Higher June 2025 Paper 5 Q6
6 Sara and Tom both make a sequence of numbers.
The first term in both sequences is 10.
The term-to-term rule for Sara’s sequence is add 14.
The term-to-term rule for Tom’s sequence is add 35.
Each sequence stops when a term reaches or goes above 500.
(a) Find the number of terms that are the same in both Sara’s and Tom’s sequence.
You must show your working. [4]
(b) Find an expression for the \(n\)th term of Sara’s sequence. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 8 with correct working | 4 | B3 for answer 7 with correct working | Correct working requires evidence of at least M2 If answer 8 and M2 earned award 4 marks If answer 7 and M2 earned award B3 |
| OR Listing: M3 for [10], 80, 150, 220, 290, 360, 430, 500 or for 70, 140, 210, 280, 350, 420, 490 or M2 for two correct lists up to at least the first common term 80 or 70 | If candidate uses both listing and calculation methods, mark the better of these methods e.g. [10,] 24, 38, 52, 66, 80 and [10,] 45, 80 or 14, 28, 42, 56, 70 … and 35, 70. isw errors beyond 80 or 70 for M2 but not M3 | ||
| Or M1 for a list with at least [10,] 24, 38, 52, 66, 80 or [10,] 45, 80 or a list with at least 14, 28, 42, 56, 70 or 35, 70 | isw any errors beyond these values | ||
| OR Calculation: M3 for (500 – 10) ÷ 70 [ + 1] oe or M2 for 2 × 5 × 7 implied by LCM = 70 | For M3 accept e.g. 10 + 70(\(n\) [ –1]) = 500 Condone e.g. HCF = 70 but 70 must come from use of prime factors | ||
| or M1 for showing prime factors of 14 and 35 [14 = ] 2, 7 and [35 = ] 5, 7 | Allow e.g. 2, 7 and 5, 7 on factor trees or in Venn diagram | ||
| If 0 or 1 scored, instead award SC2 for answer 8 with no or insufficient working If 0 scored, instead award SC1 for answer 7 with no or insufficient working | Do not award SC2 if clearly from wrong working Do not award SC1 if clearly from wrong working | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(14n - 4\) oe final answer | 2 | B1 for answer \(14n + k\) oe or \(-4 + pn\) oe \((p \ne 0)\) or for correct answer seen then spoilt | Accept unsimplified for 2 marks or B1 Condone \(n = 14n - 4\) Condone use of other variable e.g. \(14x - 4\) for 2 marks or B1 |