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AlgebraIntroduction

The Basketball Shot

Part of Quadratic Sequences — GCSE Mathematics

This introduction covers The Basketball Shot within Quadratic Sequences for GCSE Mathematics. Revise Quadratic Sequences in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 7 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 7

Practice

12 questions

Recall

22 flashcards

The Basketball Shot

Maya is practicing basketball shots and notices something interesting about the height of the ball at different time intervals. When she plots the height against time, she gets: 2m, 5m, 10m, 17m, 26m...

At first glance, this doesn't look like a simple pattern. But Maya discovers that this follows a quadratic sequence - a pattern where the differences between differences are constant!

Understanding quadratic sequences helps us model real-world phenomena like projectile motion, falling objects, and growth patterns that accelerate over time.

Keep building this topic

Read this section alongside the surrounding pages in Quadratic Sequences. That gives you the full topic sequence instead of a single isolated revision point.

Key FactsQuadratic Sequence StructureFinding the nth Term Formula: The 5-Step Method

Practice Questions for Quadratic Sequences

Which of the following is a property of a quadratic sequence?

  • A. The first differences are constant
  • B. The second differences are constant
  • C. The terms increase by equal amounts each time
  • D. Every term is a perfect square
1 markfoundation

A student says: 'The sequence 3, 7, 13, 21, 31 is quadratic because the first differences increase.' Explain whether the student is correct and how to check properly.

2 marksstandard

Quick Recall Flashcards

What are second differences?
The differences between the first differences. First differences: 4, 6, 8, 10 Second differences: 2, 2, 2 If second differences are constant, the sequence is quadratic.
What is a quadratic sequence?
A sequence where the second differences between consecutive terms are constant. Example: 2, 5, 10, 17, 26, ... First differences: 3, 5, 7, 9, ... Second differences: 2, 2, 2, ... (constant)

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