In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Mari is buying a new mobile phone. She sees two deals for the same phone, as shown below.
DEAL A PAY £19.99 NOW and then £28.99 a month for 24 months
DEAL B PAY £100 NOW and then £24.36 a month for 24 months
Which deal is the cheaper for Mari over 24 months? How much cheaper is this deal? You must show all your working. [5 + 2 OCW]
(b)
The screen size of a mobile phone is given as the length of the diagonal of the screen.
Mari is trying to find the screen size of the new phone. This phone has a rectangular screen with height 12·8 cm and width 6·3 cm. Mari has started to draw an accurate diagram below. She has drawn a line for the width of the phone.
Complete the diagram to find the screen size. Give your answer in cm, correct to 1 decimal place. [3]
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
Screen size of the new phone (correct to 1 decimal place) = …………… cm
Mark scheme (a)
Scheme
Mark
Comments
(Deal A = ) (£)19.99 + (£)28.99 × 24 AND (Deal B = ) (£)100(.00) + (£)24.36 × 24
M3
Award M2 for any one of the following
(Deal A = ) (£)19.99 + 28.99 × 24
(Deal B = ) (£)100(.00) + 24.36 × 24
Award M1 for any one of the following:
Sight of (£)28.99 × 24 or (£)695.76
Sight of (£)24.36 × 24 or (£)584.64
Sight of (£)1175.52 (BIDMAS error Deal A)
Sight of (£)2984.64 (BIDMAS error Deal B)
(Deal A = ) (£)715.75 AND (Deal B = ) (£)684.64
A1
CAO
If M0A0 awarded, award SC1 for any one of the following: (19.99 + 29 × 24=) (£)715.99 (20 + 28.99 × 24=) (£)715.76 (20 + 29 × 24=) (£)716 (100 + 24.4(0 )× 24=) (£)685.6(0) (100 + 24 × 24=) (£)676
Deal B (is cheaper by) AND (£)31.11
B1
FT the difference between ‘their derived Deal A’ and ‘their derived Deal B’ with ‘their cheaper’ deal stated provided at least one mark previously awarded. Note: For use of 12 months instead of 24 months award: SC1 for sight of (19.99 + 28.99 x 12 =) (£)367.87 SC1 for sight of (100 + 24.36 x 12 =) (£)392.32. B1 for the correct conclusion with the correct difference on follow-through (Deal A AND (£)24.45) provided at least one mark awarded.
Alternative
4(a) Alternative method for difference(printed in italics in the mark scheme)
Scheme
Mark
Comments
(Monthly payments difference =) [(£)28.99-(£)24.36] × 24 or equivalent
M1
(695.76 – 584.64)
(Deal B cheaper by = ) (£)111.12
A1
(One off payments difference=) (£)100(.00) - (£)19.99
M1
(Deal A is cheaper by = ) (£)80.01
A1
If M0A0 M0A0 awarded, award SC1 for any one of the following: (£) 31.35 from (29 – 24.36) × 24 - (100 – 19.99) (£) 31.36 from (29 – 24.36) × 24 - (100 – 20) (£) 30.15 from (28.99 – 24.40) × 24 - (100 – 19.99) (£) 30.16 from (28.99 – 24.40) × 24 - (100 – 20) (£) 39.75 from (28.99 – 24) × 24 - (100 – 19.99) (£) 39.76 from (28.99 – 24) × 24 - (100 – 20) (£) 39.99 from (29 – 24) × 24 - (100 – 19.99) (£) 40 from (29 – 24) × 24 - (100 – 20) (£) 30.39 from (29 – 24.40) × 24 - (100 – 19.99) (£) 30.4(0) from (29 – 24.40) × 24 - (100 – 20)
Deal B (is cheaper by) AND (£)31.11
B1
FT the difference between ‘their derived monthly payments difference’ and ‘their derived one-off payment difference’ with correct conclusion provided at least one mark previously awarded. Note: For use of 12 months instead of 24, award: M1 for 100 – 19.99 A1 for (£)80.01 SC1 for sight of (28.99 x 12 - 24.36 x 12) (£)55.56 and the correct conclusion with the correct difference on follow-through (Deal A and 24.45)
Scheme
Mark
Comments
Organisation and communication
OC1
For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means
Writing
W1
For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc.
Mark scheme (b)
Scheme
Mark
Comments
A line of 12·8cm ( ±2mm) (or a point) in a correct position drawn within the angle tolerance ( ±2°)
B2
If 2 ‘vertical lines’ given, mark the line that gains the most marks from the first B2
Award B1 for any one of the following:
a line drawn (or point indicated) of length 12·8cm ( ±2mm) in a correct position but out of the angle tolerance ( ±2°)
a line drawn from the given line (or point indicated) of length 12·8cm ( ±2mm) within the angle tolerance ( ±2°) but not in a correct position
Screen size = 14·3 cm ( ±2mm) OVERLAY
B1
Strict FT from their diagram. If B2 previously awarded, then award the final B1 provided:
‘their diagonal’ is measured correctly (± 2 mm) (may need to check both diagonals) AND
this measurement lies between 13.9 and 14.7 cm (i.e. 14.3 cm ± 4 mm).
If B1 or B0 previously awarded, award the final B1 for ‘their diagonal’ measured correctly ( ±2mm) (may need to check both diagonals)
Answer must be given in cm and to 1 decimal place for B1
Award SC1 for an answer of 14.3 (cm) from use of Pythagoras’ Theorem.
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