14 Patterns are made using straight lines and arcs.
(a)
More rows are added to Pattern B so that
number of straight lines : number of arcs \(\; = \;\) 10 : 9
How many rows are added? [2 marks]
(b) A different pattern is made using 20 straight lines and 16 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12 cost of one straight line : cost of one arc \(\; = \;\) 2 : 3
Work out the total cost of the metal in the pattern. [3 marks]
Mark scheme (a)
Answer
Mark
Comments
At least 3 correct pairs from 15 and 16 20 and 20 25 and 24 30 and 28 35 and 32 40 and 36 or \(9(10 + 5n) = 10(12 + 4n)\) or \(9(5n) = 10(4n + 4)\) or \(9(5 + 5n) = 10(8 + 4n)\) or 7 rows added to A
M1
oe pairs may be seen as ratios
oe equation, where \(n\) is the number of new rows (correct answer is 6) oe equation, where \(n\) is the total number of rows (correct answer is 8) oe equation, where \(n\) is the number of new rows after Pattern A (correct answer is 7) not implied by answer 7
6
A1
Additional guidance
6 with no incorrect working
M1A1
7 or 8 with no working
M0A0
Multiplication of ratio with no working worthy of M1 eg 10 : 9 20 : 18 30 : 27 40 : 36
M0A0
Mark scheme (b)
Answer
Mark
Comments
Alternative method 1
\(12 \div 20\) or 0.6(0)
M1
oe
their \(0.6(0) \times 3 \div 2\) or 0.9(0) or 14.4(0) or 26.4
M1dep
oe
26.40
A1
correct money notation
Alternative method 2
\(12 \times 3 \div 2\) or 18
M1
oe
their \(18 \div 20\) or 0.9(0) or their \(18 \div 5 \times 4\) or 14.4(0) or 26.4
M1dep
oe
26.40
A1
correct money notation
Alternative method 3
\(12 \div 5 \times 4\) or 9.6(0)
M1
oe
their \(9.6(0) \times 3 \div 2\) or 14.4(0) or 26.4
M1dep
oe
26.40
A1
correct money notation
Alternative method 4
\(16 \div 2 \times 3\) or 24 or 44
M1
oe
their \(24 \times 12 \div 20\) or 14.4(0) or their \(44 \times 12 \div 20\) or 26.4
M1dep
oe
26.40
A1
correct money notation
Additional guidance
Condone 26.40p
M1M1A1
\(20 \div 12\) or 1.66… or 1.67 with no working that is worthy of M1
M0M0A0
£18 from using £12 as the cost of one line (may give a total of £528)
