AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 1

3 marks · Easy difficulty · Short Answer

Given the first three patterns in a sequence of grids containing crosses and shaded squares, draw Pattern 4 and determine how many crosses are in Pattern 6.

Practise this question

Question

Question 1 shows three patterns made of 2-row grids. Pattern 1 is a 2 by 3 grid with three crosses across the top row, and a cross, a shaded square, and a cross in the bottom row. Pattern 2 is a 2 by 4 grid with four crosses on top, and a cross, two shaded squares, and a cross on the bottom. Pattern 3 is a 2 by 5 grid with five crosses on top, and a cross, three shaded squares, and a cross on the bottom. Part (a) asks to draw Pattern 4 on an empty 2 by 6 grid for 1 mark. Part (b) asks how many squares in Pattern 6 would have a cross (X) in them for 2 marks.

Mark scheme

Show the mark scheme Mark scheme for question 1. Part (a) gives 1 mark (B1) for a 2 by 6 grid filled with six crosses across the top row, and a cross, four shaded squares, and a cross on the bottom row, condoning omission of shading with mark intention. Part (b) gives 2 marks (B2) for 10, with B1 awarded for the sequence 5, 6, 7, 8, (9) or a drawing of pattern 6, and a special case SC1 for 16 (the total number of squares).

How to answer it

Visual Sequences: Matchstick & Grid Patterns

📋 What this question tests

This question assesses your foundational understanding of linear sequences represented through geometric diagrams:

  • Recognising how a 2D tile pattern grows step-by-step.
  • Drawing the next term in a sequence accurately onto a given grid.
  • Isolating a specific component (squares with a cross) rather than the entire pattern.
  • Extending a sequence numerically or using an nth term rule to find a later term.
Part 1 (a)

Drawing Pattern 4 on the Grid

1 Mark • Assessment Objective: AO1 (Recall and Routine Drawing)

✅ Correct Answer

Pattern 4 consists of 2 rows and 6 columns (all 12 squares of the provided grid filled):

  • Top row: 6 crosses (all squares contain an ✕)
  • Bottom row: 1 cross at each end, and 4 shaded squares in the middle
✕✕✕✕✕✕
✕✕

💡 Key Knowledge: Pattern Analysis

Look at how the dimensions grow from one pattern to the next:

  • Width (columns): Pattern n has n + 2 columns. For Pattern 4, columns = 4 + 2 = 6.
  • Top row: Entirely filled with crosses ( n + 2 crosses).
  • Bottom row: Always 1 cross on the left, 1 cross on the right, and n shaded squares in between.

🧠 Exam Technique & Mark Scheme Notes

  • Mark intention: The examiner will award the mark if it is clear you know where the crosses and shaded sections go, even if your drawing isn't perfectly neat.
  • Omission of shading: The mark scheme explicitly states: "Condone omission of shading". As long as the crosses are in the right 8 squares and the other 4 are left distinct/empty, you still achieve the mark!

❌ Common Errors to Avoid

  • Wrong number of shaded squares: Shading 3 squares (copying Pattern 3) or 5 squares instead of 4.
  • Leaving columns blank: The given 2 × 6 grid is the exact size needed for Pattern 4. Fill all 6 columns.
Part 1 (b)

Number of Squares with a Cross in Pattern 6

2 Marks • Assessment Objectives: AO1 & AO2 (Problem Solving)

📐 Step-by-Step Solution

Method 1: List the Sequence (Recommended)

  1. Count the crosses in the first few patterns:
    • Pattern 1: 3 (top) + 2 (bottom) = 5 crosses
    • Pattern 2: 4 (top) + 2 (bottom) = 6 crosses
    • Pattern 3: 5 (top) + 2 (bottom) = 7 crosses
    • Pattern 4: 6 (top) + 2 (bottom) = 8 crosses
  2. Identify the term-to-term rule: The sequence goes up by +1 each time.
  3. Continue the pattern to Pattern 6:
    • Pattern 5: 8 + 1 = 9 crosses
    • Pattern 6: 9 + 1 = 10 crosses

Method 2: Algebraic Structure (nth term)

  • Top row crosses = n + 2
  • Bottom row crosses = 2
  • Total crosses = (n + 2) + 2 = n + 4
  • For Pattern 6 ( n = 6 ): Total = 6 + 4 = 10

✅ Mark Scheme Breakdown

  • 10 [B2] — Full 2 marks for the correct final answer.
  • Partial Credit [B1]: Awarded for writing out the sequence 5, 6, 7, 8, (9) OR for drawing Pattern 6 with intention to show crosses.
  • Special Case [SC1]: Awarded for an answer of 16.

❌ The "16" Trap: Total Squares vs Crosses

Many students lose a mark here by finding the total number of squares instead of just the squares with a cross:

  • Pattern 6 has 8 columns and 2 rows, which equals 2 × 8 = 16 total squares.
  • If you write 16, examiners award a special case SC1 (1 out of 2 marks) because you found the total size of the grid, not the number of crosses!
  • Always re-read the question carefully: Did it ask for total squares, shaded squares, or crosses?

Topics

Algebra · 3.2.4 Sequences

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.