Lemmara logoLemmaraWorked solution

4MA1/1F Jan 2020, Question 4: Pattern Sequences and Special Sequences

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

L-shaped tile patterns grow by 2 tiles each time, starting with 4 tiles in Pattern 1. Draw Pattern 4, complete a table, find tiles in Pattern 30, and check Liz's 2n claim.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Draw Pattern number 4, continuing the L-shape tile sequence.

  1. 1Pattern 1 has 4 tiles, Pattern 2 has 6 tiles, Pattern 3 has 8 tiles
  2. 2Each pattern has 2 more tiles than the one before
  3. 3So Pattern number 4 has 8 + 2 = 10 tiles
  4. 4Draw Pattern number 3 again and add the next 2 tiles in the same places as before
  5. 5Pattern number 4 is that shape, made from 10 tiles

AnswerPattern number 4 drawn: the Pattern number 3 shape continued, made from 10 tiles

Part (b) · 1 mark

Complete the table of pattern numbers 1 to 5 with their numbers of tiles.

  1. 1Pattern 1: 4 tiles
  2. 2Pattern 2: 6 tiles
  3. 3Pattern 3: 8 tiles
  4. 4Increase by 2 each time, so Pattern 4: 8 + 2 = 10
  5. 5Pattern 5: 10 + 2 = 12

Answer10, 12

Part (c) · 2 marks

Calculate how many tiles are in Pattern number 30.

  1. 1The sequence of tiles: 4, 6, 8, 10, 12,... is arithmetic with first term 4 and common difference 2.
  2. 2General term: number of tiles = 4 + (n − 1) × 2
  3. 3Simplify: 4 + 2n − 2 = 2n + 2
  4. 4For n = 30: 2 × 30 + 2 = 60 + 2 = 62

Answer62

Part (d) · 1 mark

Decide whether Liz is right that Pattern n has 2n tiles, giving a reason.

  1. 1Liz says number of tiles = 2n
  2. 2But for Pattern 1: 2 × 1 = 2, but actual tiles = 4, so incorrect
  3. 3Correct formula is 2n + 2, not 2n
  4. 4So Liz is not correct because her formula gives too few tiles for each pattern

AnswerNo, because the number of tiles is 2n + 2, not 2n — Pattern number 1 has 4 tiles, not 2

Stuck on a step? Read the free lesson: Pattern Sequences and Special Sequences

Practise more pattern sequences and special sequences questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on pattern sequences and special sequences

Also searched as: 4MA1 1F January 2020 · 4MA1/1F · 4ma1 jan20 1f · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.