WJEC Unit 3 Specimen — Question 6 4 marks

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
SessionSpecimen
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeFind term or common difference
DifficultyStandard +0.3 This is a straightforward arithmetic sequence problem requiring setup of two equations (sum formula for perimeter, relationship between first and last terms) and solving simultaneously. The context is slightly unusual (fifteen-sided figure) but the mathematics is standard GCSE/AS-level algebra with no conceptual challenges beyond applying the arithmetic sequence formulas correctly.
Spec1.04h Arithmetic sequences: nth term and sum formulae
The lengths of the sides of a fifteen-sided plane figure form an arithmetic sequence. The perimeter of the figure is 270 cm and the length of the largest side is eight times that of the smallest side. Find the length of the smallest side. [4]
If smallest side is \(a\), largest side \(= 8a\)
AnswerMarks Guidance
\(8a = a + 14d\)M1
\(a = 2d\)A1 (Attempt to relate the two sides)
Perimeter \(= \frac{15}{2}[2a + 14d] = \frac{15}{2} \times 18d = 135d\)M1
\(\therefore 135d = 270\)
\(d = 2\)
Length of smallest side \(= a = 2d = 4\) cmB1
Alternative mark scheme:
Smallest side \(= a\), largest side \(= 8a\)
AnswerMarks
Perimeter \(= \frac{15}{2}[a + 8a] = \frac{15}{2} \times 9a = \frac{135}{2}a\)M1, A1
\(\therefore \frac{135}{2}a = 270\)M1
\(a = 4\)A1
Length of smallest side \(= a = 4\) cm
Total: [4]
If smallest side is $a$, largest side $= 8a$

$8a = a + 14d$ | M1 |

$a = 2d$ | A1 | (Attempt to relate the two sides)

Perimeter $= \frac{15}{2}[2a + 14d] = \frac{15}{2} \times 18d = 135d$ | M1 |

$\therefore 135d = 270$ | |

$d = 2$ | |

Length of smallest side $= a = 2d = 4$ cm | B1 |

**Alternative mark scheme:**

Smallest side $= a$, largest side $= 8a$

Perimeter $= \frac{15}{2}[a + 8a] = \frac{15}{2} \times 9a = \frac{135}{2}a$ | M1, A1 |

$\therefore \frac{135}{2}a = 270$ | M1 |

$a = 4$ | A1 |

Length of smallest side $= a = 4$ cm | |

**Total: [4]**
The lengths of the sides of a fifteen-sided plane figure form an arithmetic sequence. The perimeter of the figure is 270 cm and the length of the largest side is eight times that of the smallest side. Find the length of the smallest side. [4]

\hfill \mbox{\textit{WJEC Unit 3  Q6 [4]}}
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Q1 4 Q2 3 Q3 8 Q4 4 Q5 5 Q6 4 Q7 16 Q8 14 Q9 6 Q10 15 Q11 11 Q12 9 Q13 12 Q14 10 Q15 3