Lemmara logoLemmaraWorked solution

4MA1/1F Jan 2021, Question 5: Pattern Sequences and Special Sequences

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

A square-grid pattern grows through numbered shapes; students continue the sequence, tabulate shaded-square counts, find a later term, and justify why 50 cannot occur.

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

Part (a) · 1 mark

Draw the fourth shape of the sequence on the grid provided.

  1. 1Shade 17 squares in the pattern consistent with previous shapes, extending the sequence by adding 4 more shaded squares to the previous shape

AnswerShape number 3 continued in the same way with 4 more shaded squares, giving 17 shaded squares

Part (b) · 1 mark

Fill the missing shaded-square totals for shapes 4 and 5 in the table.

  1. 1Shape 1: 5
  2. 2Shape 2: 9
  3. 3Shape 3: 13
  4. 4Each shape increases by 4 shaded squares
  5. 5Shape 4: 13 + 4 = 17
  6. 6Shape 5: 17 + 4 = 21

Answer17, 21

Part (c) · 1 mark

Work out how many shaded squares shape 8 contains.

  1. 1Shape 5 has 21 shaded squares
  2. 2Each shape increases by 4
  3. 3Shape 6: 21 + 4 = 25
  4. 4Shape 7: 25 + 4 = 29
  5. 5Shape 8: 29 + 4 = 33

Answer33

Part (d) · 1 mark

Give a reason why 50 shaded squares is impossible for any shape in this sequence.

  1. 1The sequence of shaded squares is 5, 9, 13, 17, 21, ...
  2. 2This increases by 4 each time, starting at 5
  3. 3All terms are odd
  4. 450 is even
  5. 5So 50 cannot be in the sequence

AnswerThe numbers of shaded squares are odd numbers

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 2021 · 4MA1/1F · 4ma1 jan21 1f · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.