark) 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:
We'd like to use Google Analytics cookies to count visits and see which pages help most. They're optional, and the site works exactly the same either way. Privacy policy
